INTELLIGENCE MEASUREMENT 
A Psychological and Statistical Study Based 
upon the Block-design Tests. THE MACMILLAN COMPANY 
NEW YORK • BOSTON • CHICAGO • DALLAS 
ATLANTA • SAN FRANCISCO 
MACMILLAN & CO., Limited 
LONDON • BOMBAY • CALCUTTA 
MELBOURNE 
THE MACMILLAN CO. OF CANADA. Ltd. 
TORONTO THE BLOCK-DESIGN TEST 
Courtesy Psychological Review Co. INTELLIGENCE 
MEASUREMENT 
A Psychological and Statistical Study 
Based upon the Block-design Tests 
BY 
S. C. KOHS, Ph.D. 
PSYCHOLOGIST, COURT OF DOMES'!IC RELATIONS, PORTLAND, OREGON; 
ASSISTANT PROFESSOR OF PSYCHOLOGY, REED COLLEGE, AND 
PROFESSOR OF PSYCHOLOGY, PORTLAND CENTER, 
UNIVERSITY OF OREGON 
1Rew Jflorfe 
THE MACMILLAN COMPANY 
1923 
All rights restrved PRINTED IN THE UNITED STATES OP AMERICA 
Copyright, 1928, 
By THE MACMILLAN COMPANY 
Set up and electrotyped. Published April, 1923. 
Press of 
J. J. Little & Ives Company 
New York, U. S. A. TO 
HENRY HERBERT GODDARD 
WHOSE PIONEER INTEREST IN INTELLIGENCE MEASUREMENT 
GREATLY ACCELERATED THE RAPID PROGRESS OF THIS PROMIS- 
ING BRANCH OF SCIENCE, A MAN OF BROAD SYMPATHY, WITH 
KEEN UNDERSTANDING OF THE PROBLEMS CONFRONTING THOSE 
OF DEFICIENT MENTALITY, ONE TO WHOM THE WRITER OWES 
HIS INITIAL DIRECTION IN THIS BROADLY HUMANITARIAN FIELD, 
THIS BOOK IS 
GRATEFULLY 
DEDICATED PREFACE 
New mental test methods of demonstrated validity are 
always welcome, and this is especially true just now of 
those which are relatively independent of the language 
factor. Other things being equal, any psychologist 
prefers to rate the intelligence of his subjects by what 
they can do rather than by what they say. Very often 
the “other things” are not equal, and the test which 
uses language possesses certain advantages that are not 
to be lightly set aside. The carefully worked out per- 
formance test, however, has a wide field of usefulness, as 
all who have engaged in clinical work will readily admit. 
The need for such tests has never been adequately met, 
largely because really valid ones are much more difficult 
to devise than is the case with tests which utilize lan- 
guage. In the upper ranges of intelligence, especially, 
most performance tests have but little differentiating 
value, simply because they do not draw heavily enough 
upon the higher mental processes. In the Block-design 
test, Dr. Kohs has largely overcome this difficulty, and 
has given us an intelligence scale which is certain to 
prove extremely useful. His success, we believe, is the 
direct result of his thoroughgoing appreciation of the 
real nature of the mental processes involved in what we 
call intelligence. 
Lewis M. Terman. 
VII INTRODUCTION 
“What is the nature of mind?” This question, pro- 
pounded when man first became conscious of himself, 
still remains but inadequately answered. Nevertheless, 
some evident progress has been made. The light of 
scientific progress is gradually penetrating the various 
nooks and recesses of our mental life, and the machinery 
of thought, although dimly revealed, is becoming more 
apparent in its operation. This monograph is but a mere 
fragment, explaining little if anything regarding the 
dynamics of mental process, yet it hopes to place a 
variety of perplexing problems in a new perspective. 
We shall have occasion, for example, to examine some 
current definitions of intelligence, and we shall indicate 
wherein our research into the value and significance of 
completion and combination tests forces us to a recon- 
sideration of the criteria of intelligence and to a restate- 
ment and a redefining of some fundamental principles. 
By mentioning in this connection the great importance 
of the “analytic-synthetic” tendency characteristic of 
all mental behavior, from the simplest sensory, ideational, 
and affective states to the most complex, wre are really 
anticipating a later discussion of these matters. Suffice 
it to say that psychology has not yet interpreted our 
mental constructs in terms of a synthetic principle, 
although our philosophers have already blazed a some- 
what ambiguous trail. 
IX X 
INTRODUCTION 
It has often been urged that the position of neutrality 
is one full of danger for its claimant. Although this may 
be adjudged a “ behaviorist ” study, nevertheless full 
weight has been given to those contributions of “ struc- 
turalists’’ and “functionalists” which have thrown light 
upon our particular problem. The psychological family 
is at discord unless each member is willing, not alone to 
see the others’ point of view with tolerance, but to accept 
at its real value any scientific contribution no matter 
what the standpoint of the experimenter. This is no 
apology for the present study — the remarks are intended 
merely to emphasize our community of problems, and 
the possibility that each school of method may throw 
some light on all of them. We are all confronted with 
the question, “What is the nature of mind?” Knowing 
the futility of any complete reply, we have accustomed 
ourselves either to ignore the question or to maneuver 
a Freudian “escape from reality” by losing ourselves in 
metaphysical speculation. If this piece of work yields 
but a little toward an additional understanding of this 
baffling problem our efforts will, indeed, be wrell rewarded. 
S. C. Kohs. 
Portland, Oregon, 
August 30, 1921 CONTENTS 
PAGE 
Dedication to H. H. Goddard v 
Preface by Dr. L. M. Terman vii 
Introduction ix 
PART A: THE PSYCHOLOGY OF ANALYSIS AND 
SYNTHESIS 
1. Philosophical Orientation 3 
2. Psychological Orientation 7 
3. Neurological Orientation 27 
4. Summary 32 
PART B: THE BLOCK-DESIGN TEST 
CHAPTER 
I. Statistics Regarding the Subjects Who Were 
Given the Block-design Tests .... 39 
II. The Test Material 
1. The Material 64 
(a) The Blocks 
(b) The Designs 
(c) The Score Card and the Method of Scoring 
(d) The Norms 
2. The Directions for Applying the Tests ... 74 
III. Standardization Technique 
1. The Year-Scale Method 78 
2. The Percentile Method 80 
3. The Point-scale Method 98 
4. The P. E. or Linear Projection Method ... 99 
IV. The Standardization of the Block-design Tests 
1. Introduction .102 
XI XII 
CONTENTS 
CHAPTER PAGE 
2. Age Standardization 104 
(a) Mental Age Norms 
(b) Sex Differences (Mental Age Norms) 
(c) Chronological Age Norms 
(d) Sex Differences (Chronological Age Norms) 
(e) Graphic Presentation of Norms 
(/) Final Year Scale 
3. P. E. Standardization 130 
(a) Method 
(b) Time and Move Norms 
(c) Result: The P. E. Scale 
4. Final Revision 161 
(a) Eliminations 
(b) Sex Differences 
(c) Final Norms 
V. The Results 
1. Do the Block Designs Measure Intelligence ? . 168 
2. Validity 172 
3. Diagnostic Value of the Tests 233 
4. Serviceability 235 
VI. Supplemental Observations 
1. Average Mental Age of Adults 237 
2. Increasing Divergence vs. Parallel Progress of 
Mental Development 262 
3. A Performance Intelligence Scale 271 
PART C: APPENDICES 
I. Grouped Distributions op Ability 273 
II. New Correlation Method 289 
III. Elaboration op Sheppard’s Table 296 
IV. Typical Block-design Records 300 
Index 305 PART A 
THE PSYCHOLOGY OF ANALYSIS 
AND SYNTHESIS THE PSYCHOLOGY OF ANALYSIS AND 
SYNTHESIS 
The Place of Synthetic and Analytic Functioning in 
Psychic Activity 
I. PHILOSOPHICAL ORIENTATION 
The psychology of combinative or completive ability 
leads us back through the early history of psychology to 
the time when philosophers psychologized and psycholo- 
gists philosophized. The limited confines of our study 
compel brevity, and we need go back no farther than 
the “associationist” school. 
Hobbes, a staunch materialist, the contemporary of 
Bacon, Descartes, and Galileo, may rightly be called the 
father of “associational” psychology. Hobbes “mate- 
rialized” mental activity. Psychic behavior was inter- 
preted as mental physics or chemistry. All knowledge 
arises through sensations, which, combined in certain 
definite forms, yield the various complex mental pro- 
cesses. Conscious states are due to the refined move- 
ments of mental atoms controlled by the laws of asso- 
ciation, the foundation-stones of mental functioning. 
Words are nothing but mere symbols, markers. It is 
their combination, their addition, their subtraction, 
which yields thought. 
3 4 
INTELLIGENCE MEASUREMENT 
The legitimate successor of Bacon and Hobbes was 
John Locke. From a psychological point of view, it 
may be of interest to note that his “Essay on the Human 
Understanding” grew out of his attempt to answer the 
question: “What is the nature of sensations?” He 
began by asserting that there are no “innate ideas,” 
in opposition to the position of Descartes and to the 
later views of Spinoza and Leibniz. At the beginning, 
mind is a “white piece of paper,” upon which impres- 
sions are marked. Ultimately “nothing is in the intel- 
lect that has not been first in the sense.” But the mind 
is not a passive receptacle. It can manipulate and com- 
bine ideas. These ideas are derivates of “simple ideas” 
out of which the more complex have been compounded. 
This compounding is explainable in terms of the laws 
of association. 
Hume, an outstanding sensationalist, maintained that 
no ideas existed which were not derived from impressions, 
a position to which many of our present-day psycholo- 
gists would claim adherence. Impressions are of two 
kinds: sensational (outer) and affective (inner). And 
ideas are copies or echoes of these simple elemental 
states. Much of his psychology is devoted to a discus- 
sion of the compounding or the combination of ideas, 
and this to such a degree, that his whole psychology be- 
comes warped in its exaggeration of the actual part 
played by associational processes. The differences be- 
tween conception, memory, imagination, judgment, and 
so on, are largely differences in the forms by means of 
which ideas combine. All mental behavior is just asso- 
ciation between ideas. Ideas possess “forces” or “de- PHILOSOPHICAL ORIENTATION 
5 
terminations ” which tend to bring and keep them 
together. The individual then is helpless, since these 
“forces” follow fixed, mechanical laws. 
Leaving the “associationists,” we find Kant, among 
philosophers, giving perhaps the clearest exposition of 
the hierarchies of mental functioning, progressing 
through hierarchies of mental “synthesis.” 
Kant, perhaps, has dealt more extensively with “men- 
tal synthesis” than any other single philosopher. His 
task as a philosopher was largely epistemological. His 
metaphysical structure, although promised, never ap- 
peared complete. It remained for others, Fichte, Hegel, 
Schelling, Herbart, and Schopenhauer, to take the step 
beyond. Kant was interested in the processes which give 
us knowledge. He postulated a threefold world: one, 
of subjective states (inner consciousness), another of 
phenomena (knowledge), and another of absolute reality 
(Ding-an-Sich). The first realm each individual can 
alone experience, the last no one can experience, the 
second, however, is common property and can be intel- 
ligently discussed by all of us. To Kant, subjective 
states are synthetic products, different in every one of 
us. And in each of his three books which compose his 
“Critique of Pure Reason” he discusses the different 
levels of synthetic activity: (a) in perception, (b) in 
understanding, (c) in reason. In his search for the pro- 
cesses which yield knowledge, he concluded that the im- 
portant factor was the synthetic power of mind. In this 
sense mental functioning is dynamic. If one can imagine 
an individual who lacks this synthetic power, the ticking 
of a clock would be nothing more than tock, tock, tock. 6 
INTELLIGENCE MEASUREMENT 
To those, however, who do possess it, the clock’s 
ticking is perceived as one, two, three, etc. The 
experience is cumulative, each item including its prede- 
cessors. 
Kant very clearly differentiated between mental end- 
results and synthesis — one a product, the other a 
process. Synthesis is not subject to volitional vicissi- 
tudes, but is a heritage common to all. It is for that 
reason that we can agree upon such matters as physical 
laws, time-estimates, standards, and so on. Racial 
differences in thought and knowledge are differences 
largely of synthetic potentiality. Groups, therefore, 
may misunderstand each other because of this basic 
difference, since differences in synthetic power will lead 
to differences in thought and behavior. “The world is 
my representation,” says Kant. Knowledge is a com- 
bination of sensations or ideas, “a unification of the 
manifold.” And the expression of knowledge is through 
the judgment, which may be analytic or synthetic. Kant 
discusses quite extensively the distinction between the 
two types, but there is no need of our following his 
argument farther. 
Few, if any, of the terms we use to express our thoughts 
come to us as an immutable, unchanged, and unchange- 
able heritage. Although we continue using the same 
terms, these take on changing meanings with the changes 
in our notions regarding the character of the individual 
and of the cosmos. Therefore, although we shall fre- 
quently utilize the terms “analysis” and “synthesis” 
throughout this monograph, thev are not to be construed 
other than as here defined. PSYCHOLOGICAL ORIENTATION 
7 
1. By “synthesis” we mean, on the one hand, the 
intensity of that fundamental force or condition innate 
in nervous protoplasm which binds neurons into complex 
systems, and, on the other hand, the capacity of a living 
organism to construct out of mental elements and frag- 
mentary experiences, concepts and notions of a higher 
order. The fuller elaboration of these statements is left 
for the succeeding paragraphs. 
2. By “analysis” we mean the capacity for observing 
or discovering parts or differences in objects or qualities 
which for themselves seem unitary. 
3. Although one can only speculate on these matters, 
it seems reasonable that analysis and synthesis are but 
the head and tail of a single function-tendency. This 
“analytic-synthetic” activity may be regarded a funda- 
mental property characteristic of all irritable tissue, and 
more markedly so of nervous tissue. All forms and 
degrees of this function-tendency seem possible, from 
the simplest to the most complex. 
2. PSYCHOLOGICAL ORIENTATION 
If one thumb through the average psychology for a 
description and an analysis of the mental process of 
synthesization, integration, fusion, discrimination, differ- 
entiation, comparison, combination, blending, assimila- 
tion, and analysis, one’s search will prove rather barren. 
Yet, as we shall have occasion to observe in greater 
detail later, these processes appear most fundamental 
for normal mental development. 
The elements or primary structures of consciousness 
escape our observation. What we experience, what we 8 
INTELLIGENCE MEASUREMENT 
observe when we introspect, are fused or synthesized 
products of these elements. It has been said with justice 
that “Whoever would understand the facts of experience 
must know how they are built up out of the combination 
of elements.”1 Take mental functioning anywhere along 
the line, from the simplest type of perception to the most 
complex higher thought process, and at every point evi- 
dences of synthetic activity are observable or may safely 
be postulated. Percepts are synthesized sensations, 
ideas are synthesized percepts, images are recalled traces 
of these synthesized products, coordinations are orderly 
combinations of reflexes, judgments are orderly combina- 
tions of ideas, reasoning results from an orderly combina- 
tion of judgments — emotion, will, learning, habit, all 
are combinations of some elementary form of mental 
process, these conscious states becoming more complex 
with the increase in complexity of the integrative 
pattern. 
“Consciousness is not a shower of shot,”2 a mass of 
disconnected elementary states, but at every stage it 
consists of a fusion of elementary processes into those 
more complex, and these finally into a functional unity. 
Psychology may well be defined as the science devoted 
to a study of mental elements, sensations, images, and 
affections, and the manner, condition, laws, concomitants, 
and effects of their combination at different develop- 
mental levels, phylogenetic and ontogenetic, normal 
and abnormal. This is a task alike for the structuralist, 
1 Judd, 13; 28. All references are to the bibliography at the end of 
Part A. 
* Royce, 24; 108. PSYCHOLOGICAL ORIENTATION 
9 
the behaviorist, the functionalist. It cannot be pre- 
empted by one, nor completely dealt with except by all. 
At the bottom of this conception of mental elaboration 
is an implication which approaches the speculative. We 
cannot, however, on that account escape the force of 
its bearing on a reasonable explanation of observed con- 
ditions. In chemistry and physics the phenomenon of 
crystallization is thoroughly familiar. Given a fluid 
containing the proper ingredients, under certain condi- 
tions crystallization will take place. The canons of 
science justify our inquiry into the “how” but not the 
“why.” Nevertheless, the postulation of a force or of 
forces, closely bound up perhaps with the atoms or the 
molecules, acting concertedly under fixed law and 
resulting in a new product, is a postulation which few 
will attempt to deny scientific scrutiny. So, too, in 
considering the mechanics of mental elaboration, to 
postulate a fundamental force or forces making for higher 
degrees of mental organization and for varieties of higher 
thought forms need not be considered irrelevant. The 
fundamental “ability” to “synthesize” or “combine” 
is not one which we may “will” to possess or not. We 
“synthesize” entirely independent of our personal choice 
in the matter. Just as we can exercise little if any control 
on the hyperfunction or hypofunction of some of the 
other organs of the body — for example, the kidney, the 
thyroid, the intestines — so also is our interference 
with brain function nominal. It seems evident that if 
one is born with good mental endowment his brain will 
“synthesize” to a degree and in a manner impossible to 
one whose native mental endowment is poor. Of course, 10 
INTELLIGENCE MEASUREMENT 
it is left, more or less, to individual initiative to exercise 
this inherited endowment efficiently. And yet, tests 
of “completion” or “combination” may measure this 
“synthesizing ability” in a very rough fashion, quite 
independent of schooling or other formalized training. 
Differences in level of mental ability may some day be 
explained, among other things, on the basis of differences 
in fundamental synthesizing ability, or the capacity of 
the nervous system to fuse elementary states of conscious- 
ness into higher thought forms. And perhaps the dif- 
ferences between a superior intelligence and a deficient 
intelligence may be found largely due to differences in 
this original basic synthesizing capacity. 
Hobhouse has stated: 
“ Where there is mind there is order and system, corre- 
lation and proportion, a harmonising of forces, an inter- 
connection of parts. The organism which is gifted with 
intelligence shows it by arranging its actions on a certain 
plan. It adapts means to ends, which is one sort of 
correlation, and in so doing it perhaps brings a past 
experience to bear, interpreting a perception, for exam- 
ple, by memory; and this is another sort of correlation.”1 
Wherever we find traces of mental functioning there we 
inevitably observe the organization and correlation of 
mental elements into hierarchies. And this organization 
of mind on any functional level is evidenced by a parallel 
organization of behavior. In general, it might be stated 
that organized action is a product of intelligence, un- 
organized action the result of the absence or non-use of 
intelligence. And throughout the realm of mental func- 
1 Hobhouse, io; 6. PSYCHOLOGICAL ORIENTATION 
11 
tioning we note rather clearly the tendency for the fusion 
of elemental, conscious states into more complex forms, 
forms which serve more readily for individual adapta- 
tion to environmental demands. 
“Our assimilations have not merely to do with the 
processes of perception and memory: they appear on the 
highest level of the intellectual life. All our thinking 
involves assimilation. When a novel object puzzles us, 
or when a problem baffles us, that is because we have not 
yet learned to assimilate the new experience to our former 
fashions of conduct. But when our puzzle is thought- 
fully satisfied, this occurs because we have learned to 
assimilate the new facts to the old principles, i.e., to adjust 
our former methods of conduct, with a minimum of 
change, to the new situation. When the problem is 
solved, that is because what baffled us about a question 
which was asked, but to which we could not respond, 
disappears, because we have assimilated the matter at 
issue by remembering from our former experience an 
answer that serves the purpose. To be sure, such assimi- 
lation may be accompanied with alterations of habits 
that will need to be considered later under the head of 
Mental Initiative. But every thoughtful process is, in at 
least one respect, a process of assimilation1 
In what manner is this concept of a synthesizing, or 
an assimilative, or combinative, or integrative principle 
different from our earlier and now discarded view that 
“associations of ideas” serve as a complete explanation 
of the varieties of mental experience? Our present hy- 
pothesis is rather one which assumes nervous tissue to 
possess the property or tendency of becoming integrated 
into higher units of complexity, as well as the tendency 
1 Royce, 24; 245. 12 
INTELLIGENCE MEASUREMENT 
for organizing environmental stimuli which appeal to 
various sense modalities into a consistent, understand- 
able, and assimilable unity. The “association of ideas” 
is perhaps the most obvious superficial result of this 
synthetic-analytic tendency. It should be kept in mind, 
however, that “associations” evidence the result and 
not the process of this fundamental integrative force. 
The process is inherent in nervous tissue, and the result 
is present in consciousness as “associations between 
ideas.” Titchener admirably summarizes the situation 
in seven words: “The brain associates, and meanings 
are associated.” 1 
In general, it may be said that “the entire process of 
elaborating . . . objects of perception by the senses, 
presupposes for its explanation a constant activity of 
the mind ... in combining the sensations into ever 
more complex forms. This combining activity is best 
called ‘syntheticor ‘constructive”2 Nevertheless, there 
is an analyzing activity of mind which apparently is as 
important as the synthesizing. And perhaps analysis 
and synthesis are merely two aspects of nerve cell 
mechanism. Although antonyms, and expressing oppo- 
site tendencies, analysis and synthesis show evidences 
of each reenforcing and aiding the other. 
Our aim is not to make hair-splitting distinctions be- 
tween the processes of synthesis, assimilation, blending, 
combination, completion, induction, fusion, on the one 
hand, and analysis, comparison, deduction, differentia- 
tion, discrimination, on the other. It is sufficient to 
1 Titchener, 29; 149. 
2 Ladd and Woodworth, 14; 384. PSYCHOLOGICAL ORIENTATION 
13 
state that the process or processes to which these terms 
refer are fundamental and may represent innate, dynamic 
potentialities characteristic of all nervous tissue. Many 
have attempted to differentiate the analytic activity 
from the synthetic. Our immediate purpose, however, 
will not necessitate any other assumption than that 
brain substance fundamentally manifests this activity 
— analysis and synthesis. Whether there are different 
“types”1 is irrelevant to the present discussion. It 
perhaps is true, however, that at different age levels 
the character of the analyses and syntheses is different, 
the processes themselves changing as one passes through 
infancy to childhood, to adolescence, to adulthood, and 
finally through senescence. 
Thorndike remarks that “the intellectual life of man 
seems to consist as much in discriminating, abstracting, 
taking apart, as in associating or connecting.”2 Al- 
though “fusion of some kind is always present in expe- 
rience,”3 nevertheless, the other aspect cannot be over- 
looked: 
“Closely allied to the fact of focalness of thinking is 
the fact of analysis, the fact of breaking up a total fact 
into its elements, parts, or aspects. It is only as a result 
of such a process of breaking up total facts into their 
qualities that the elements of color, size, shape, weight, 
pressure, and the like are felt, in place of a ‘big, blooming, 
buzzing confusion.’ It is only as a result of such a 
process that many feelings of meanings and of intellectual 
relationships arise at all.”4 
1 Meumann, 17. 
2 Thorndike, 27; 35 
3 Judd (ist ed.), 13; 137* 
4 Thorndike, 28; 105. 14 
INTELLIGENCE MEASUREMENT 
James clearly and with due emphasis maintains: 
“After discrimination, association!”1 In speaking of 
these two processes, he says: 
“It is obvious that the advance of our knowledge 
must consist of both operations; for objects at first 
appearing as wholes are analyzed into parts, and objects 
appearing separately are brought together and appear 
as new compound wholes to the mind. Analysis and 
synthesis are thus the incessantly alternating mental 
activities, a stroke of the one preparing the way for a 
stroke of the other, much as, in walking, a man’s two 
legs are alternately brought into use, both being indis- 
pensable for any orderly advance.” 2 
Hobhouse expresses a somewhat similar idea: 
“Analysis rests on comparison, which is an act of 
synthesis, since it brings different experiences into rela- 
tion; and gains in explicitness, pari passu with the com- 
mon character on which the comparison turns. And not 
only does the concept rest on a synthesis, but its essen- 
tial function is to make a further synthesis possible . . . 
There is thus in the free usage of detached concepts a 
synthetic process always at work articulating what has 
been disarticulated by analysis.” 3 
The process of comparison stands out clearly in many 
writings and experiments as perhaps the most important 
feature of the analyzing procedure. 
“By deliberate comparison I mean a mental confront- 
ing of the two objects, and a transition of attention from 
the one to the other, so as to discover some respect in 
which similar things differ in spite of their similarity, or 
in which different things agree in spite of their diversity, 
1 James, 11; 550. 
2 James, 11; 550. 
3 Hobhouse, 10; 294. PSYCHOLOGICAL ORIENTATION 
15 
and also a fixing of the precise nature of this agreement 
or difference.”1 
Stout has so ably described this activity of “com- 
paring” that this lengthy quotation may be pardoned: 
“ Comparison in all but a most rudimentary form is an 
ideational activity. Even when the objects compared 
are both present to the senses, each is scrutinised in 
turn. For anything more than a vague awareness of 
resemblance or difference, it is necessary to keep before 
the mind the ideal representation of the one object in 
the very act of examining the other. Only in this way 
can each detail and characteristic in turn be selected for 
comparison, so as to distinguish the points of difference 
from the points of agreement. Hence we may attribute 
the absence of comparison in animals in all but its most 
vague and rudimentary form, to the absence or extremely 
imperfect development of ideational activity in general. 
“When the process of deliberate comparison plays an 
important part in the mental life, it involves a corre- 
sponding development in conceptual thinking, in the dis- 
tinction of the general or universal from the particular. 
To compare is always to compare in some special respect. 
Some theoretical or practical end is to be subserved by 
the comparison. The difference or agreement to be dis- 
covered is not any difference or agreement, but one which 
has significance for the guidance of conduct or for the 
solution of a theoretical difficulty. Thus comparison 
takes place only in regard to the characteristics which 
happen to be interesting at the moment, other character- 
istics being disregarded or set aside as unimportant. 
Objects in other ways most diverse may yet in a certain 
respect be compared and found more or less similar, and 
objects in other ways most similar may be compared in 
a certain respect and found more or less unlike.”2 
1 Stout, 26; 452. 
2Stout, 26; 455-456. 16 
INTELLIGENCE MEASUREMENT 
It may be of interest to recall at this point that Binet, 
with his unusually clear insight into the problems related 
to the development of intelligence, realized that the 
observation of the ways in which two things are alike 
is of as great a diagnostic value in determining intelli- 
gence level as the observation of ways in which two things 
are different. For that reason he devised tests for the 
purpose of determining a child’s capacity to note simi- 
larities as well as differences. Terman, recognizing the 
importance of both processes, has included tests which 
measure both capacities in his revision and extension 
of the Binet scale. These tests, however, deal with 
concrete objects. Additional tests might be devised 
to measure the ability to note differences, using abstract 
material. Thus, 
“To note the fall of an apple is to analyze out a com- 
paratively obvious feature; to distinguish falling as a 
feature of the moon’s revolution about the earth is still 
analysis, proceeding in much the same manner, but deal- 
ing with more difficult material and working with much 
more refined and elaborate tools.” 1 
That there are individual differences in ability to 
compare and in ability to note similarities and differences 
seems obvious. According to James: 
“Some people are far more sensitive to resemblances 
and far more ready to point out wherein they consist, 
than others are. They are the wits, the poets, the in- 
ventors, the scientific men, the practical geniuses. A 
native talent for perceiving analogies is reckoned by 
Professor Bain (‘Study of Character,’ p. 317) and by 
1 Ladd and Woodworth, 14; 606-607. PSYCHOLOGICAL ORIENTATION 
17 
others before and after him, as the leading fact in genius 
of every order.” 1 
The extent to which two things which are compared 
may appear different, may run from one extreme to the 
other. Two occurrences or things or facts may be so 
strikingly different that discrimination is relatively easy. 
On the other hand, the difference in the detail of the two 
objects under inspection may be so fine as to escape the 
notice of all but the most mature or the most expert. 
“We all cease analyzing the world at some point, and 
notice no more differences. The last units with which 
we stop are our objective elements of being. Those of a 
dog are different from those of a Humboldt; those of a 
practical man from those of a metaphysician. . . . And 
when the omitted things are discovered and the unnoticed 
things are laid bare, it is not that the old thoughts split 
up, but that new thoughts supersede them, which make 
new judgments about the same objective world.” 2 
A phenomenon closely linked with the matters men- 
tioned above, and of considerable significance for mental 
progress, is that to which Mach has called attention,3 
namely, the inborn nature of experimentation in man — 
not the organized, thoroughly planned experimentation 
of the scientist, but the searching and the testing, the 
manipulating and the trying so characteristic of any 
normally developing child. 
An item of great relevancy at this point is the question 
of individual differences in this experimenting attitude, 
the differences in the character of the observations 
(analyses), and the differences in the final syntheses. 
1 James, 11; 53c. 
2 James, 11; 489. 
3 Mach, 15; 180. 18 
INTELLIGENCE MEASUREMENT 
Let us assume two children observing an object for the 
first time, one of superior and one of inferior mental 
ability. The little objective data which we now possess 
tend to show that the later imagery of this experience is 
markedly different in the two. The initial attitude is 
different. The observational procedure is different: the 
analyzing, the comparing, the selecting, the assimilating 
processes are different. “This selective activity not 
only differs from individual to individual, but even in 
the same individual it varies with the progress of his 
development and of his knowledge.” 1 It is evident, 
therefore, that the final syntheses or products of observa- 
tion will be different in the two. Many students of the 
graphic functions have frequently pointed out the devel- 
opment of a child’s ability in drawing through distinct 
stages. Thus, the first phase is that of purposeless draw- 
ing— a mere scribbling for scribbling’s sake; details, 
if observed at all, are detached entities, synthesis 
appearing only in its crudest form. Then follows a 
second stage, in which the child attempts a reproduction 
of objects seen, but synthetic incapacity is evident 
through inability to evaluate properly and place the 
numerous details into a reasonable whole. Thus, in 
drawing a picture of a human being the head is of enor- 
mous proportions, the limbs being appended from the 
chin, while other important parts of the body are omitted. 
In the final stage keenness of perception, a well-developed 
capacity for discrimination of detail, a knowledge and an 
experience of the laws of perspective, harmony, and 
balance, together with rigid self-criticism, are operative. 
1 Meumann, 16; io, n. PSYCHOLOGICAL ORIENTATION 
19 
These steps in the development of mental ability are 
more or less duplicated in any variety of specific fields. 
For example, an average child of three can do no more 
than merely enumerate objects in a picture: the rela- 
tionships between objects are not perceived. At seven, 
however, he can observe that the details bear some rela- 
tion to one another and that some activity is portrayed. 
Only relationships of an obvious sort are observed. 
While at twelve, not only does he observe certain activi- 
ties, but he obtains something more than is directly 
presented: he reads an interpretation into the picture, 
and perceives the subtle meanings underlying a given 
situation. Each higher stage requires a higher degree of 
mental synthesis, of combinative power. So, again, the 
same is true of ability to copy a circle, a square, a dia- 
mond, and a design. Each one of these figures seems to 
require a higher form of analytic-synthetic ability for 
successful performance. It is in this respect that the 
feeble-minded are characteristically defective. The con- 
summation of associations or synthesizations of higher 
order, especially if of an abstract nature, are very difficult 
if not impossible for them. 
Meumann summarizes the differences observable in 
children of different age levels in this capacity to elabo- 
rate and assimilate their worldly experiences.1 He 
distinguishes three levels. On the first, synthesis is most 
predominant. Each object is cognized as a unit, its 
detail being distinguished separately in but a very inade- 
quate fashion. A true analytic tendency is not yet 
observable. Whatever meager characteristics are noted 
1 Meumann, 17; 116 fit. 20 
INTELLIGENCE MEASUREMENT 
by the child are combined into a most illusory and 
fantastic notion. It is this stage which Meumann 
designates as the “Imaginative-Synthetic Period.” This 
stage ends at about the age of eight or nine. Then fol- 
lows a period which is characterized by a pronounced 
tendency toward analysis. The parts, peculiarities, and 
relationships of things are more attentively observed. 
The child develops a more truthful, a more accurate 
knowledge of objects. Imaginative combinations, elab- 
orations, and interpretations become far less frequent. 
At about adolescence another period follows which is 
again synthetic, but of distinctly different character. 
The trend now is toward logical, reasonable combinations 
of impressions characteristic of the adult. “In that first 
period the child lives as in a fairy-world, in the third 
the sensing of reality appears normally active.”1 
There have been many attempts to divide “mental 
types” into the synthetic and the analytic. Whatever 
one’s own reaction to the question of “types,” it is never- 
theless of interest to note some of the generalizations 
which have been made. Rignano2 distinguishes between 
the synthetic and analytic “mentality” as follows: the 
possessor of the first is the discoverer of new concepts, 
he prefers comparison, analogies, the study of the 
broader relationships of cause and effect, and gives us an 
insight into the broad realm of any given field of en- 
deavor. The analyst, on the other hand, is reflective, 
patient, persevering, deductive in his method; an experi- 
menter, he prefers long, patient reasoning, and calculations 
complicated and almost unending. He appears to ad- 
1 Meumann, 17; 117. 
2Rignano, 22; 96. PSYCHOLOGICAL ORIENTATION 
21 
vance prudently and surely, taking but a single step at a 
time. Among the synthesizers Rignano would place 
men such as Galileo, Newton, Faraday, Darwin, Comte, 
and among the analyzers, Watt, Stephenson, and Marconi. 
Maudsley distinguishes between assimilative and dis- 
criminative types. The first observes small, delicate 
resemblances which are imperceptible to others, the latter 
possesses predominantly the capacity for recognizing 
points of difference.1 
Again, Meumann, who has devoted so much of his dis- 
cussion of individual differences to “types,” distinguishes 
between the “analytic type” of person who is especially 
capable in the solution of single problems, in exact and 
analytic observation, a critic, a classifier — and the syn- 
thetic type, who is the builder of systems, one who 
manipulates and fashions whole regions of science.2 
The analyzer is concerned more with differences, the 
synthesizer more with similarities, with the search for 
similarity and analogy.3 The first is “keen-sensed,” 
the latter is “deep-sensed” or especially capable of noting 
wider and wider relationships. The highest type is that 
in which both attain their highest development in a 
single individual. 
Meumann distinguishes still other types, which need 
not concern us for the present. 
Some data from animal and genetic psychology have 
an application to the questions under discussion. 
Biologists have almost entirely abandoned the search 
1 Maudsley, “The Physiology of Mind,” 283. 
1 Meumann, 17; 159 ff. 
sMeumann, 17; 161. 22 
INTELLIGENCE MEASUREMENT 
for that elusive if existent principle or trait which sepa- 
rates plants from animals. It would be rather generally 
conceded that all organisms manifest to some degree 
practically all the traits now claimed for higher animals.1 
The difference has been maintained to be one merely of 
degree or proportion. This view seems to be especially 
agreeable to those Weismannian disciples who believe 
that the primordial organism possessed, in the form of 
germinal determiners, all the potentialities for the devel- 
opment of all the higher species. 
From the simplest one-celled organism up to man, 
Jennings finds evidence of perception, discrimination, 
choice, attention, fatigue, desire, pleasure, pain, fear, 
memory, habit, and even • intelligence.2 Of course, the 
lower down the scale the animal, the simpler are its 
mental mechanisms. But the germs of man’s psychic 
activity are assumed to exist as far down the phylogenetic 
line as the protozoa. There is a string of unbroken 
continuity between the behavior of lower and higher 
species. Hobhouse distinguishes four stages in mental 
evolution, each representing a separate degree of mental 
correlation and adaptation, which basically reduces to 
differences in the character and development of the 
processes of synthesis and analysis at each of the four 
levels.3 Ladd and Woodworth conclude that “greater 
power of analysis or discrimination belongs to man”4 
as compared with animals. 
1 Tashiro, “A Chemical Sign of Life.” 
2 Jennings, 12. 
* Hobhouse, 10. 
4 Ladd and Woodworth, 14; 555. PSYCHOLOGICAL ORIENTATION 
23 
All experiments upon learning, animal and human, 
have clearly indicated the importance of attention, dis- 
crimination, and association in this process. This is illus- 
trated in the attempt of Ladd and Woodworth to term 
the ‘Trial and error” learning in animals “learning by 
varied reaction through selection of the successful 
variants.” 1 Without variation in behavior-habit the 
right method would not have been hit upon by the animal 
in his learning efforts. And without attention, discrimi- 
nation, and association, even if chance success favored 
the animal, nothing would be gained which would be of 
future service in the same situation. 
James cites an instance where a dog, arriving with its 
master before a rowboat which they were in the habit 
of using, found it full of water. A sponge was generally 
used to bale this out. On this occasion the sponge had 
been left at home, about a third of a mile away. The 
master, disliking to make the trip, made gestures of clean- 
ing out the boat, at the same time saying to the dog, 
“Sponge, sponge; go get the sponge.” The dog ran off 
and brought back the desired article. To James this 
was evidence of nothing but contiguous association. If 
the dog had been unable to find the sponge and had 
brought back a dipper or a mop instead, “such a substi- 
tution would have shown that embedded in the very 
different appearances of these articles, he had been able 
to discriminate the identical partial attribute of capacity 
to take up water, and had reflected, ‘For the present 
purpose they are identical.’ ”2 It is this power to analyze 
1 Ladd and Woodworth, 14; 550. 
2 James, 11; 349-350. 24 
INTELLIGENCE MEASUREMENT 
out a detail common to a series of objects, acts, or phe- 
nomena, which possibly differentiates man from brute, 
and the superior among men in intelligence from those 
who are inferior. This process has its analogue in ab- 
straction. Miss Fisher found that the experience of 
similarity “was the most important component detail 
in the process of generalizing abstraction” 1 and that the 
“experience of similarity and that of generality were 
in themselves strikingly akin.” 2 
In the case of animals it is a question to what extent 
varieties of past experience are interpreted in the light 
of a new situation. Thorndike doubts whether animals 
possess such generalized elements of thought as ideas. 
And although Hobhouse’s attitude is strongly affirmative, 
nevertheless 
“if we attribute ideas to an animal, they are not ideas 
arrived at by any breaking-up, analysis, or other elabora- 
tion of what is given in perception. None of my animals 
(with the possible exception now and again of the mon- 
keys) showed the least understanding of the how or why 
of their actions, as distinct from the crude fact that to 
do such and such a thing produced the result they 
required. It is this want of what one may call analysis, 
that made, for example, the push-back bolt such a diffi- 
culty. What Jack or the elephant knew was, crudely, 
that they had to push this bolt. That the reason why 
they had to push it was to get it clear of the staple they 
obviously never grasped.” 3 
How remarkably analogous is the mental functioning 
of the animal as here pictured with that of the high-grade 
moron, who knows what is right and what wrong, but 
1 Fisher, 7; 97. 
2 Fisher, 7; 208. 
* Hobhouse, io; 200-201 PSYCHOLOGICAL ORIENTATION 
25 
fails to grasp the “why.” Is it a question of synthetic- 
analytic incapacity? We shall have occasion to return 
to this matter again later. 
“If then, positively, these experiments suggest ‘prac- 
tical ideas,’ negatively, they strongly suggest absence of 
any sort of analysis in the genesis of those ideas. An 
animal can shift its attention to this or that object, or 
change within the sphere of perception; but it cannot 
apparently follow out the structure of any complex object 
with any minuteness and accuracy.” 1 
Some contributions from the field of genetic psychol- 
ogy are illuminating. We are frequently told that the 
child deals with the concrete; the adult with the ab- 
stract. This means, presumably, that the child deals 
with the isolated, with objects as they have been imme- 
diately perceived — the adult, however, has generalized 
and has abstracted common properties and deals with 
these idealizations by means of word symbols or physio- 
logical set. To experience the meaning of “twenty,” or 
of “promise,” or of “opposite,” or of “justice,” is 
apparently beyond the power of children’s mental 
capacity. Progress in this respect comes with chrono- 
logical age and with the character of native mental en- 
dowment. It is quite apparent that “ In mental growth 
connection and analysis, association and dissociation, 
putting things together and breaking things up into 
parts, constantly work together.”2 
There are a few pedagogical implications worth men- 
tioning with regard to this synthetic-analytic activity. 
Education, according to Royce, involves, first, “acts of 
1 Hobhouse, 10; 201 
2 Thorndike, 28; 219-220 26 
INTELLIGENCE MEASUREMENT 
sensory observation, of recalling images, of repeating 
words, of drawing diagrams, of performing experiments, 
and so on, indefinitely. Then we acquire gradually the 
power to ‘survey at a glance/” and “this process of 
surveying at a glance involves a high degree of differen- 
tiation of our simultaneous conscious states. ”1 This 
ability to bring to consciousness a mass of related facts, 
data, information, experiences, to pick out the essentials 
necessary for the purposes of the particular moment, or 
to select and epitomize, or summarize relevant details 
for interpretation as a unit — that is truly mental func- 
tioning close to its apex of development. Meumann 
emphasizes the importance of combinative ability when 
he speaks of difficulties in work of the schoolroom, in 
geography, for example: 
“Defective capacity to learn geography may be due 
either to sub-normal ability to deal with concrete visual 
imagery (maps and the like'); or when normal visual 
imagery and normal memory of names is present, it 
may be due to an inability to combine concrete visual 
images with the auditory-motor images of words.”2 
In the aphasias we possess excellent illustrations of total 
absence of specific combinative potentialities, which of 
course have clearly demarked neurological bases. Royce 
has conceived the educative process as “ an attainment 
of synthesis by means of analysis.” 3 And analysis “is 
manifestly one of the most incessantly performed of all 
our mental processes.”4 
By emphasizing the importance of analysis and synthe- 
1 Royce, 24; 254. 
2 Meumann, 16; 204. 
* Royce, 24; 258 
James, 11; 502. NEUROLOGICAL ORIENTATION 
27 
sis for normal mental functioning we are not claiming a 
berth for a new “faculty.” Evidence of every kind is 
again and again demonstrating the unity of mind, and 
the integrative character of its physical substrate: the 
nervous system. We cannot localize “analysis” and 
“synthesis.” These tendencies seem to be properties 
inherent in nervous protoplasm, present the very 
moment an aggregate of nerve cells become organized 
into any form of functional unit. This fact emphasizes 
again Wundt’s declaration that 
“there is, in reality, but one psychical center; and that 
is the brain as a whole, with all its organs. For in any 
at all complicated psychical process, these organs are 
brought into action, if not all together, at any rate over 
so wide a range and in such various quarters as to forbid 
the delimitation of special psychical centers within the 
functional whole.” 1 
And one wonders if James was not correct when, in dis- 
cussing “analysis” he apologized for the short space 
devoted to this activity and insisted: “I think I empha- 
size it enough when I call it one of the ultimate founda- 
tion-pillars of the intellectual life.”2 
3. NEUROLOGICAL ORIENTATION 
Our discussion of mental mechanisms invariably 
forces us to a consideration of the anatomical and the 
physiological structures underlying them. Comparative 
psychology has often emphasized the slight differences 
in the sensory capacities between man and animal. 
And wherever the difference has been emphasized it has 
1 Wundt, 34; 218. 
2 James, n; 530. 28 
INTELLIGENCE MEASUREMENT 
often been stressed in favor of animals. Our studies of 
the feeble-minded reveal slight, if any differences, in the 
sensory capacities of normal and mentally deficient. It 
seems that the factors which make for intelligent be- 
havior do not reside in a refined sense-organ, necessarily, 
although refined sense-organs are extremely desirable. 
Intelligence is something cerebral. We, therefore, 
naturally look for the clearest exemplification of the 
activity of the analytic-synthetic tendency in the func- 
tion of the cerebrum. 
Most anatomists and neurologists agree that no true 
nervous elements are evident in our progress from lower 
to higher organisms until we reach the coelenterates. 
The Protozoa possess no nervous system. The Metazoa 
do. Jennings finds no evidence to explain the behavior 
of the Metazoa as different on the basis of their posses- 
sion of a nervous system. What the Metazoa do, the 
Protozoa can also do. “The possession of a nervous 
system brings with it no observable essential changes in 
the nature of behavior. We have found no important 
additional features in the behavior when the nervous 
system is added.”1 In Vorticella, Jennings found that 
the receptive end is ciliated peristome. Stimuli of cer- 
tain kinds will be transmitted and contractions of the 
myoid filament at the fixed end of the cell will be notice- 
able. In multicellular organisms the same simplicity of 
nervous mechanism is observed, with this exception: 
increased complexity of the nervous fabric is correlated 
with greater delicacy of individual readjustment to 
changes in environmental conditions. What is of espe- 
1 Jennings, 12; 263. NEUROLOGICAL ORIENTATION 
29 
cial significance is the fact that “ the peculiar properties 
of the nerve cells are properties of protoplasm in general, 
but somewhat accentuated.”1 Each cell of our body, 
although there are comparatively few like itself, never- 
theless is capable of uniting in function with others 
strikingly different in structure. The nature of those 
conditions making for unity of function out of a diversity 
of structure, certainly implies a synthesis of a most 
subtle nature, true for somatic protoplasm as well as for 
nervous. 
The work of Sherrington, epoch-making in its contri- 
butions toward our understanding of nervous mech- 
anisms, throws some light on our question. 
“The nervous system in its simplest forms is diffuse — 
a number of scattered mechanisms performing merely 
local operations with much autonomy save that they 
have communication with their immediate neighbors 
across near boundaries.2 ... It is ill suited, therefore, 
to produce the integration of a large and complex indi- 
vidual as a whole.3 . . . Yet the coordination it brings 
about in its own local field may be strikingly effective.”4 
The earthworm is a good example of a segmented or 
metameric nervous system. Each metamere leads an 
almost independent existence. But “the integrative 
function of the nervous system is seen to perfection in the 
welding together of metameres into the unity of an 
animal individual.”5 There are hierarchies of nervous 
integration paralleled by hierarchies of functional 
organization. 
“By longitudinal integration short series of adjoining 
1 Jennings, 12; 280. 
2 Sherrington, 25; 311. 
1 Sherrington, 25; 311. 
4 Sherrington, 25; 312. 
5 Sherrington, 25; 3x4. 30 
INTELLIGENCE MEASUREMENT 
segments become in respect to some one character com- 
bined together, so as to form in respect to that character 
practically a single organ.1. . . And it is in the inte- 
gration of long series, or of the whole series, of segments 
one with another, that, apart from psychical phenomena, 
the nervous system seems to reach its acme of achieve- 
ment.”2 
Jennings has presented a great mass of evidence dem- 
onstrating the constant “feeling about” of all lower or- 
ganisms, the attempting of new directions, the retiring 
from those which are harmful, and the persisting in those 
which are of advantage to the organism.3 This feeling 
about, this avoiding and persisting, force one to grant 
some degree of discrimination to the animal, and once 
that is granted, the existence of a fundamental analytic- 
synthetic element logically follows. 
Present-day evidence has demonstrated that the neu- 
ron is an anatomic, genetic, physiologic, trophic, and 
functional unit. Each neuron is a complete cell in and 
of itself. Nevertheless, the complexity of interconnec- 
tion between neurons is beyond human comprehension. 
From the simplest reflex to the most complex higher 
thought process a basic tendency of “ get-together-ness ” 
and “ stay-together-ness ” is observable among neurons. 
And where it is absent or defective, mental progress 
from infancy to adulthood can hardly be conceived. 
The passage of stimuli through sensory pathways and 
the complexity of interconnection between what Sher- 
1 Sherrington, 25; 344. 
2 Sherrington, 25; 344. 
* See Jennings’ description of the behavior of an amoeba in pursuing 
another for the purpose of devouring it. — Jennings, 12; 16, 17. NEUROLOGICAL ORIENTATION 
31 
rington designates the “silent areas,” illustrate the com- 
plexity underlying mental mechanism. The terminal 
nuclei and the thalamus are among the important way- 
stations to cerebral connection. But 
“the thalamus, since it possesses many short fibres con- 
necting its own parts, is probably something more than 
a mere way-station. Apparently, the sensory impulses 
from the different receptors come together here and 
join in such a way that the impulses which pass from 
here to the cortex are already organized to a certain 
extent.”1 
What function other “relay” stations or connecting 
links play in synthesizing and organizing primary mental 
states can only be conjectured. Throughout his book 
Sherrington stresses the interconnecting or “integrative” 
function of the nervous system, which makes for a unity 
of action out of a diversity of organs.2 
In running through the evidence presented on the 
mental changes which result from cortical ablations, 
one is amazed by the contradictory results which have 
been found in various quarters. Careful experimentation 
in the last few years, notably that of Franz in this coun- 
try, is demonstrating with greater and greater conclusive- 
ness that the integrity of the cortex is necessary for the 
integrity of mental functioning. Meynert makes a good 
deal of the fact that disorganization of any portion of 
the cortex manifests itself in some form of psychic dis- 
turbance.3 Morat stresses the fact that the brain may 
1 Ladd and Woodworth, 14; 93. 
* Sherrington, 25. 
* “ Populare Vortrage,” 2 ff. 32 
INTELLIGENCE MEASUREMENT 
be regarded “a prodigy of unity” as well as “a prodigy 
of complexity.”1 Mach concludes that “A review of 
anatomic, physiologic, and psychopathologic findings 
forces one to the conclusion, that the integrity of con- 
sciousness is dependent upon the integrity of the cor- 
tex.”2 And finally, the careful work of Franz leads 
him to the generalization that, “Both the clinical and 
the physiological evidence points to a dependence of 
certain mental processes on the integrity of the frontal 
lobes and, in fact, on the integrity of the brain as a 
whole.”3 
4. SUMMARY 
To summarize: Whether we investigate the purely 
mental aspects of our behavior, or whether we observe 
the integrating of nerve element with nerve element, we 
are struck with the significance of synthesis for normal 
mental functioning. We shall have occasion in a later 
chapter to consider the current definitions of intelligence, 
and with this new orientation we shall suggest another 
definition which perhaps will take us back to something 
more fundamental than “adaptation.” 
1 Morat, 18; 1. 
2 Mach, 15; 42. 
8 Franz, 8; 64. BIBLIOGRAPHY 
33 
Bibliography 
1. Bartlett, F. C., “An Experimental Study of Some 
Problems of Perceiving and Imaging;” British Journal 
of Psychology, 1916, 8: 222-267. 
2. Bergson, Henri, “Creative Evolution.” (New York; 
Holt & Co., 1913; 407 pp.; transl. by A. Mitchell.) 
3. Bolton, J. S., “The Brain in Health and Disease.” 
(London, Arnold, 1914; 479 pp.) 
4. Book, W. F., “Psychology of Skill.” (University of 
Montana Publication in Psychology.) 
5. Bryan, W. L., and Harter, N., “Studies in Physiology 
and Psychology of the Telegraphic Languages,” 
Psychological Review, 1899, 6: 345-375. 
6. Duprat, L., “Association mentale et causalite psycholo- 
gique.” Revue Philosophique, 1913, 75: 452-470. 
7. Fisher, Sara Carolyn, “The Process of Generalizing 
Abstraction; and Its Product, The General Concept.” 
{Psychological Monographs, 1916, vol. 21, No. 2; 
213 pp.) 
8. Franz, Shepherd Ivory, “On the Functions of the 
Cerebrum; the Frontal Lobes.” {Archives of Psy- 
chology, 1907, vol. 1, No. 2; 64 pp.) 
9. Gregor, A., “ Untersuchungen liber die Entwicklung 
einfacher logischer Leistungen (Begriffserklarung). 
{Zsch.f. angew. Psychol., 1915, 10: 339-451.) 
10. Hobhouse, L. T., “Mind in Evolution.” (London, 
Macmillan, 1901; 415 pp.) 
11. James, W., “The Principles of Psychology.” (New 
York, Holt & Co., 1890; vol. 1, 689 pp.; vol. 2, 
704 pp.) 
12. Jennings, H. S., “Behavior of the Lower Organisms.” 
(New York, Columbia University Press, 1915; 366 pp.) 34 
INTELLIGENCE MEASUREMENT 
13. Judd, Charles H., “Psychology; General Introduction.” 
(Boston, Ginn & Co., 1917, [2d. ed.]; 358 pp.) 
14. Ladd, George T., and Woodworth, Robert S., “Ele- 
ments of Physiological Psychology.” (New York, 
Scribner’s, 1911; 704 pp.) 
15. Mach, E., “Erkenntnis und Irrtum.” (Leipzig, Barth, 
1905; 461 pp.) 
16. Meumann, E., “The Psychology of Learning.” (New 
York, D. Appleton & Co., 1913; 393 pp.; transl. by 
J. W. Baird.) 
17. Meumann, E., “Vorlesungen zur Einfiihrung in die 
experimentelle Padagogik.” (Leipzig, Engelmann, 
1911; 725 pp.) 
18. Morat, J. P., “Physiology of the Nervous System.” 
(London, Constable & Co., 1914; 680 pp.) 
19. Pillsbury, W. B., “Attention.” (London, Swan Son- 
nenschein & Co., 1908; 346 pp.) 
20. Rtbot, Th., “Essay on the Creative Imagination” 
(Chicago, Open Court Publishing Co., 1906; 370 pp.; 
transl. by A. H. N. Baron.) 
21. Ribot, Th., “Evolution of General Ideas.” (Chicago, 
Open Court Publishing Co., 1899; 231 pp.; transl. by 
F. A. Welby.) 
22. Rignano, Eugenio, “Les diverses mentalites logiques,” 
Scientia, 1917, 22: 95-125. 
23. Rignano, Eugenio: Qu’est-ce que le raisonnement? 
Scientia, 1913, 13 (supplement): 30-57. 
24. Royce, Josiah, “Outlines of Psychology.” (New York) 
Macmillan, 1904; 392 pp.) 
25. Sherrington, C. S., “The Integrative Action of the 
Nervous System.” (New York, Scribner’s, 1906; 
411 pp.) 
26. Stout, G. F., “A Manual of Psychology.” (New York, 
Hinds, Noble & Eldridge, 1899; 643 pp.) BIBLIOGRAPHY 
35 
27. Thorndike, E. L., “Educational Psychology.” Vol. 2: 
“The Psychology of Learning.” (New York, Teachers 
College, Columbia University, 1913; 452 pp.) 
28. Thorndike, E. L., “The Elements of Psychology.” 
(New York, Seiler, 1905; 351 pp.) 
29. Titchener, E. B., “A Beginner’s Psychology.” (New 
York, Macmillan, 1916; 362 pp.) 
30. Titchener, E. B., “Experimental Psychology of the 
Thought-Processes.” (New York, Macmillan, 1909; 
318 pp.) 
31. Watson, John B., “Behavior.” (New York, Holt, 
1914; 439 PP-) 
32. Wundt, W., “Grundziige der physiologischen Psycho- 
logic.” (1910, 3 vols. [6 ed.]) 
33. Wundt, W., “Lectures on Human and Animal Psychol- 
ogy.” (454 PP-) 
34. Wundt, W., “Principles of Physiological Psychology.” 
(London, Swan Sonnenschein & Co., 1904; 347 pp.) 
35. Ziehen, Th., “Leitfaden der physiologischen Psy- 
chology.” (Jena, Gustav Fischer, 1914 (Zehnte 
Auflage); 504 pp.) PART B 
THE BLOCK-DESIGN TEST THE BLOCK-DESIGN TEST1 
CHAPTER I 
Statistics Regarding the Subjects who Were Given the 
Block-design Tests 
In the following division we shall present tables giving 
the chronological ages of the subjects, arranged by- 
source; the Binet mental ages of the subjects, arranged 
by source, the Binet mental ages and the intelligence 
quotients arranged by sex and source; the correspond- 
ence of chronological and mental ages, totaled separately 
for sex and source; the age-grade distribution, classified 
by sex; an age-progress table, classified by sex; nation- 
ality; place of birth; social class; home conditions; 
and teachers’ estimates of intelligence. The question- 
naire on p. 61 was utilized to obtain most of this infor- 
mation. The aim was to make certain that the group 
selected was typical, and if atypical, in what direction 
and to what extent. The results seem to show that the 
children selected were representative of the larger dis- 
tribution of children at large and consequently the final 
norms seem valid. Mayfield yielded children somewhat 
inferior, Palo Alto yielded children somewhat superior, 
and Menlo Park more of an average type. 
Table I shows the life ages of the children tested. At 
almost every year the cases number between 20 and 30, 
and the years range from 4 to 16 in the case of the pub- 
lic school children, and from 9 to about 37 in the case 
1The complete set of material may be obtained from C. H. 
Stoelting Co., 3037-3047 Carroll Ave., Chicago, Illinois. 
39 40 
INTELLIGENCE MEASUREMENT 
Chronological Age 
Boys 
Girls 
Total 
4- 
TO 
5- 
5- 
TO 
6- 
6- 
TO 
7- 
7- 
TO 
8- 
8- 
TO 
9- 
9- 
TO 
10- 
10- 
TO 
11- 
11- 
TO 
12- 
12-7 
TO 
13-6 
13- 
TO 
14- 
14- 
TO 
15- 
15- 
TO 
16- 
16- 
TO 
17- 
17-7 
TO 
22-6 
22-7 
TO 
37-6 
37-7 
TO 
over 
Mayfield . 
I 
2 5 
5 4 
2 5 
2 3 
8 8 
5 3 
3 5 
3 9 
4 4 
44 
2 
2 
41 
52 
93 
Palo Alto High 
1 
2 1 
4 2 
43 
56 
2 
18 
12 
3° 
P.A. Intermed. 
1 
4 5 
3 1 
3 1 
1 I 
I 
12 
9 
21 
P. A. Lytton . 
I 2 
6 2 
4 7 
6 5 
7 4 
4 3 
3 2 
1 1 
1 
33 
26 
59 
Menlo Park . 
3 2 
3 7 
4 6 
8 3 
4 2 
8 6 
4 2 
7 5 
6 3 
1 1 
2 
2 
50 
39 
89 
I 
6 9 
1413 
10 18 
16 11 
1914 
1713 
15 14 
16 17 
18 10 
10 9 
88 
4 2 
154 
138 
292 
Normal Total 
P. S. Group 
I 
i5 
27 
28 
27 
33 
30 
29 
33 
28 
19 
16 
6 
Vineland . 
1 
2 
2 
2 
2 1 
11 
2 1 
5 3 
3 1 
1 
14 
14 
28 
Eldridge . 
1 
2 
2 
1 
1 
2 2 
5 11 
8 9 
2 1 
24 
23 
47 
1 
1 
2 
2 
2 2 
4 1 
1 
2 1 
4 3 
10 14 
1110 
2 2 
38 
37 
75 
F. M. Total . 
1 
I 
2 
2 
4 
5 
1 
3 
7 
24 
21 
4 
I 
6 9 
1413 
10 18 
17 11 
20 14 
1715 
15 l6 
18 19 
22 11 
119 
10 9 
8 5 
10 14 
11 10 
2 2 
Grand Total . 
I 
i5 
27 
28 
28 
34 
32 
31 
37 
33 
20 
19 
13 
24 
21 
4 
192 
175 
367 
Dark figures 
Female 
TABLE I 
Light figures 
Male STATISTICS REGARDING SUBJECTS 
41 
of the feeble-minded. The Mayfield cases numbered 93, 
the Palo Alto no, the Menlo Park 89. There are 28 
feeble-minded cases included from the Vineland, N. J., 
Training School, and 47 feeble-minded cases from the 
California State Home for the Feeble-minded, making a 
grand total of 367 cases. Each of these was given the 
block designs, the two Trabue tests (B and C), the 
Binet test, and the dissected sentences test. The time 
spent in the examination of each case varied from one 
hour to three hours, the average being about two hours. 
Almost all of the examinations required two sittings, in 
some cases three. At no single time was a subject kept 
over an hour and a half. Conditions for examination 
were always excellent. The writer, who did all the ex- 
amining, always had a room apart, free from disturb- 
ances and distractions. 
In Table II are given the mental ages of the subjects 
examined. It will be observed that most of the ages are 
clustered between 6 and 13. All considered, this is an 
excellent range, the number of cases at each age varying 
from 20 to 50. 
In Table III are given the Mental Ages and I. Q.’s for 
the public school boys and girls. The modal I. Q. for 
both groups, separately and combined, is 100. Table IV 
gives the I. Q.’s for the feeble-minded. The median 
I. Q. for the feeble-minded falls in the 50 I. Q. group. 
It is evident from these tables that there is a positive 
correlation between increase of mental age and increase 
of intelligence quotient. Supposedly we would expect 
no correlation. But our school group is evidently se- 
lected. In the grammar grades there has been some 42 
INTELLIGENCE MEASUREMENT 
Mental Age 
Boys 
Girls 
Total 
2- 
TO 
3- 
3- 
TO 
4- 
4- 
TO 
5- 
5- 
TO 
6- 
6- 
TO 
7- 
7- 
TO 
8- 
8- 
TO 
9- 
9- 
TO 
10- 
10-7 
TO 
11-6 
11- 
TO 
12- 
12-7 
TO 
13-6 
13- 
TO 
14- 
14- 
TO 
15- 
15- 
TO 
16- 
16- 
TO 
17- 
17- 
TO 
18- 
18- 
TO 
19- 
Mayfield . . 
i 
2 
i 5 
5 7 
9 8 
4 4 
4 II 
3 6 
7 3 
33 
I 2 
I 2 
I 
41 
52 
93 
P. A. High . 
2 
2 3 
S 2 
4 3 
3 1 
4 I 
18 
12 
30 
P. A. Inter. . 
3 3 
3 3 
2 
4 2 
I 
12 
9 
21 
P. A. Lytt. . 
I 
2 2 
4 1 
4 6 
S 6 
7 3 
3 <> 
2 
3i 
2 
I 
33 
26 
59 
Menlo Park . 
3 6 
3 4 
7 8 
7 3 
10 3 
8 5 
6 4 
43 
I 2 
I 
I 
5° 
39 
89 
i 
3 
6 13 
12 12 
2022 
16 13 
21 17 
17 20 
18 10 
12 7 
8 8 
4 6 
5 5 
4 3 
3 l 
4 I 
154 
138 
292 
P. S. Group . 
i 
3 
19 
24 
42 
29 
38 
37 
28 
19 
16 
10 
10 
7 
4 
5 
Vineland . . 
I 2 
3 2 
i i 
2 3 
1 2 
1 1 
2 2 
2 
1 
1 
14 
14 
28 
Eldridge . . 
I 
5 4 
3 4 
1 1 
3 4 
3 1 
2 2 
4 2 
2 
2 
1 
1 
1 
24 
23 
47 
I 2 
4 2 
6 5 
5 7 
2 3 
4 5 
5 3 
4 2 
4 3 
1 2 
2 
1 
1 
1 
38 
37 
75 
F. M. Total . 
3 
6 
ii 
12 
5 
9 
8 
6 
7 
3 
2 
1 
1 
1 
X 2 
5 2 
9 5 
11 20 
1415 
24 27 
21 16 
25 19 
21 23 
19 12 
12 9 
8 9 
5 6 
6 5 
4 3 
3 1 
4 I 
Grand Total 
3 
7 
14 
3i 
29 
Si 
37 
44 
44 
3i 
21* 
17 
11 
11 
7 
4 
5 
192 
175 
367 
Dark figures 
* One case no block-designs given. 
Female 
TABLE II 
Light figures 
Male STATISTICS REGARDING SUBJECTS 
43 
Mental Age 
Intelligence Quotients 
26-35 
36-45 
46-55 
56-65 
66-75 
76-85 
86-95 
96-105 
106-115 
116-125 
126-135 
136-145 
Total 
2-7 to 3-6 . . 
0 O 
3-7 to 4-6 . . 
I 
I 0 
4-7 to 5-6 . . 
2 
1 
3 0 
5-7 to 6-6 . . 
1 
2 
4 
5 
2 
5 
6 13 
6-7 to 7-6 . . 
I I 
2 2 
2 
6 
3 
3 
4 
12 12 
7-7 to 8-6 . . 
I I 
4 
3 
5 
3 
4 
6 
5 4 
1 5 
20 22 
8-7 to 9-6 . . 
2 1 
4 
2 
2 
3 
7 
5 
1 2 
16 13 
9-7 to 10-6 . . 
I 
1 2 
4 
4 
7 
3 
4 
5 
3 1 
2 1 
21 17 
10-7 to 11-6 . . 
2 1 
4 
5 
3 
7 
5 
4 
3 2 
1 
17 20 
11-7 to 12-6 . . 
1 
5 
2 
6 
2 
3 
4 
1 
3 
18 10 
12-7 to 13-6 . . 
1 
3 
2 
2 
1 
3 
3 
4 
1 
12 7 
13-7 to 14-6 . . 
2 
4 
1 
1 4 
2 1 
1 
8 8 
14-7 to 15-6 . . 
1 
1 
2 
2 
r 2 
I 
4 6 
15-7 to 16-6 . . 
3 
1 
3 
2 I 
S 5 
16-7 to 17-6 . . 
1 
2 1 
1 
I 
1 
4 3 
17-7 to 18-6 . . 
1 
1 1 
1 
3 1 
18-7 to 19-6 . . 
1 
2 
2 
4 I 
I 
2 3 
8 8 
26 22 
36 30 
41 
41 
21 20 
12 12 
4 2 
3 
154 138 
Total . . . . 
I 
5 
16 
48 
66 
82 
4I, 
24 
6 
3 
292 
98-91 
Dark figures 
TABLE III —P. S. Group 
MENTAL AGE AND I. Q. 
Modal Group = I. Q. ioo 
Female 
Light figures 
Male 44 
INTELLIGENCE MEASUREMENT 
elimination of the mentally retarded, and this is especially 
striking in the high school grades. Our schools seem to 
demand higher mental ages and higher I. Q.’s for prog- 
ress through the grades. In the primary grades I. Q.’s 
fall as low as 56. In the intermediate school there was 
only one case below 76, and in the high school there was 
TABLE IV 
Intelligence Quotients 
20 
30 
40 
50 
60 
70 
80 
go 
IOO 
Vineland 
i 
8 
S 
7 
5 
1 
1 
Eldridge 
9 
8 
9 
7 
9 
2 
2 
I 
Total . 
i 
17 
13 
16 
12 
10 
3 
2 
I 
75 
F. M. Group 
Median I. Q. = 50 
not a single case with an I. Q. less than 86. Another 
item of importance: the upper right-hand section of 
Table III includes children who are accelerated men- 
tally but retarded pedagogically, and the lower left-hand 
section of the table includes children who are retarded 
mentally, but accelerated pedagogically. 
In the public school group, 189 out of the 292 have 
I. Q.’s between 86 and 115 — in other words, 64.7 per 
cent have average intelligence. 
Table IV gives the distribution of I. Q.’s for the 
feeble-minded cases. And Table V summarizes the 
totals in Tables III and IV. 
Tables VI to XII present in detail the I. Q. dis- 
tributions for each source, with its median I. Q. The 
median I. Q.’s (crude) for the various schools were, STATISTICS REGARDING SUBJECTS 
45 
l6 TO 
25 
26 TO 
35 
36 TO 
45 
46 TO 
55 
56 TO 
65 
66 to 
75 
76 TO 
85 
86 to 
95 
96 TO 
105 
106 TO 
115 
116 TO 
125 
126 TO 
135 
136 TO 
145 
Total 
P. S. Group .... 
F. M. Group .... 
1 
17 
I 
13 
16 
S 
12 
16 
IO 
48 
3 
66 
2 
•N M 
00 
41 
24 
6 
3 
292 
75 
Total .... 
1 
17 
14 
16 
17 
26 
Si 
68 
83 
41 
24 
6 
3 
367 
192 
TABLE V 
MENTAL AGE AND I. Q. 
P. S. and F. M. Groups Combined 
(Boys and Girls) 46 
INTELLIGENCE MEASUREMENT 
Mayfield, 90; Palo Alto High, no; Palo Alto Inter- 
mediate, 100; Palo Alto Lytton, 100; Menlo Park, 90; 
Vineland, 45; Eldridge, 50. 
TABLE VI 
Mental 
Age 
Intelligence Quotients 
Total 
40 
So 
6o 
70 
8o 
go 
100 
no 
120 
4 
X 
1 
5 
I 
I 
2 
6 
I 
I I 
3 
1 5 
7 
i 
2 2 
2 
I I 
1 2 
5 7 
8 
I 
2 
2 
3 1 
3 
3 
1 
1 
9 8 
9 
I I 
2 
1 
2 
1 
4 4 
IO 
i 
2 
I 
3 
2 
1 4 
1 
4 II 
XI 
I 
I 
3 
2 
1 1 
3 6 
12 
3 
2 
I 
1 1 
2 
7 3 
13 
i 
2 
2 
1 
3 3 
14 
I 
2 
1 2 
IS 
1 
I 
1 
I 2 
16 
1 
I 
i 
2 I 
4 6 
ii 15 
10 7 
6 16 
,5 
6 
2 1 
41 52 
Total 
i 
3 
IO 
26 
17 
22 
11 
3 
93 
Mayfield Cases 
Median I. Q. = 90 
TABLE VII 
Mental Age 
Intelligence Quotients 
70 
80 
sfo 
IOO 
no 
120 
Total 
XI . 
1 
1 1 
2 
1 
3 3 
12 
1 
2 I 
2 
3 3 
13 • • 
1 
X 
2 
14 • • 
1 
1 1 
2 1 
4 2 
IS • • 
16 
1 
I 
1 
2 1 
2 3 
3 2 
2 2 
2 1 
12 9 
Total . 
1 
3 
5 
5 
4 
3 
21 
Palo Alto Intermediate 
Median I. Q. = ioo 
Boys 
Light figures 
Girls 
Dark figures STATISTICS REGARDING SUBJECTS 
47 
TABLE VIII 
Palo Alto High 
Mental Age 
Intelligence Quotients 
Total 
90 
IOO 
no 
120 
130 
140 
14 . . 
2 
2 
IS • • 
I I 
1 I 
I 
2 3 
16 
3 
I 
2 1 
S 2 
17 • . 
1 
2 I 
1 
1 
I 
4 3 
18 . . 
I 
1 1 
1 
3 l 
19 . . 
1 
2 
2 
4 I 
1 3 
4 2 
.3 3 
4 3. 
.3 1 
3 
18 12 
Total . 
4 
6 
6 
7 
4 
3 
30 
Median I. Q. = no 
Boys 
Light figures 
Girls 
Dark figures 
TABLE IX 
Mental Age 
Intelligence Quotients 
Total 
8o 
go 
IOO 
no 
120 
130 
5 • 
i 
I 
6 . 
i 
I 
i 
1 
2 
2 
7 
2 
2 
1 
4 
I 
8 . 
i 
I 
i 
2 
I 
i 
i 
2 
4 
6 
9 • 
i 
I 
i 
4 
3 
i 
5 
6 
IO 
i 
2 
3 
i 
2 
I 
7 
3 
ii 
I 
i 
i 
2 
I 2 
I 
3 
6 
12 
i 
i 
2 
13 
3 
I 
3 
I 
14 
i 
1 
2 
15 • 
1 
1 
1 * 
8 
3 
15 
9 
6 4 
2 
5 
1 1 
33 
26 
Total 
5 
ii 
24 
IO 
7 
2 
1 59 
Palo Alto Lytton 
Light figures 
Median I. Q. = ioo 
Boys 
Girls . 
Dark figures 48 
INTELLIGENCE MEASUREMENT 
TABLE X 
Mental Age 
Intelligence Quotients 
Total 
6o 
70 
8o 
go 
IOO 
no 
120 
6 . . 
i 
2 4 
I I 
3 6 
7 • • 
i 
3 2 
I 
3 4 
8 . . 
i 
2 
i i 
2 2 
2 2 
2 
7 8 
9 • • 
I 
2 
i 
3 2 
I 
7 3 
xo . . 
I 
3 
3 3 
I 
2 
io 3 
ii . . 
I 
2 1 
2 2 
2 I 
2 
8 5 
12 . . 
I I 
I 
3 I 
I I 
I 
6 4 
13 • • 
2 
I 
2 2 
4 3 
14 . . 
I I 
I 
I 2 
IS • • 
I 
I 
16 . 
I 
I 
2 
.3 2 
12 2 
IS 14 
13 I2 
5 5 
2 2 
5° 39 . 
Total 
• 
2 
5 
14 
29 
25 
IO 
4 
89 
Menlo Park 
Median I. Q. = 90 
TABLE XI 
Eldridge 
Mental Age 
Intelligence Quotients 
30 
40 
So 
6o 
70 
8o 
go 
IOO 
Total 
4 ... 
I 
i 
5 ... 
4 4 
I 
5 4 
6 ... 
i 4 
I 
i 
3 4 
7 . . . 
i i 
i I 
8 ... 
3 4 
3 4 
9 . . . 
i 
2 
I 
3 i 
IO . . . 
2 2 
2 2 
ii ... 
4 2 
4 2 
12 
2 
2 
13 . . . 
2 
2 
14 • . . 
I 
I 
IS • • • 
I 
I 
16 
I 
I 
5 4 
3 5 
4 5 
5 2 
5 4 
2 
I I 
I 
24 23 
Total . 
9 
8 
9 
7 
9 
2 
2 
I 
47 
Median I. Q. = 50 
Boys 
Light figures 
Girls 
Dark figures STATISTICS REGARDING SUBJECTS 
49 
TABLE XII 
Vineland 
Mental Age 
Intelligence Quotients 
20 
30 
40 
SO 
6o 
70 
8o 
Total 
3 • • 
i 
2 
I 2 
4 • • 
2 2 
I 
3 2 
S • • 
I 1 
I I 
6 . . 
2 2 
I 
2 3 
7 • • 
I 
I 
i 
I 2 
8 . . 
I 
i 
I I 
9 • • 
2 I 
i 
2 2 
IO . 
2 
2 
ii . . 
I 
I 
12 . 
I 
I 
i 
3 5 
2 3 
.5 2 
2 3 
I 
I 
14 14 
Total 
i 
8 
5 
7 
5 
I 
I 
28 
Median I. Q. = 45 
Boys 
Light figures 
Girls 
Dark figures 
In Table XIII are presented the mental age and 
chronological age distributions for the public school 
group. It is evident from this table that there is a some- 
what larger percentage of those who are retarded men- 
tally than accelerated: 36 (12 per cent) are accelerated 
more than one year, and 81 (28 per cent) are retarded 
more than one year. In Table XIV the data of Table 
XIII are summarized for years of retardation and ac- 
celeration. It will be observed that 59 per cent are at 
age mentally, or within one year; 22 per cent are 
within two years; 9 per cent are within three years; 
7 per cent are within four years; 2 per cent within 
five; and of 1 per cent within six years of their 
mental age. 50 
INTELLIGENCE MEASUREMENT 
Chrono- 
Mental Age 
Total 
Age 
3 
4 
S 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
IS 
16 
17 
18 
19 
5 
I 
1 
1 
6 
X 
S 7 
1 
1 
6 
9 
IS 
7 
I 
i 3 
5 
5 
7 
5 
14 
13 
27 
8 
I 
3 
4 
1 
2 
9 
2 
3 
1 
2 
IO 
18 
28 
9 
1 
2 
4 
2 
6 
5 
4 
1 
2 
16 
11 
27 
IO 
1 
1 
6 
4 
2 
2 
5 
4 
2 
2 
2 
I 
1 
19 
14 
33 
XI 
1 
2 
3 
6 
4 
4 
4 
2 2 
I 
I 
17 
13 
30 
12 
1 
1 
2 
2 
1 
2 
4 
3 3 
3 
T 
2 3 
1 
IS 
14 
29 
13 
1 
2 
1 
3 
4 
2 
4 
3 1 
3 
; 
x 2 
I 
I 
1 
1 
16 
17 
33 
14 
1 
4 
3 
3 1 
1 
4 1 
2 2 
I 2 
1 
2 
18 
10 
28 
IS 
1 
1 
2 2 
3 
2 
I I 
I I 
1 
2 I 
IO 
9 
19 
16 
1 
2 1 
2 
I I 
I 2 
1 1 
2 1 
8 
8 
16 
17 
1 
1 
1 
1 
I 
1 
4 
2 
6 
I 
3 
6 13 
12 12 
20 22 
16 13 
21 17 
17 20 
18 IO 
12 
7 
8 8 
4 6 
5 5 
4 3 
3 1 
4 I 
Total 
I 
3 
i9 
24 
42 
29 
38 
37 
28 
19 
l6 
IO 
IO 
7 
4 
5 
154 138 
292 
Dark figures 
CHRONOLOGICAL AND MENTAL AGES 
Girls 
TABLE XIII 
(P. S. Group) 
Light figures 
Boys STATISTICS REGARDING SUBJECTS 
51 
Mental Age 
Boys 
Girls 
Total 
5 yrs. . 
4 “ 
3 “ • 
4 
4 
Above 
3 
2 
3 
1 
6 
3 
- 36 
2 “ . 
IO 
13 
23 
i “ 
26 
20 
46 
At Age 
41 
43 
84 
173 
i yr. 
25 
18 
43 
2 yrs. . 
21 
19 
40 
Below 
- 
3 “ • 
12 
13 
25 
83 
4 “ • 
9 
6 
15 
5 “ • 
I 
1 
2 
6 “ . 
1 
1 
Total . 
154 
138 
292 
TABLE XIV 
In Graph i is presented graphically the retardation 
and acceleration of the 292 public school cases. A skew 
is observable toward the right. This is again manifest 
in Graph 2, which graphically represents the distribution 
of I. Q.’s for the same group of children. In making a 
comparison between the grouped distributions of I. Q. 
obtained by Terman in his revision of the Binet for 
905 cases and our results, we note the following: Ter- 
man found 35 per cent having I. Q.’s above average, in 
our cases 25.4 per cent were above average; he also 
found 33.9 per cent average (96 — 105 I. Q.), in our 
cases 28 per cent were average; and he found 31.3 per 
cent below average, while in our cases 46.6 per cent were 
below average. Our inferior group is 15 per cent larger, 
the average group is about 6 per cent smaller, and the 
superior group is about 10 per cent smaller. The fact 
that Terman excluded the foreign-born, which have 
been included in our data and amount to about 5 per 52 
INTELLIGENCE MEASUREMENT 
Number of Children 
at, Above and Below Age 
GRAPH 1 
Public School 
Group 
Number 
.Percent 
Below 
At 
Age 
Above 
Distribution of I. Q. 
GRAPH 2 
Public School 
Group 
Number 
Percent 
Class 100 Includes 
I. Q.s from 96-105 
Intelligence Quotient 53 
STATISTICS REGARDING SUBJECTS 
Grade 
uAL 
I 
2 
3 
4 
s 
6 
7 
8 
I 
II 
III 
5 
6 
I 
6 
9 
1 
6 
7 
9 
7 
5 5 
i 
14 
13 
8 
3 
5 .8 
I 
7 
10 
18 
9 
i 
2 2 
8 
7 
3 
2 
2 
16 
11 
IO 
2 I 
8 
3 
5 
3 
3 6 
I 
I 
19 
H 
ii 
2 
I 
5 
2 
8 5 
2 
3 
2 
17 
13 
12 
I 
2 
I 
4 I 
3 
4 
3 7 
1 1 
1 
15 
14 
13 
2 
2 2 
4 
3 
3 9 
3 * 
2 
2 
16 
17 
14 
I 
3 
i 
3 4 
7 3 
4 
2 
18 
10 
15 
2 I 
5 
2 
I 
1 2 
1 
10 
9 
16 
3 2 
2 
3 
3 2 
1 
8 
8 
17 
2 2 
2 
4 
2 
21 
19 
4 16 
20 
19 
!7 
8 
20 14 
,!3 
12 
II 23 
20 14 
11 
8 
6 4 
1 I 
1 4 !38 
Total 
• 
• 
• 
40 
30 
39 
25 
34 
25 
34 
34 
19 
10 
2 
292 
Dark figures 
AGE-GRADE DISTRIBUTION 
TABLE XV 
Girls 
Light figures 
Boys 54 
INTELLIGENCE MEASUREMENT 
cent of the public school cases, would help account for 
the discrepancy. We have also made no eliminations 
because of race or nationality. As Pintner has so ably 
stated, the mere fact of large numbers of cases is no safe- 
guard for reliability of standardization; and in obtain- 
ing accurate norms, individuals of all classes and degrees 
should be included.1 We have stressed careful technique 
rather than multiplicity of cases, or perfection in sam- 
pling. 
Table XV is the age-grade distribution of our public 
school cases. What is striking here is the practically 
symmetrical distribution as compared with the skewed 
curve for the mental ages and I. Q.’s. This is clearly 
brought out in Table XVI, which summarizes briefly 
the data of Table XV. It will be observed that 35 per 
cent are at age pedagogically, 31 per cent are acceler- 
ated, and 34 per cent are retarded. The percentage at 
or within one year of grade is 83 per cent. 
TABLE XVI 
Boys 
Girls 
Total 
Per Cent 
3 yrs. . . 
i 
1 
4 
Above grade - 
2 yrs. . . 
8 
6 
14 
47 
I yr. . . 
3i 
45 
76 
26.0 
At age for grade . . 
S3 
49 
102 
349 
i yr. . . 
38 
26 
64 
21.9 
2 yrs. . 
17 
9 
26 
9.0 
Below grade 
3 yrs. . . 
6 
2 
8 
27 
4 yrs. . . 
1 s yrs. . . 
I 
X 
•4 
Total 
154 
138 
292 
100.0 
1 See R. Pintner and D. G. Paterson, “A Scale of Performance Tests,” 
pp. 73 ff. 55 
Years in School 
Grades 
Less 
THAN 
One 
I 
2 
3 
4 
s 
6 
7 
8 
9 
IO 
II 
12 
Total 
i 
H 8 
3 8 
7 3 
21 
19 
2 
I 2 
12 12 
I 2 
1 
14 
17 
3 • 
8 
IS 9 
5 2 
20 
19 
8 
4 • 
7 2 
6 4 
4 2 
17 
5 • 
2 
8 6 
S 2 
0 3 
I 
I 
20 
14 
6 . 
1 
00 
10 
4 2 
2 I 
I 
1 
13 
12 
7 • 
2 
6 7 
3 II 
I 
I 
I 2 
11 
23 
8 . 
2 2 
8 6 
6 
4 
3 1 
r 
1 
20 
14 
I 
2 
3 
7 
1 
2 3 
11 
7 
II 
1 
1 
1 
1 
4 2 
6 
4 
III 
1 
I 
1 
1 
ii 8 
4 10 
19 23 
23 15 
20 12 
16 15 
18 14 
13 23 
18 
9 
7 6 
4 3 
1 
154 138 
Total 
• 
19 
14 
42 
38 
32 
31 
32 
36 
27 
13 
7 
1 
292 
Dark figures 
GRADE-PROGRESS DISTRIBUTION 
TABLE XVII 
Girls 
Light figures 
Boys 56 
INTELLIGENCE MEASUREMENT 
Tables XVII and XVIII are concerned with the cor- 
relations between grade and progress, or the number 
of years spent in school: 40 per cent had made normal 
progress, 41.5 per cent had made accelerated, and 18.5 
per cent had made retarded progress. The percentage 
TABLE XVIII 
Boys 
Girls 
Total 
Per Cent 
f 4 yrs. . . 
Accelerated I 3 yrs. . 
Progress | 2 yrs. . 
1 1 yr. • • 
Normal progress 
Retarded f 1 r‘ 
v, <2 yrs. . 
Progress | _ 
2 
1 
4 
54 
60 
29 
2 
2 
2 
IO 
48 
57 
15 
5 
1 
2 
3 
14 
102 
X17 
44 
7 
3 
•7 
1.1 
4-7 
349 
40.0 
I5-I 
2.4 
1.1 
Total . 
154 
138 
292 
100.0 
making normal progress, or within one year of it, 
amounted to 90 per cent. The numbers making rapid 
progress are unusually large. This is accounted for by 
the fact that a good part of the testing came in February 
and March (1918) when children had just been promoted 
to a new grade. They were thus given credit for progress 
in that grade in which they had not yet made any 
progress at all. Taking this into account, the grade- 
progress distribution is of about the same type as the 
age-grade. 
In Table XIX are given the numbers and per cents 
of boys and girls who are at grade or within one year 
of it by chronological age (termed “in the right grade”), 
and who are between 86 to 115 I. Q. (termed “right 
I. Q. ”). It is clear from the table that 60 per cent of the STATISTICS REGARDING SUBJECTS 
57 
TABLE XIX 
GRADE LOCATION AND I. Q. 
Number 
Per Cents 
Total 
PerCent 
Boys 
Girls 
Boys 
Girls 
In right grade and 
of right I. Q.. . 
91 
85 
59% 
62% 
176 
60% 
Neither right grade 
nor right I. Q. . 
25 
12 
16% 
9% 
37 
13% 
Right I. Q. only . 
7 
6 
5% 
4% 
13 
4% 
Right grade only . 
3i 
35 
20% 
25% 
66 
23% 
Total . 
154 
V 
138, 
100% 
100% 
292 
100% 
292 
By “Right Grade” is meant at grade or within one year of it for 
chronological age. 
By “Right I. Q.” is meant an I. Q. between 86 to 115. 
children are what may be termed “average” and these 
help stabilize any tendency toward deviation from the 
absolute norm. 
In Table XX is given a list of geographical divisions 
and the number claiming descent from the nations of 
that region. Ranked for frequency, the leading nationali- 
ties came in the following order: North European, 
American, and combinations of North European and 
American. These accounted for over 80 per cent of all 
the cases. The descendants from northern groups num- 
bered 80.4 per cent, from southern groups 11.7 per cent, 
Orientals 3.4 per cent and from those not stating 4.5 
per cent. 
The data on birthplace by states, summarized for 
geographical division, and for birthplace in California 58 
INTELLIGENCE MEASUREMENT 
or outside of the state, are here presented: 74 per cent 
were born in California, 26 per cent were born elsewhere. 
The Pacific Coast States contributed 76.5 per cent, 
Mountain States 5.2 per cent, East North Central 4.5 
NATIONALITY AND BIRTHPLACE 
TABLE XX 
Number 
Per Cent 
(i) North European 
108 
37-0 
(2) South European 
22 
7.6 
(3) American 
91 
3II 
(4) Oriental 
10 
34 
(5) American and N. European 
36 
12.3 
(6) American and S. European.... 
5 
1-7 
(7) N. European and S. European . 
7 
2.4 
(8) ? or not stated 
13 
45 
Total 
292 
100.0 
per cent. The smallest numbers came from the East 
South Central States (.7 per cent) and from the New 
England States (o per cent). 
Tables XXI to XXIII and Graphs 3 to 5 give the 
results of teachers’ estimates of intelligence, home con- 
ditions, and social class. The writer has devised a 
series of tables for grouped measures of variability which 
are given in the appendix and which are here utilized 
for the purpose of comparing the percentages actually 
found with what one would expect theoretically. It 
will be noted that the average discrepancy for intelli- 
gence estimation is only 2 per cent, for estimation of 
home conditions 3 per cent, and for social status 4 per 
cent. This increase is to be expected, for to teachers, 
intellectual performance is under their observation STATISTICS REGARDING SUBJECTS 
59 
continually, and this is not as true for home conditions 
or social status. 
TABLE XXI 
TEACHERS’ ESTIMATES 
Number 
Per Cent 
Theoretical 
Expectation 
Discrepancy 
Very inferior. . 
4 
14 
0.2* 
+ 1.2 
Inferior .... 
II 
3 7 
4.0 
-0.3 
Below average 
S2 
17.8 
24.O 
—6.2 
Average .... 
133 
455 
43-6 
+ i-9 
Above average 
68 
23.2 
24.0 
—0.8 
Superior .... 
21 
7-3 
4.0 
+3-3 
Very superior . . 
3 
1.1 
0.2 
+0.9 
Total .... 
292 
100.0 
100.0 
Intelligence 
Average (A. M.) Discrepancy = 2.1% 
* See Appendix I. 
TABLE XXII 
TEACHERS’ ESTIMATES 
Home Conditions 
Number 
Per Cent 
Theoretical 
Expectation 
Discrepancy 
Very inferior. . 
2 
0.7 
0.2* 
+o-S 
Inferior .... 
17 
6.0 
4.0 
+ 2.0 
Below average 
57 
20.2 
24.O 
“3-8 
Average .... 
113 
40.0 
43 6 
-3-6 
Above average 
56 
19.6 
24.O 
-4.4 
Superior .... 
26 
9.2 
4.0 
+ 5-2 
Very superior . 
12 
43 
0.2 
+4-i 
? 
9 
Total .... 
283 
100.00 
100.0 
Average Discrepancy = 3.4% 
* See Appendix I. 60 
INTELLIGENCE MEASUREMENT 
TABLE XXIII 
TEACHERS’ ESTIMATES 
Social Status 
Number 
Per Cent 
Theoretical 
Expectation 
Discrepancy 
Very inferior. . 
5 
1-7 
0.2* 
+ i-5 
Inferior .... 
16 
57 
4.0 
+ i-7 
Below average 
47 
16.8 
24.O 
-7.2 
Average .... 
132 
47-3 
43-6 
+3-7 
Above average 
48 
17.4 
24.0 
—6.6 
Superior .... 
21 
7-5 
4.0 
+3-5 
Very superior . 
10 
3-6 
0.2 
+3-4 
? 
13 
Total .... 
279 
100.0 
100.0 
Average Discrepancy = 3.9% 
* See Appendix I. 
TEACHER’S ESTIMATES 
Intelligence 
GRAPH 3 
Per Cent 
Number 
Very 
Infer. 
Infer. 
Bel. 
Aver. 
Aver. 
Above 
Aver. 
Super. 
Very- 
Super. STATISTICS REGARDING SUBJECTS 
61 
Home Conditions 
Per Cent 
GRAPH 4 
Number 
Social Status 
Per Cent 
GRAPH 5 
Number 
Very 
Infer. 
Infer. 
Bel. 
Aver. 
Aver. 
Above 
Aver. 
Super. 
Very 
Super. 
Summing it all up, we have tested a fairly representa- 
tive group of school children, on the whole perhaps not 
markedly different from average children in other parts 
of this country. 
Sample of Questionnaire 
To the Teacher 
The information rendered on this blank will be held 
strictly confidential, will be used for statistical purposes 62 
INTELLIGENCE MEASUREMENT 
only and without the mention of any child’s name. 
The information will aid greatly in the standardization 
of a series of block-design tests. 
1. Name of school 
2. Name of pupil 
3. Date of birth 
4. Grade (when test was made) 
5. Years attended school... Grades skipped... Repeated... 
6. Place of birth 
(what state if American, what country if foreign). 
7. Descendant of what nationality 
(E.g., Scotch-Irish, Portuguese, German-American, etc.) 
8. Language spoken at home 
9. Occupation of father 
10. Quality of the child’s work (as compared with average 
children for this grade). (Write appropriate number, 
see rating scale) 
11. Teacher ’ s estim ate of the 
child’s intelligence (as 
compared with aver- 
age children of the 
same age). 
(Write appropriate 
number, see rating 
scale) 
12. Home conditions (con- 
sider neatness, size, 
comfort, provision of 
life necessaries, rela- 
tions between the par- 
ents, parental super- 
vision). 
(Write number) 
Rating Scale 
In your ratings indicate 
1. Very Inferior by 4 
2. Inferior by 5 
3. Below Average by 6 
4. Average by 7 
5. Above Average by 8 
6. Superior by 9 
7. Very Superior by 10 STATISTICS REGARDING SUBJECTS 
63 
13. Social class (consider culture, intelligence, social posi- 
tion of the group from which the child comes). 
(Write number) 
14. What is the character of the child’s work in the following 
school subjects (use rating scale). 
(Write number) 
1. Reading 
2. Writing 
3. Spelling 
4. Language 
5. Arithmetic 
6. History 
7. Geography 
8. Drawing 
9. Nature Study 
10. Music 
11. Manual Training 
12. Household Arts 
13. Science 
14. Deportment 
15. If this child were given a mental test involving chiefly the 
use of language, or the ability to understand and 
handle language symbols (as contrasted with a test 
requiring silent observation and performance), would 
you expect him (her) to pass 
Very low 
Low 
Below Average 
Average 
Above Average 
High 
Very High 
Note. — Put an X before 
the appropriate word 
16. Additional information which will throw light on the 
child’s intelligence, school success or failure, social 
status, peculiarities of any sort, etc. will be especially 
welcome and appreciated. We thank you. CHAPTER II 
The Test Material 
I. THE MATERIAL 
(a) The Blocks 
The blocks which are used are manufactured by The 
Embossing Co., are called “Color Cubes,” and may 
be secured at any of the large department stores and at 
the various distributing centers of Milton Bradley’s. 
There are sixteen cubes of one inch dimension and all 
are painted as follows: 
One side red, 
One side blue, 
One side white, 
One side yellow, 
One side blue and yellow (divided on the diagonal), 
One side red and white (divided diagonally). 
The character of the colors is indicated on the pages of 
designs printed in this monograph. A slight difficulty, 
experienced by possibly one or two subjects out of every 
one hundred, was a just perceptible but nevertheless dis- 
concerting difference in shade between the blue and yel- 
low on the full faces and the same colors on the diagonal 
sides. This can be remedied in the later standardization 
of the test material. One set of six blocks will last 
through the examination of from four to five hundred 
64 THE TEST MATERIAL 
65 
children without showing much wear and tear. After 
that the cubes can be repainted without difficulty. 
It is interesting to watch the response of children and 
even adults when they are given colored cubes to handle. 
There is no doubt that an appeal exists which touches the 
roots of some very fundamental original tendencies. Of 
all the subjects tested, not one has manifested any 
absence of a desire to combine these cubes in some 
fashion. The experimenter needs only to direct this 
natural interest toward a specific end and then apply a 
scientific measuring technique to evaluate the results. 
(b) The Designs 
On pages 66-67 are presented the designs utilized 
in this study. The Roman numerals refer to the num- 
bers given the designs during the time when the tests 
were being standardized. The Arabic numerals designate 
the final numbering of each design. The original number 
was thirty-five, but fifteen were eliminated in a few of 
the early preliminary testings. The designs are graded 
in difficulty which increases by modifying the designs 
at various stages in the following manner: 
1. By the use of the full colors; 
2. By the use of few diagonaled sides; 
3. By the use of all diagonaled sides; 
4. By turning the design on one of its corners; 
5. By eliminating the outside boundary line; 
6. By increasing the number of blocks to be used; 
7. By increasing dissymmetry in design; 
8. By decreasing the number of different colors used 
in each design. Design 1 
Design 7 
Design 11 
Design 2 
Design 3 
Design 3 
Design 12 
Design 4 
Design 9 
Design 13 
Design 5 
red 
Design 10 
white 
Courtesy Psychological 
Review Co. 
yellow 
Design 6 
■blue THE TEST MATERIAL 
67 
Design 14 
Design 16 
Design 15 
Design 17 
red 
Courtesy 
Psychological 
Review Co. 
White 
yellow 
Trial Design A 
blue 68 
INTELLIGENCE MEASUREMENT 
To perform the test, utilizing the twenty designs, one 
averaged about an hour or an hour and a half. In the 
final revision three designs have been eliminated, leaving 
seventeen, thus decreasing somewhat the time necessary 
to apply the tests with no significant decrease of relia- 
bility. The criteria for rejection were based on correla- 
tions with those arrays of evidence presuming to yield 
an index of intelligence, such as is obtained through 
the use of the Binet scale, and also upon the basis of the 
diagnostic value of each design, determined by the pro- 
gress of its curve with increasing chronological age. The 
results at present indicate that the block designs are as 
good as any single test in the Binet scale (though better, 
perhaps, in the sense of diagnostic value), as good as the 
Trabue Language Completion Tests, or any other similar 
single type test, whether involving the use of language 
or whether mere performance. 
The designs, appropriately colored, are printed on 
medium-thick, white, semi-gloss cardboard. The di- 
mensions of the card are three by four inches. The 
printed designs, placed in the center of the card, are one- 
fourth the size of the actual designs when the cubes are 
used. In other words, the face of a cube represented on 
the designs is only one-half of an inch on each of its sides. 
Thus design No. i is one inch square, design No. io is 
one and a half inches square, and design No. 14 is two 
inches square. 
The writer has found it of assistance to place in the 
lower right-hand corner the time limit for each design. 
These values follow: THE TEST MATERIAL 
69 
Time Limits for Each Design 
TABLE XXIV 
Design 
(Number) 
Time Limit 
(Minutes) 
Design 
(Number) 
Time Limit 
(Minutes) 
Design 
(Number) 
Time Limit 
(Minutes) 
I 
7 • • 
2 
13 • • 
3'A 
2 
i Vi 
8 . . 
2 
14 • • 
s'A 
3 • • 
i A 
9 • • 
2 
IS • • 
4 
4 • • 
2 
IO . 
3 
16 
4 
5 • • 
2 
ii 
3^ 
17 .. . 
4 
6 . . 
2 
12 
3^ 
The time limit set for each design is about one minute 
longer than the time within which a correct response 
may reasonably be expected. 
It may be of interest to remark that if the full limit 
is allowed on each test the working-time totals only 
forty-five minutes for all of the seventeen designs. With 
practice an examination should average about thirty 
to forty minutes. In some cases it may take only fifteen 
or twenty minutes, in others perhaps an hour. 
(c) The Score Card and the Method of Scoring 
In the succeeding table are presented the score values 
of each of the seventeen designs and the number of score 
points to be deducted if a design is successfully com- 
pleted with excess time and with excess moves. 
To clarify the table, one or two illustrations will be 
utilized. For example, design No. 2 has a score value 
of 5. This full amount is attained if a reagent completes 
the design successfully in less than 31 seconds and with 
less than 7 moves. If 31 or more seconds are utilized, 
one point is deducted from the score, and if 7 or more 70 
INTELLIGENCE MEASUREMENT 
moves are made an additional point is deducted. Take 
again design No. 13, which has a score value of 9. This 
full amount is attained if the subject completes the de- 
sign successfully in less than 2 minutes and 21 seconds, 
and with less than 31 moves. If completed between 
TABLE XXV 
Score Card 
Design 
No. 
Score 
Value 
Points 
Points to be Subtracted 
Excess Time 
Excess Moves 
1 Point 
i Point 
2 Points 
I 
3 
21" and over 
6 and over 
2 
5 
31" and over 
7 and over 
3 
6 
21"to 35" 
36 " and over 
8 and over 
4 
7 
31" to 1' 0" 
i' 1" and over 
10 and over 
5 
7 
36" to 1' 5" 
1' 6" and over 
11 and over 
6 
7 
36" to 1' 0" 
i' 1 "and over 
12 and over 
7 
7 
41" to i'io" 
1'11" and over 
11 and over 
8 
8 
41"to 55" 
56" and over 
10 and over 
9 
9 
56" to i'io" 
1'11" and over 
15 and over 
IO 
9 
I'56" to 2'io" 
2'n" and over 
22 and over 
ii 
8 
I'46" to 2'3o" 
2'3i" and over 
19 and over 
12 
9 
2'26" to 2'4o" 
2'41" and over 
30 and over 
13 
9 
2'2l" tO 2'33" 
2'34" and over 
31 and over 
14 
9 
2'26" tO 2'4o" 
2'41" and over 
32 and over 
IS 
9 
2'4l" to 3' 0" 
3' 1 "and over 
32 and over 
16 
IO 
2'4l"t03' 5" 
3' 6" and over 
31 and over 
17 
ii 
2'4l"tO 2'55" 
2'56" and over 
30 and over 
Maximum score —133 points. 
2 minutes 21 seconds and 2 minutes 33 seconds, one 
point is deducted; and if 2 minutes 34 seconds or more 
are spent on the problem, two points are deducted. 
And if 31 or more moves are made an additional point is 
deducted from the score value of the design. 
The scoring of a performance is a very simple matter. 
This will be self-evident from the following examples: THE TEST MATERIAL 
71 
Example one: Design No. 7 successfully completed 
in 1 minute and 23 seconds and at the end of 9 moves. 
Score 7, for successful completion, less 2 points for 
excess time. Final score 5. 
Example two: Design No. 10 successfully completed 
in 1 minute 48 seconds, and after 19 moves. Score 9, 
for successful completion. No deductions for excess time 
or excess moves. Final score, 9. 
Example three: Design No. 16, successfully completed 
in 3 minutes 27 seconds, and after 48 moves. Score 10, 
for successful completion. Deduct 2 points for excess 
time, and one point for excess moves. Final score 7. 
It may be worth remarking that successful perform- 
ance, speed, and what may be termed accuracy are 
combined in the final score. Successful performance 
receives greatest weight, speed next, and accuracy next. 
The weight ratio as explained elsewhere in the mono- 
graph is roughly 4:2:1. This ratio has been empi- 
rically determined. The prevalent opinion that speed 
and accuracy cannot be combined in one score, does 
not hold with the Block-design Tests. The writer felt 
that success, speed, and accuracy each had its own 
diagnostic importance, and in order to make the tests 
most effective all should, and must, be taken into ac- 
count in the final score summation. For a more detailed 
discussion of this matter see a later section. 
(1d) The Norms 
The procedure involved in obtaining norms for the 
different designs was quite a complicated one, requiring 
a great deal of careful statistical work. In this effort 72 
INTELLIGENCE MEASUREMENT 
the writer utilized the currently accepted standardization 
methods, with but slight modification. An explanation 
of the general procedure utilized, together with a de- 
scription of various methods of checking the results has 
Mental Age Equivalents 
of Score Points 
GRAPH 6 
SCORE POINTS 
Courtesy Psychological Review Co. 
AGE 
been left for a later chapter. Suffice it to say that the 
score points mentioned in Table XXV are to be inter- 
preted in the same light as those of Buckingham in his 
standardization of his Spelling Tests, of Trabue in his 
standardization of his Language-Completion Tests, and THE TEST MATERIAL 
73 
of Woody in his standardization of his Arithmetic Tests. 
In this section the final results, merely, will be presented. 
Graph 6 is the curve indicating the scores to be 
expected at the various ages from 3 years to 19 years and 
6 months. This curve has been smoothed but slightly 
TABLE XXVI 
Mental Age Equivalents of Score Values 
Score 
Points 
Mental 
Age 
Score 
Points 
Mental 
Age 
Score 
Points 
Mental 
Age 
Score 
Points 
Mental 
Age 
o 
5~ 3 
or -below 
33 
10- 9 
66 
13- 5 
99 
15- 9 
i 
5“ 7 
34 
10-10 
67 
13- 6 
100 
15-10 
2 
6- 0 
35 
10-11 
68 
13- 6 
101 
15-n 
3 
6- 3 
36 
11- 0 
69 
13- 7 
102 
16- 9 
4 
6- 6 
37 
11- 1 
70 
13- 8 
103 
16- 1 
5 
6- 9 
38 
11- 2 
7i 
13- 9 
104 
16- 2 
6 
7- 0 
39 
11- 3 
72 
13- 9 
i°5 
16- 3 
7 
7- 3 
40 
11- 4 
73 
13-10 
106 
16- 4 
8 
7- 6 
4i 
11- 5 
74 
13-n 
107 
16- s 
9 
7- 8 
42 
11- 6 
75 
14- 0 
108 
16- 7 
IO 
7-10 
43 
11- 7 
76 
14- 1 
109 
16- 8 
ii 
8- 0 
44 
11- 8 
77 
14- 1 
no 
16- 9 
12 
8- 2 
45 
11- 9 
78 
14- 2 
III 
16-10 
13 
8- 4 
46 
11-10 
79 
14- 3 
112 
16-11 
14 
8- 5 
47 
ii-ii 
80 
14- 4 
113 
17- 1 
IS 
8- 7 
48 
12-0 
81 
14- 5 
114 
17- 2 
16 
8- 9 
49 
12- 1 
82 
14- 6 
ns 
17- 4 
17 
8-10 
50 
12- 2 
83 
14- 7 
116 
17- 5 
18 
9- 0 
5i 
12- 3 
84 
14- 7 
117 
17- 6 
19 
9- 1 
52 
12- 4 
85 
14- 8 
118 
17- 8 
20 
9~ 3 
53 
12- 5 
86 
14- 9 
119 
17- 9 
21 
9- 4 
54 
12-6 
87 
14-10 
120 
17-10 
22 
9- 6 
55 
12- 7 
88 
14-11 
121 
18- 0 
23 
9~ 8 
56 
12- 8 
89 
15- 0 
122 
18- 2 
24 
9“ 9 
57 
12- 9 
90 
15- 0 
123 
18- 3 
25 
9-11 
58 
12-10 
9i 
15- 1 
124 
18- S 
26 
10- 1 
59 
12-10 
92 
15- 2 
125 
18- 7 
27 
10- 2 
60 
12-11 
93 
15- 3 
126 
18- 9 
28 
10- 3 
61 
13- 0 
94 
15- 4 
127 
18-n 
29 
10- 4 
62 
13- 1 
95 
15- 5 
128 
19- 1 
30 
10- s 
63 
13- 2 
96 
15- 6 
129 
19- 3 
31 
10- 7 
64 
13- 3 
97 
15- 7 
130 
19- 7 
32 
10- 8 
65 
13- 4 
98 
15- 8 
131 
19-n 74 
INTELLIGENCE MEASUREMENT 
within the range of ages below io, though rather con- 
siderably from 15 to 19. This was necessarily the result 
of a deficiency in the number of cases at the higher ages. 
The median score is represented by a circlet placed above 
each age. 
In Table XXVI are presented the mental age equiv- 
alents of each score from 1 (mental age 5 years and 7 
months) to 131 (mental age 19 years and n months). 
These values were derived from Graph 6. 
2. THE DIRECTIONS EOR APPLYING THE TESTS 
Preliminaries: Seat the S comfortably at a table, 
noting that his visual angle when working with the 
tests is not less than 45 degrees. Be sure that no designs 
are visible in your preliminary instructions, nor more 
than a single design at any one time. The blocks which 
are not being utilized should be kept in a box, apart, 
so that they are either invisible to the S, or if visible, 
the blocks should be arranged so that the top sides are 
all of the same color. 
Method: Part i. For Subjects Who Can Understand 
Spoken Language 
(Section A) Take a block. (Instructions to S are 
placed in quotation marks. For design i four blocks 
will have been removed from the box.) “Here are some 
blocks — give me the name of the color on this side.” 
Sides with the full colors are presented first. Place your 
finger on the side designated. After S has responded, 
turn to another side. “And what is the color on this 
side?” — “Now the color here?” — “And what is the THE TEST MATERIAL 
75 
color here? ” — If S has succeeded in naming the colors 
correctly, proceed with the experiment. (If he has 
failed, further instructions are given below, in Part 2.) 
Then the experimenter explains: “Now on this side we 
have blue and yellow (point), and on this side red and 
white (point). And all the blocks are painted in the 
same way.” 
(Section B) “What you are to do is this: Take these 
blocks” (shuffle them so that when finally placed before 
S, no more than one quarter of the blocks have topside 
colors which are present in the design, the separate 
blocks being placed apart, flat on table, and not piled 
one on top of another), “pick out the right colors, put 
them together, and make them look, on top, just like 
this” (point to design 1). Give no further hints or sug- 
gestions if the directions have been understood. Caution: 
Be sure that all the blocks are thoroughly shuffled before 
the design is presented. The purpose is to eliminate 
the possibility of studying the design before being ready 
to begin work with the cubes. 
(Section C) If S has not understood what is meant, 
E may perform trial design (A)x slowly, using pantomime 
freely, S watching closely, after which S is requested to 
repeat the operation. This may be repeated any num- 
ber of times until S understands. When he does, proceed 
with the designs in order, beginning at (Section B), and 
continuing with (Section D). 
1 Trial design (A) is represented on the pages with the other designs 
and is used only when under the provisions of Section C further pre- 
liminary explanation is necessary. Trial design A is a four-block design, 
two full white sides above, two full yellow sides below. 76 
INTELLIGENCE MEASUREMENT 
(Section D) After the first design has been com- 
pleted or failed, the blocks are again shuffled, observing 
the cautions in (Section B), and the S is told again to 
“take these blocks, pick out the right colors, put them 
together, and make them look on top just like this.” 
(Point to design No. 2.) These instructions remain the 
same for all the designs. The S is not told at any time 
the number of the blocks he is to use. 
Record: Both time and moves are recorded. A move 
is counted when a block is given its initial position on 
the table. Each separate and distinct change in the 
position of a block is counted a move. Sometimes a 
child will make three or four changes in the position of 
a cube, the topside remaining the same color (especially 
true of diagonal sides, e.g. red — white). But each 
change in position is counted a separate move. If 
success is not attained within the time limit, no credit 
is assigned. The time limits are indicated on the design 
cards. 
The whole test is not regarded as complete unless 
there are, ordinarily, at least five consecutive" failures 
on designs after the last success, and where doubt exists 
as to the inability in the later designs, give as many 
designs beyond the last success as is deemed wise. 
Part 2. For Subjects Who Do Not Know the Names 
of the Colors 
Take all the blocks out of the box and place on the 
table so that the single-colored faces are all on the top 
side of the cubes. Have an equal number of reds, 
yellows, blues, and whites. Point to a red-topped THE TEST MATERIAL 
77 
block and ask the child to point to all the blocks that 
have the same color on top. Do the same for the other 
three colors. If the child can distinguish the colors, 
proceed with the test at Section B. 
Part 3. For Subjects Who Cannot Understand Spoken 
Language 
By means of gestures and pantomime go through the 
procedure in Part 2. If S can distinguish the colors, 
proceed with Section C, and through the various designs. 
The method of recording remains the same. CHAPTER III 
Standardization Technique 
1. The Year-Scale Method 
2. The Percentile Method 
3. The Point-Scale Method 
4. The P. E. or Linear Projection Method 
The past few years have seen such a rapid develop- 
ment in the technique of scale-making for the purpose 
of measuring mental capacities and pedagogical progress 
that any reasonable discussion of this branch of psycho- 
logical and educational statistics would be entirely too 
extensive and consequently out of place in this mono- 
graph. However, there are four distinct methods which 
have had more or less ready application and it is to 
these alone that the writer will confine his discussion. 
I. THE YEAR-SCALE METHOD 
This is the method which has been utilized in standard- 
izing the various versions of Binet-Simon Measuring 
Scale for Intelligence. After tests have been selected 
and applied to large numbers of unselected children of 
different ages, each test in the scale is considered sepa- 
rately and the percentage passing the test at the various 
life ages is determined. The fundamental assumption 
is that if a test is a measure of intelligence development, 
there will be an increase in the per cent passing the test 
with increase of age. (Increases due to differences of 
78 STANDARDIZATION TECHNIQUE 
79 
maturity or experience apart from intelligence, are, of 
course, ruled out.) A criterion which Binet used is to 
locate a test at a specific age if about 75 per cent of the 
children at that age pass the test. Usually the per- 
centage fluctuates between 60 and 85 or 90 per cent. 
There are a number of distinct objections to this arbi- 
trary procedure, which have been pointed out by A. S. 
Otis 1 and T. L. Kelley.2 A test, however, is generally 
regarded as most useful which shows the most rapid 
advance with age, and which is placed in the year level 
at which about 75 per cent begin to pass. Although 
the writer recognizes the superiority of the 50 per cent 
criterion, nevertheless to make the results of our year- 
scale comparable with the Binet, we have continued the 
use of the 75 per cent criterion. To have used the 50 per 
cent criterion would have made the tests more difficult, 
because less age credit would have been assigned the 
successful completion of a design in the series. 
The procedure in the use of this performance scale is 
the same as that for the regular Binet, except that for 
those unable to speak or understand verbal directions, 
gestures and imitation are the means utilized to present 
the problem. It is necessary, therefore, that the trial 
design should be utilized before entering upon the exami- 
nation proper. For detailed instructions, however, the 
reader is referred to an earlier section (Part B, Chap. II, 
Section 2). 
1 “ Some Logical Aspects of the Binet Scale,” Psychol. Rev., 1916, 23: 
129-152, 165-179. 
2 “ Further Logical Aspects of the Binet Scale,” Psychol. Rev., 1916, 
23: 407-411. 80 
INTELLIGENCE MEASUREMENT' 
2. THE PERCENTILE METHOD 
Because of some important statistical fallacies under- 
lying this method as now utilized — fallacies which only 
one or two have as yet pointed out1 — we shall devote 
a rather extended discussion to this procedure. 
The developments in the field of differential psychology 
have doomed forever that much popular slogan: “We 
are all born free and equal.” The scientific study and 
analysis of individual differences has amply demonstrated 
that a given individual may rank first in one trait, last in 
another, and somewhere in between in another, and that 
this combination of ranks may be different for each 
individual. Thus in a group of one hundred, person A 
may rank ist in intelligence, ioth in motor coordination, 
85th in general reaction time, 100th in height, and so 
on. Person B may rank 12th in intelligence, 57th in 
motor coordination, 3d in general reaction time, 7th in 
height, and so on. Person C may present an entirely 
different array of traits. This principle has been utilized 
by the Russian psychologist Rossolimo, for the measure- 
ment and the graphic representation of developed mental 
processes, which he designates the “ Psychological Profile 
Method.”2 
1 See J. B. Miner: “Deficiency and Delinquency.” Warwick and 
York, 1918; 3SS pp. See esp. pp. 275-279. 
S. C. Kohs: “Percentile Norms for Scaling Data,” J. of Educ. Psychol., 
1918, 9: 101-102. 
2 G. Rossolimo: “Die psychologischen Profile. Zur Methodik der 
quantitativen Untersuchung der psychischen Vorgange in normalen und 
pathologischen Fallen. Eine experimentell-psychologische Skizze.” Klin, 
f. psych, u. nerv. Krankh., 1911, 6: 249-294. — English translation: B. STANDARDIZATION TECHNIQUE 
81 
Traits may be compared either for their quantitative 
or qualitative differences. At the present time we have 
developed a finer methodology for the former than for 
the latter. Thus our comparisons of one individual with 
another, or of one individual with a group, are largely 
comparisons of a quantitative nature. 
Theoretical Considerations: 
The percentile method or the percentile system is a 
method for determining or locating the rank or the posi- 
tion of an individual within a group. All the members 
of a group are ranked with respect to a given trait, the 
lowest member at one end and the highest member at 
the other. This arrangement is illustrated in Graph 6 A, 
and the curve therefor has been called the “ogive” by 
Galton. Assume, for purposes of illustration, that we 
are studying the heights of 58 four-year-old boys. We 
arrange these measures in increasing order, the lowest is 
866 mm., and the highest is 1165 mm. (See Smedley’s 
Tables.) The curve connecting the separate heights of 
the 58 children is the ogive. Now if we run along the 
base from the 1st to the 6th case, the 6th case represents 
the 10th per cent case, and the height at this point is 
called the 10th percentile (964 mm.). Twice that dis- 
tance along the base brings us to the 12th case, and the 
height at this point is called the 20th percentile (968 
mm.). And three times the original distance brings us 
Parker: “The Psychograph of Rossolimo,” Amer. J. of Insanity, 1916, 
73: 273-293. 
See also Titchener Memorial Volume. 
For criticism see Ed. Claparede: “Profiles psychologiques gradues 
d’aprSs l’ordination des sujets.” Archives de Psychol., 1916, 16: 70-81. 82 
INTELLIGENCE MEASUREMENT 
to case 17, the height at this point, 997 mm., representing 
the 30th percentile. And so on, for the 40th, 50th, to 
the 100th percentile. 
On the basis of this arrangement we may compare 
either two or more individuals for relative positions 
within the group, or we may compare the rank of one 
GRAPH 6A 
The Ogive 
Millimeters 
Heights of 58 four-year-old Boys 
arranged in order from lowest to 
highest. ( After Smedley.) 
in the light of the ranks of the other members of the 
group. 
With this orientation let us turn to the question of 
tests. The last five years have seen a rapid multiplica- 
tion of graded tests and scales, some intellectual, some 
pedagogical, some involving performance as distinct 
fom those tests involving the use of language symbols. 
With this growth has come the frequent suggestion that 
tests should be evaluated and interpreted in terms of STANDARDIZATION TECHNIQUE 
83 
percentile norms, and that we utilize the percentile 
method for grading and comparing individuals. In fact, 
four of the most extensive studies made within recent 
years, by Smedley, by Woolley and Fischer, by Doll, 
and by Pintner and Paterson, have made use of just this 
principle.1 
In the last instance particularly, has the value of the 
percentile method been emphasized: 
“The percentile method seems to offer the best possi- 
bilities for future work. The percentile divisions used 
can be made as small as the delicacy of the tests will 
warrant. This method is especially desirable because 
it permits us to compare an individual’s performance 
with the performance of other individuals of the same 
age. It would seem at present, however, to require, for 
purpose of standardization, a very great number of un- 
selected individuals at each age.” (p. 212.) 
A fundamental fallacy, however, underlies the present 
practice in the construction and the use of percentiles. 
The quite recent report that the percentile method is 
1 F. W. Smedley: “Report of the Department of Child-Study and 
Pedagogic Investigation. 1900-1901.” Child Study Report No. 3. 
Chicago Public Schools, 1902. 
H. T. Woolley and C. R. Fischer: “Mental and Physical Measure- 
ments of Working Children.” Psychol. Monogr., 1914, Vol. 18, No. 1. 
247 p. 
H. T. Woolley: “A New Scale of Mental and Physical Measurements 
for Adolescents and Some of its Uses.” J. of Educ. Psychol., 1915, 
6: 521-550. 
E. A. Doll: “Anthropometry as an Aid to Mental Diagnosis.” Re- 
search Publication No. 8, Vineland, N. J. Training School, Feb. 19x6. 
91 p. 
R. Pintner and D. G. Paterson: “A Scale of Performance Tests.” 
New York, Appleton & Co., 19x7. 218 p. 84 
INTELLIGENCE MEASUREMENT 
not meeting expectations cannot help but reinforce the 
writer’s opinion that the source of the trouble lies perhaps 
in the weaknesses of our present technique. “The corre- 
lation of the percentile method with the Yerkes-B ridges 
is the lowest of the four methods and at present does not 
seem of much value. Possibly this is due to the compara- 
tively small number of cases tested at each age.”1 
Among the important cautions to be observed in scale- 
making are two: First, be certain of the zero point; 
second, be sure that the units of the scale are equal. 
This latter is of vital importance where scores of various 
tests in a scale are totaled or averaged, and then eval- 
uated in terms of percentile norms. All percentile 
differences should have a constant, not a variable 
connotation, and each percentile value should repre- 
sent a definite and constant position on the normal 
frequency curve. This is far from true with our present 
technique. 
Perhaps the chief and most destructive criticism of 
the present percentile method for scale construction is 
this: Equal percentile differences on the base of our orgive 
do not represent equal differences in ability between 
individuals. No one will argue that the amount of mental 
ability represented between percentiles io and o, equals 
that between 20 and 10, equals that between 30 and 20, 
equals that between 40 and 30, equals that between 50 
and 40, and so on. In fact, we know from the psychology 
of individual differences that the differences in ability 
1Pintner, R., and Reamer, Jeanette C.: “Children Tested by the 
Point Scale and the Performance Scale.” Psychol. Clinic, 19x7,11: 142- 
151. p. 150. STANDARDIZATION TECHNIQUE 
85 
of adjacent cases among average, or mediocre, or most 
typical individuals is very small indeed, whereas the 
differences in ability of adjacent cases among extreme 
variates is, on the contrary, very great. 
For a clearer elucidation of this problem we must turn 
to the actual normal probability curve. 
The first clear explanation of the meaning and sig- 
nificance of the normal frequency curve came through 
the medium of an astronomer, Laplace — a mathema- 
tician, Gauss — and an anthropologist, Quetelet. The 
first two were engaged in efforts to determine the laws 
underlying the occurrence of purely accidental events, 
the last devoted a good part of his lifetime toward finding 
the “average man,” lost somewhere midst a confusion 
of diversity. (It might not be amiss to mention here 
that just in that realm where one would least expect the 
operation of fixed laws, the realm of chance and accident, 
we actually do find a clear-cut subserviency to funda- 
mental laws that definitely determine the frequency with 
which events occur.) 
If we should toss eight pennies (perfectly symmetrical) 
some few million times, then once out of every 256 times 
they would all come down heads; 8 times out of every 
256 times they would come down 7 heads and 1 tail; 
28 times out of 256 they would come down 6 heads and 
2 tails; 56 out of 256, 5 heads and 3 tails; 70 out of 256, 
4 heads and 4 tails; and once out of every 256 times they 
would all come down tails (theoretically). If we plotted 
these data as a column diagram we would obtain Graph 7. 
Or plotted as a smooth frequency curve we could graphi- 
cally represent the above facts as Graph 8. 86 
INTELLIGENCE MEASUREMENT 
GRAPH 7 
Theoretical Frequency 
8 Pennies tossed 258 times 
Frequency 
No. of Heads 
GRAPH 8 
Theoretical Frequency 
8 Pennies Tossed 258 Times 
Frequency 
No. of Heads STANDARDIZATION TECHNIQUE 
87 
Laplace and also Gauss derived a formula for the 
theoretical normal probability curve which is given in 
Graph 9. 
GRAPH 9 
The Normal Curve 
Sum of Ordinates: 
125.3318 
Curve Equation: 
Interval: 0.2 Units 
y=e~r 
Frequency 
(After Yule: 
‘‘Theory of Statistics,” 
1912. - See Table 
p. 303) 
Area: 10V 
or 25.06 + 
Units of Measure 
The probable occurrence of the different physical and 
mental traits possessed by human beings also distribute 
themselves, in many instances, in this bell-shaped 
fashion.1 Thus, in Graphs io, n, and 12, are represented 
1 In this connection the writer wishes to call attention to an excellent 
article by E. G. Boring: “The Logic of the Normal Law of Error in 
Mental Measurement,” Amer. J. Psychol., 1920, 31: 1-33, dealing with 88 
INTELLIGENCE MEASUREMENT 
the frequencies of the heights of fifteen-year-old girls, 
fifth-grade ability in arithmetic and the differences in 
the intellectual ability of 905 unselected children ex- 
amined with the Stanford-Binet Scale. 
GRAPH 10 
Heights of 158 
15-year-old Girls 
Frequency 
Centimeters 
(from figures by B.T. Baldwin, p.15, 
'Physical Growth and School Progress”, 19U). 
For the purpose which we have set before ourselves 
at the beginning of this discussion, we cannot separate 
the normal probability curve from the ogive. Thus, for 
a given table of data, Table XXVII, Graph 13 is the 
ogive, and Graph 14 the frequency curve, both being 
plotted on the same coordinates. 
this particular matter, in which he points out the fallacy of a too general 
application of the “ normal curve ” to measurements of mental 
phenomena. STANDARDIZATION TECHNIQUE 
89 
GRAPH 11 
No. of Addition Problems 
Solved by 687 Pupils 
in Grade 5 
GRAPH 12 
905 Children 
Intelligence Distribution 
Frequency 
Frequency 
Problems 
Quotients 
(from figures by C. Woody, 
“measurements of Some Achievements 
in Arithmetic,” 1916, p.27). 
{from figures by Terman: “Measurement 
of Intelligence," 1916, p.66). 
TABLE XXVII 
Starch Arithmetic Scale A * 
Scores in a 7th Grade 
Score 
s 
6 
7 
8 
9 
IO 
II 
12 
X3 
14 
is | Total 
Frequency. . 
i 
2 
X 
s 
9 
6 
S 
2 
I 
2 
1 I 35 
♦From Fig. 19, Starch: “Educational Psychology,” 1920, p. 35. 90 
INTELLIGENCE MEASUREMENT 
In these diagrams items are numbered and their 
position on the ogive and on the column diagram may be 
clearly followed. It is of great importance to keep this 
relationship in mind, for in the confusion of the two 
curves lies the fallacy at the bottom of pretty nearly all 
the work in percentile scale making. 
Median: 8.9 
Qi: 7.9 
Q8: 10.5 
Q: 2.6 
Total Range: 3.8Q 
GRAPH 13 
GRAPH 14 
Arithmetic Score 
Arithmetic Score 
Frequency 
Cases in Consecutive Order 
In Graphs 13 and 14 the crosses on the base of the ogive 
represent equal percentile (decile) differences between 
measures. These may be followed through to the base 
of frequency curve. On the other hand, the arrows 
represent equal units, decile or percentile, on the base 
of the frequency curve, these then are referred back to STANDARDIZATION TECHNIQUE 
91 
ogive base. The marked lack of equality between the 
corresponding divisions is quite apparent. It should 
be emphasized that equal distances along the base of 
our ogive cannot, except under a combination of ex- 
tremely unusual circumstances, yield equal distances 
along the base of our frequency curve. But scale values 
must be equal if we are going to equate, add, subtract, 
multiply, divide, or compare percentile scores. It is 
equally true that equal units along the base of our 
frequency curve will not yield corresponding equal units 
on the base of our ogive. 
Another fact which requires mention is this: If we are 
going to determine the ability of a given individual, 
judged by reactions to more than one test, and utilizing 
the percentile method for determining his absolute score, 
then our percentile scale must be made up of score-values 
obtained from the base of our normal frequency curve, 
and not from the base of our ogive. The reason for this 
will be apparent from a study of the normal frequency 
distribution. It is evident that equal distances along 
the base of our normal curve represent equal differences 
in ability. This, unfortunately, is not true for the ogive. 
Consequently, if we take any percentile table in the 
current psychological or educational literature, ability 
represented by the difference between the ioth and 20th 
percentiles is far from equal to the ability represented by 
the difference between the 20th and 30th percentiles. 
But this would have been the case if the percentile scale 
had been laid off on the base of the normal frequency 
curve. These differences in ability represented by differ- 
ences in consecutive percentiles must be equal, if we are 92 
INTELLIGENCE MEASUREMENT 
going to add, subtract, multiply, divide, equate, com- 
pare, percentile scores. 
To sum up the remarks above: Percentile scales should 
be so constructed that the various steps or units represent 
equal differences in ability. For devising a percantile 
scale, the normal frequency curve should be utilized 
and not the ogive as the base for operations. 
Practical Considerations 
In the following section will be indicated the wide 
divergence of percentile-scale values obtained by present 
methods, and percentile-scale values obtained by sug- 
gested methods. 
Example One 
Smedley, in Child-Study Report No. 3 (1902), Chicago 
Public Schools, gives the following data for Grip of Left 
Hand, Fourteen-year-old Boys (p. 17): 
TABLE XXVIII 
Percentiles 
IOO 
go 
80 
70 
60 
5° 
40 
30 
20 
IO 
O 
L. Hand Grip 
SI 
36 
32 
30 
28 
26 
25 
23 
21 
19 
14 
This table is merely chosen as typical. Any other might 
have been taken in his report to illustrate the con- 
ditions. 
These percentiles were obtained in the following 
manner: 
“The individual cards on which the measurements 
were recorded when the child was tested were arranged 
according to the size of the pupils in each measurement, 
grouped separately for each age in years. The minimum STANDARDIZATION TECHNIQUE 
93 
measurement in each group gave the zero percentile for 
that group. To determine the ten percentile for that 
group, ten per cent of the number of cards was removed, 
beginning at the minimal end, and the highest measure- 
ment on the cards so removed was recorded as the desired 
ten percentile. Similarly the other percentiles were 
determined, the maximum measurement being recorded 
as the one hundred percentile.” (P. 13.) 
It is evident that the ogive rather than the normal 
frequency curve was used to determine percentile values. 
Since 359 cases were used by Smedley, it is a simple 
matter to reconstruct his initial table, which is here 
presented: 
TABLE XXVIIIA 
Left Hand Grip of 359 Boys 
No. or 
Cases 
L. Hand 
Grip 
No. OF 
Cases 
L. Hand 
Grip 
No. OF 
Cases 
L. Hand 
Grip 
No. OF 
Cases 
L. Hand 
Grip 
3 
14 
22 
24 
9 
34 
2 
44 
4 
IS 
24 
25 
10 
35 
0 
45 
6 
16 
21 
26 
8 
36 
0 
46 
8 
17 
15 
27 
8 
37 
1 
47 
9 
18 
23 
28 
6 
38 
0 
48 
ii 
19 
19 
29 
7 
39 
0 
49 
16 
20 
16 
30 
5 
40 
0 
5° 
IQ 
21 
17 
31 
2 
4i 
I 
51 
25 
22 
12 
32 
0 
42 
20 
23 
IO 
33 
0 
43 
The point we have attempted to emphasize in this 
discussion is that in determining percentile differences 
among individuals, the curve of reference should be the 
frequency curve and not the ogive. The table given by 
Smedley is based on differences obtained from equal ogival 
distances. We herewith outline a procedure and present 
a table of percentile differences based on equal distances 94 
INTELLIGENCE MEASUREMENT 
along the base line of the frequency curve, given in terms 
of standard deviation units or quartile deviation (P. E.) 
units. To find a score, then, corresponding to a given 
percentile, o, or io, or 20, and so on, it is merely neces- 
sary to determine the case which falls nearest that 
percentile, then by interpolation to obtain the refined 
score of the case. That value, then, is the score corres- 
ponding to the desired percentile. 
To illustrate: In the above example the range in score 
is from 14.17 to 51.50 (scores refined by interpolation), 
or a difference of 37.33 Kg. The percentiles then, in 
terms of this range, are as follows: 
TABLE XXIX 
Range Divided into Percentiles 
Percentile 
Range Value 
Percentile 
Range Value 
o 
0.000 
60 
22.398 
IO 
3-733 
70 
26.131 
20 
7.466 
80 
29.864 
30 
11.199 
90 
33-597 
40 
I4-932 
100 
37-33° 
So 
18.665 
Now, adding these separate values to the initial score, 
14.17, the final step in the formation of the percentile 
table is taken: 
TABLE XXX 
Percentile 
Score 
Percentile 
Score 
o 
14.170 
60 
36.568 
IO 
17.903 
70 
40.301 
20 
21.636 
80 
44.034 
30 
2S-369 
90 
47-767 
40 
29.102 
100 
SI-SOO 
So 
32.835 
Score Values op Percentiles STANDARDIZATION TECHNIQUE 
95 
For purposes of comparison let us place in parallel 
position the two percentile tables, one obtained by the 
ogive method, the other by the frequency method, and 
then compare the scores. 
TABLE XXXI 
The Two Score Values Corresponding to the Same Percentile 
Compared 
Percentile 
Score 
Percentile 
Score 
Ogive 
Method 
Frequency 
Method 
Ogive 
Method 
Frequency 
Method 
o 
14 
14.170 
60 
28 
36.568 
IO 
19 
17.903 
70 
30 
40.301 
20 
21 
21.636 
80 
32 
44.034 
3° 
23 
25-369 
90 
36 
47.767 
40 
25 
29.102 
100 
Si 
5i-5oo 
SO 
26 
32.835 
Let us also note the cases which locate the various 
percentiles by the two methods: 
TABLE XXXII 
The Cases Which Locate the Percentile by the Two Methods 
Percentile 
Case Number 
Percentile 
Case Number 
Ogive 
Method 
Frequency 
Method 
Ogive 
Method 
Frequency 
Method 
o 
1 
I 
60 
215 
324 
IO 
36 
21 
70 
251 
35° 
20 
72 
70 
80 
287 
356 
30 
X08 
152 
90 
323 
358 
40 
144 
226 
TOO 
359 
359 
5° 
180 
289 96 
INTELLIGENCE MEASUREMENT 
The significance of this new percentile table1 lies in 
the fact that the difference in ability between the first 
and 21st cases is equal to that between the 21st and 70th, 
the i52d and 226th, the 356th and 358th, or the 358th 
and 359th, and so on. By the ogive method percentiles 
are determined by grouping all of one’s cases into ten 
equally numbered groups. By the frequency method, 
however, the number of cases between percentiles is 
markedly unequal, thus in our table the number of cases 
between consecutive percentiles is 20, 49, 82, 74, 43, 35, 
26, 6, 2, 1. These numbers mean that it takes 2 in- 
dividuals at one portion of the distribution to show as 
much difference in ability as is shown at other portions 
by 83, or at another by 20. 
To make the differences between the two methods 
more apparent, the following two figures (Graphs 15 
1 In the above table for grips, the range in score is from 14.17 to 51.50, 
or 37-33- The arithmetic mean = 26.8 and the standard deviation is 6.46. 
Therefore, each unit of a = 5.78 units of the range • The total 
0.40 
range, then, from the o percentile to any other is equal to the sigma 
corresponding to that percentile multiplied by 5.78. Since sigma = 6.46, 
the sigmas corresponding to the different percentiles are 
TABLE XXXIII 
Sigmas Corresponding to Various Percentiles 
Percentile 
Percentile 
o 
. . . 0.000 
60 . 
• 3-876 
. IO 
. . . 0.646 
70 . . 
• 4-522 
. 20 
. . . 1.292 
80 . . 
. 5.168 
3° 
. . . 1.938 
90 . . 
. 5-814 
40 
. . . 2.584 
100 . . 
. 6.460 
50 
. . . 3-230 
The same, of course, would hold true for Quartile (P. E.) values. STANDARDIZATION TECHNIQUE 
97 
and 16) have been drawn to demonstrate first, the 
differences in score for each of the percentiles, and 
second, the differences in the positions of the individuals 
on the ogive who determine these percentile values. 
GRAPH 15 
Score Difference 
between Two Methods 
Frequency Method 
More J Less 
Percentile 
Kilograms 
The block designs were not given percentile ratings, 
since it is an open question whether this method is an 
improvement either over the Year Scale Method or the 
P. E. Scale Method, both of which have been utilized 
in standardizing the block designs. In fact the per- 
centile method correctly used reduces this standardiza- 98 
INTELLIGENCE MEASUREMENT 
tion method merely to a variation of the linear pro- 
jection method which is discussed later 
GRAPH 16 
Case Locating Percentiles 
Ogive 
Method 
Frequency- 
Method 
Case Number 
3. THE POINT SCALE METHOD 
A valuable discussion of this procedure (used by 
Yerkes, Bridges, and Hardwick) is found in Pintner and 
Paterson’s “A Scale of Performance Tests” to which 
we have had occasion to refer in some earlier sections. 
They very clearly point out its shortcomings. The allot- 
ment of points is absolutely arbitrary. There is no guid- 
ing principle, the method is purely haphazard, and the STANDARDIZATION TECHNIQUE 
99 
only check is the fear of making the mass of points 
cumbersome and unwieldy. Yet, that point scales are 
desirable is evidenced by the careful work of Otis {Jour, 
of Educ. Psychol., igi8). However, none of the point 
scales now in use are free from statistical and psychologi- 
cal objections which are inherent in the method and can 
only be removed by discarding entirely that method of 
standardization. 
4. the p. e. scale method (Linear Projection Method) 
This method has been used extensively at Columbia 
under the direction of Thorndike, and we have adopted 
that methodology with some modifications to a stand- 
ardization of our block designs. The work of Bucking- 
ham in spelling, of Trabue with language scales, and of 
Woody with arithmetic scales, are examples. The chief 
advantage of this method of scaling tests is that each 
test in the series is given a definite weight depending on 
the successes or failures of children at each age. The 
normal probability curve is utilized in determining the 
location of a test on a P. E. Scale, the units of which are 
all equal. Each P. E. Scale has its zero point and each 
test is placed one above the other, depending upon the 
relative difficulty of each. By this means we have been 
able to project each design on a linear scale, each test 
being given a weight corresponding to its position on 
this scale. We were also interested in giving due weight 
to time and moves. For this purpose the times and 
moves for each design were correlated with life age. 
We found a most interesting situation, new to the 
standardization of mental tests. In correlating (a) suc- 100 
INTELLIGENCE MEASUREMENT 
cess or failure in the designs, (b) time, and (c) moves, 
with age, we discovered that with age (a) yielded a 
correlation coefficient of about 80, (b) about 40, and 
(c) about 20! In other words, the respective weights 
for success, time, and moves are 4:2:1. Therefore, 
when we obtained the P. E weights for each design, 
time and moves were each given their respective weights 
depending on the initial value of the design. (See Chap. 
IV.) 
Our final standardization includes, therefore, a year 
scale such as the Binet, and a point scale derived by the 
P. E. scale method. The former may be supplemented 
by series of tests which others have standardized; the 
latter is a short scale complete in itself. 
A word in conclusion. Periodically, statisticians 
engaged in standardizing mental or pedagogical tests 
should take stock of their methods, technique, and 
fundamental assumptions. It is an attitude of mind well 
worth cultivating not to regard as final any set procedure 
by means of which scales are at present derived.. We 
are, unquestionably, inclined too frequently to forget 
that we are carrying over into education and psychology 
highly refined instruments which are of accepted service 
in biology, chemistry, and astronomy, but may not be 
utilized with the same degree of assurance and finesse in 
those sciences involving the human factor, such as 
sociology, psychology, and education. Well-merited 
criticism has already been launched against our blind 
utilization of correlation formulae and of transmutation 
tables, and our incessant worship of the “normal curve” 
fetish. STANDARDIZATION TECHNIQUE 
101 
In this chapter on standardization technique the writer 
is well aware of the many weaknesses in the methods for 
which preference is expressed. Until further progress is 
made, however, we must accept what we have with 
scientific caution, subjecting our procedures, at least, to 
the pragmatic test. CHAPTER IV 
The Standardization of the Block-Design Tests 
1. Introduction 
2. Age Standardization 
(a) Mental Age Norms 
(b) Sex Differences (Mental Age Norms) 
(c) Chronological Age Norms 
(d) Sex Differences (Chronological Age Norms) 
(e) Graphic Presentation of Norms 
(/) Final Year Scale 
3. P. E. Standardization 
(a) Method 
(b) Time and Move Norms 
(c) Result: The P. E. Scale 
4. Final Revision 
(a) Eliminations 
(b) Sex Differences 
(c) Final Norms 
I. INTRODUCTION 
The block-design tests used for standardization con- 
sisted of a series of twenty designs, graduated in difficulty 
(seepp. 66-67) and a set of sixteen specially colored cubes 
which were given to the S with the request to put the 
blocks, four, or nine, or sixteen, together and have the 
design on the tops of the blocks when complete resemble 
102 BLOCK-DESIGN TESTS 
103 
the design as indicated on the card set before him. In 
this manner we had hoped to carry over into performance 
tests Ebbinghaus’s idea of a 11 Kombinations-methode” 
In this we were doing no pioneer work, having been pre- 
ceded by Healy, Knox, and Pintner, but this particular 
combination of method and apparatus is new. The cube 
material is described more in detail in Chapter II, Sec- 
tion i. 
Every one who has been given the test, from the young- 
est child to the adult, has manifested a keen interest in 
manipulating the material. There seems to be some 
fascination about performance tests in general which it 
would indeed be interesting to fathom. The directions 
which were given the S’s have already been stated in full 
elsewhere. (See Chapter II, Section 2.) A record was 
kept of success or failure, enough time being allowed for 
success if that seemed at all possible, and our final results 
show, in fact, that we were too lenient to the extent of 
anywhere from a half-minute to a minute in the case of 
each design. The final time limits have all been reduced 
as a result of our findings. The original time limits for 
the designs, upon which success or failure mentioned in 
the succeeding tables was based, were: 
Designs I-IX, minutes 
Designs X-XI, 3 minutes 
Designs XII-XVII, 4 minutes 
Designs XVUI-XIX, minutes 
Design XX 5 minutes 
Moves and time were both recorded, the latter in whole 
seconds. These two factors, however, did not here 
affect the score: “passed” or ‘Tailed.” For an explana- 104 
INTELLIGENCE MEASUREMENT 
tion of what was considered a move, see previous section 
on directions for applying the tests. 
In the final standardization by the linear projection 
method three designs, XI, XIII, and XVII, were omitted 
and the others were assigned the following Arabic num- 
erals : 
Design I 
now Design 
i 
Design IX 
now 
Design 
7 
ii 
ii 
ii 
ii 
2 
ii 
X 
a 
ii 
IO 
a 
hi 
ii 
ii 
3 
a 
XII 
a 
ii 
ii 
a 
IV 
ii 
ii 
4 
a 
XIV 
a 
a 
14 
a 
V 
ii 
ii 
5 
a 
XV 
a 
a 
12 
a 
VI 
ii 
ii 
6 
a 
XVI 
a 
a 
13 
a 
VII 
ii 
a 
9 
a 
XVIII 
a 
a 
15 
a 
VIII 
ii 
a 
8 
a 
XIX 
a 
a 
l6 
Design XX now Design 17 
2. AGE STANDARDIZATION 
We shall utilize both chronological and mental age 
standards in assigning age values to each of the designs. 
Some may object to the use of mental ages for standard- 
ization, but we have found no valid reasons for rejecting 
this criterion; in fact there are obvious reasons for its 
utilization. First, it serves as a check on an impartial 
selection of children — if they happen to be somewhat 
retarded or accelerated, the mental age difference will 
weight the norms accordingly. Secondly, we wish to 
translate our norms in terms of Binet mental age, so that 
a mental age obtained by this performance scale will 
possess the same significance as a Binet mental age. 
Nevertheless, Pintner and Paterson1 maintain “Why 
should we know the mentality of the children we are 
1 “A Scale of Performance Tests,” p. <?2. BLOCK-DESIGN TESTS 
105 
testing? What we want to arrive at is the ability of 
children of a specific age on a certain test, and we ought 
not to be influenced by other estimates of their ability. 
Our sole endeavor must be to get a fair sampling of cases 
at each age. If we standardize according to mental age 
arrived at by any scale, we are moving in a circle and 
presupposing that our determination of mentality is 
accurate and final.” That we do not move in a circle, 
however, is clearly evident from the close correspondence 
between the chronological and mental age norms as 
indicated in the graphs. And the attempt to obtain a 
“fair” sampling at each age is rarely a statistical success. 
(a) Mental Age Norms 
We have utilized here the reactions of three different 
groups, (i) the whole P. S.1 group, (2) theF. M.2 and the 
P. S. groups, and (3) a group consisting only of children 
having I. Q.’s between 86 and 115. In this manner, the 
children of I. Q.’s between 86 and 115 have weighted 
our mental age norms to an extent of 3, the rest of the 
P. S. children, the accelerated and retarded, to an extent 
of 2, and the F. M. group to an extent of 1. This reduces 
any defect in the norms obtained because of the possible 
inaccuracy of the Binet scale in a few cases, this inac- 
curacy being more likely to occur with the so-called 
F. M., the seriously retarded, or the greatly accelerated. 
Tables XXXIV, XXXV and XXXVI give the num- 
bers and per cents passing for each of the sexes and as a 
total for the whole P. S. group. (Age 4 on the table 
includes ages between 3 years 7 months and 4 years 6 
months, and so on for each age.) 
1 Public School. 
1 Feeble-minded. 106 
INTELLIGENCE MEASUREMENT 
Mental 
No. OF 
Design Number 
Age 
Cases 
I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
XIII 
xrv 
XV 
XVI 
xvn 
xvm 
XIX 
XX 
4 
i 
o 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
5 
3 
o 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
6 
6 
33 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
12 
IOO 
66 
33 
25 
8 
17 
8 
8 
8 
0 
0 
8 
0 
0 
0 
0 
0 
0 
0 
0 
8 
20 
95 
85 
85 
40 
25 
20 
10 
20 
25 
0 
5 
10 
0 
5 
0 
0 
0 
0 
0 
0 
9 
16 
IOO 
87 
94 
63 
56 
38 
0 
38 
38 
6 
0 
0 
6 
13 
6 
13 
13 
13 
0 
6 
IO 
21 
IOO 
86 
86 
71 
71 
43 
33 
52 
48 
24 
29 
38 
5 
24 
10 
24 
24 
10 
10 
0 
ii 
17 
IOO 
IOO 
94 
88 
94 
6S 
47 
59 
65 
47 
35 
47 
35 
4i 
47 
29 
65 
24 
24 
18 
12 
18 
IOO 
IOO 
IOO 
89 
94 
83 
44 
67 
83 
39 
50 
56 
39 
61 
33 
44 
67 
39 
II 
0 
13 
ii 
IOO 
91 
9i 
73 
73 
64 
36 
55 
64 
27 
45 
45 
27 
27 
36 
36 
45 
27 
18 
18 
14 
8 
IOO 
IOO 
IOO 
IOO 
88 
75 
63 
80 
88 
63 
63 
63 
38 
63 
5° 
75 
88 
50 
38 
25 
IS 
4 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
5o 
75 
IOO 
75 
IOO 
5° 
75 
75 
75 
75 
75 
16 
5 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
60 
80 
IOO 
80 
40 
IOO 
80 
80 
IOO 
IOO 
IOO 
80 
80 
60 
17 
4 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
IOO 
5° 
IOO 
18 
3 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
67 
IOO 
IOO 
67 
IOO 
67 
IOO 
67 
67 
IOO 
19 
4 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
IOO 
IOO 
IOO 
5° 
75 
Mental Age Norms (P. S. Group) 
TABLE XXXIV 
Per Cent Passing {Boys) BLOCK-DESIGN TESTS 
107 
Design Number 
Age 
Cases 
I 
II 
111 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
XIII 
XIV 
XV 
XVI 
XVII 
XVIII 
XIX 
XX 
6 
13 
69 
38 
38 
15 
0 
8 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
12 
75 
25 
33 
8 
17 
8 
8 
8 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
8 
22 
95 
73 
94 
4i 
27 
22 
9 
22 
32 
5 
5 
0 
0 
0 
0 
0 
0 
0 
0 
0 
9 
13 
100 
69 
85 
3i 
38 
38 
8 
15 
15 
8 
8 
8 
8 
0 
0 
0 
0 
0 
0 
0 
IO 
17 
100 
100 
76 
94 
76 
53 
24 
59 
47 
6 
24 
4i 
12 
6 
12 
24 
18 
18 
0 
0 
IX 
20 
100 
100 
95 
85 
75 
75 
3° 
60 
65 
25 
3° 
30 
15 
IO 
IS 
20 
30 
20 
5 
0 
12 
10 
100 
80 
90 
90 
80 
70 
5° 
60 
60 
20 
IO 
3° 
IO 
3° 
50 
40 
60 
20 
0 
0 
13 
7 
100 
100 
IOO 
71 
7i 
86 
43 
7i 
57 
29 
57 
57 
29 
43 
43 
57 
57 
29 
0 
14 
14 
8 
100 
100 
IOO 
IOO 
IOO 
88 
63 
88 
IOO 
25 
93 
93 
25 
93 
50 
38 
75 
5° 
38 
25 
IS 
6 
100 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
83 
83 
67 
5° 
83 
17 
5° 
5° 
97 
97 
97 
33 
33 
16 
5 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
60 
80 
IOO 
80 
60 
60 
80 
80 
80 
80 
80 
80 
60 
40 
17 
3 
100 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
67 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
67 
67 
18 
1 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
19 
1 
100 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
Mental Age Norms (P. S. Group) 
Per Cent Passing (Girls) 
TABLE XXXV 108 
INTELLIGENCE MEASUREMENT 
Mental 
No. OF 
Design Number 
Age 
Cases 
I 
n 
m 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
XIII 
XIV 
XV 
XVI 
XVII 
xvm 
xrx 
XX 
4 
i 
O 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
5 
3 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
c 
0 
0 
6 
19 
58 
26 
26 
IO 
0 
5 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
24 
88 
46 
33 
17 
13 
13 
8 
8 
4 
0 
0 
4 
0 
0 
0 
0 
0 
0 
0 
0 
8 
42 
' 5 
79 
74 
41 
26 
21 
IO 
21 
29 
2 
5 
5 
0 
2 
0 
0 
0 
0 
0 
0 
9 
29 
100 
79 
90 
48 
48 
38 
4 
28 
28 
7 
4 
4 
7 
7 
4 
7 
7 
7 
0 
4 
IO 
38 
100 
92 
82 
82 
74 
47 
29 
56 
47 
16 
26 
39 
8 
16 
11 
24 
21 
13 
5 
0 
ii 
37 
100 
100 
95 
86 
84 
70 
38 
59 
65 
35 
32 
38 
24 
24 
30 
24 
46 
22 
14 
8 
12 
28 
100 
93 
96 
89 
89 
79 
46 
64 
75 
32 
3^ 
46 
29 
50 
39 
43 
64 
32 
7 
0 
13 
18 
100 
94 
94 
72 
72 
72 
39 
61 
61 
28 
50 
5° 
28 
33 
39 
44 
50 
28 
11 
17 
14 
16 
100 
100 
100 
100 
94 
81 
63 
88 
94 
44 
63 
63 
3i 
63 
50 
56 
81 
50 
38 
25 
IS 
10 
100 
100 
100 
100 
100 
100 
90 
90 
90 
60 
60 
90 
40 
70 
5° 
70 
70 
70 
5° 
50 
16 
IO 
100 
100 
100 
100 
100 
100 
60 
80 
100 
80 
5° 
80 
80 
80 
90 
90 
90 
80 
70 
50 
17 
7 
100 
100 
100 
100 
100 
100 
100 
100 
100 
86 
86 
100 
100 
100 
86 
100 
100 
100 
57 
86 
18 
4 
100 
100 
100 
100 
100 
100 
100 
100 
100 
100 
75 
100 
100 
75 
100 
75 
100 
75 
75 
100 
19 
5 
100 
100 
100 
100 
100 
100 
80 
100 
100 
TOO 
100 
100 
80 
100 
100 
100 
100 
100 
60 
80 
Mental Age Norms (P. S. Grout) 
Per Cent Passing {Total) 
TABLE XXXVI BLOCK-DESIGN TESTS 
109 
Mental 
No. OF 
Design Number 
Age 
Cases 
I 
II 
in 
IV 
V 
VI 
VII 
VIII 
DC 
X 
XI 
XII 
xm 
XIV 
XV 
XVI 
XVII 
xvra 
XIX 
XX 
5 
I 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
6 
16 
So 
18 
13 
18 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
16 
88 
56 
38 
25 
6 
13 
6 
6 
6 
0 
0 
6 
0 
0 
0 
0 
0 
0 
0 
0 
8 
27 
96 
44 
70 
41 
26 
22 
7 
19 
3° 
3 
7 
3 
0 
3 
0 
0 
0 
0 
0 
0 
9 
20 
100 
80 
90 
35 
35 
25 
0 
5 
10 
10 
0 
0 
0 
5 
5 
5 
5 
5 
0 
0 
IO 
23 
100 
9i 
83 
83 
87 
6l 
22 
61 
52 
22 
22 
52 
9 
22 
13 
26 
30 
13 
9 
0 
ii 
24 
100 
100 
92 
88 
92 
71 
46 
58 
67 
33 
38 
42 
21 
29 
29 
21 
46 
21 
8 
8 
12 
l6 
100 
100 
100 
88 
94 
88 
63 
75 
94 
25 
44 
56 
31 
63 
50 
56 
81 
44 
13 
0 
13 
12 
100 
92 
92 
75 
75 
83 
42 
67 
67 
25 
50 
So 
25 
33 
42 
42 
50 
25 
25 
17 
14 
12 
100 
100 
100 
100 
92 
75 
58 
83 
92 
42 
58 
50 
33 
50 
42 
50 
75 
58 
25 
25 
IS 
9 
100 
100 
100 
100 
100 
100 
89 
89 
89 
56 
56 
89 
44 
78 
44 
67 
67 
67 
56 
56 
16 
7 
100 
100 
100 
100 
100 
100 
43 
7i 
100 
7i 
29 
7i 
71 
7i 
86 
86 
86 
86 
57 
29 
17 
4 
100 
100 
100 
100 
100 
100 
100 
100 
100 
75 
75 
100 
100 
100 
100 
100 
100 
100 
75 
75 
18 
1 
100 
100 
100 
100 
100 
100 
100 
100 
100 
100 
0 
100 
100 
0 
100 
100 
100 
100 
100 
100 
Mental Age Norms (P. S. Group) (I. Q. between 86 and 115) 
TABLE XXXVII 
Per Cent Passing 110 
INTELLIGENCE MEASUREMENT 
Mental 
No. OF 
Design Number 
Age 
Cases 
I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
XIII 
XIV 
XV 
XVI 
XVII 
XVIII 
XIX 
XX 
3 
3 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
4 
7 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
S 
14 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
6 
3i 
ss 
23 
19 
c 
0 
32 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
29 
86 
48 
38 
21 
14 
18 
7 
7 
4 
0 
0 
4 
0 
0 
0 
0 
0 
0 
0 
0 
8 
Si 
90 
76 
71 
37 
27 
20 
10 
18 
25 
2 
4 
4 
0 
2 
0 
0 
0 
0 
0 
0 
9 
37 
97 
78 
86 
49 
43 
38 
3 
24 
24 
8 
5 
5 
5 
8 
5 
8 
8 
5 
0 
3 
IO 
44 
98 
86 
82 
73 
68 
45 
25 
50 
4i 
14 
23 
34 
7 
14 
9 
20 
18 
11 
5 
0 
ii 
44 
100 
95 
9i 
80 
80 
65 
39 
55 
59 
32 
3° 
36 
23 
25 
3° 
23 
43 
23 
14 
9 
12 
3i 
IOO 
94 
97 
87 
90 
81 
45 
65 
74 
32 
35 
45 
26 
52 
42 
45 
61 
29 
7 
0 
13 
20 
100 
95 
95 
75 
75 
70 
35 
60 
60 
25 
45 
45 
25 
30 
35 
40 
45 
25 
10 
15 
14 
17 
IOO 
IOO 
94 
IOO 
88 
76 
59 
82 
88 
41 
59 
59 
29 
59 
47 
53 
76 
47 
35 
24 
IS 
II 
IOO 
IOO 
IOO 
IOO 
IOO 
91 
86 
9i 
86 
55 
55 
86 
36 
64 
45 
64 
64 
64 
45 
45 
16 
II 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
64 
73 
IOO 
73 
55 
86 
86 
73 
9i 
9i 
9i 
86 
64 
55 
17 
7 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
86 
86 
IOO 
IOO 
IOO 
86 
IOO 
IOO 
IOO 
57 
86 
18 
4 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
75 
IOO 
IOO 
75 
IOO 
75 
IOO 
75 
75 
IOO 
19 
5 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
80 
IOO 
IOO 
IOO 
IOO 
IOO 
80 
IOO 
IOO 
IOO 
IOO 
IOO 
60 
80 
Mental Age Norms (F. M. and Total P. S. Combined) 
TABLE XXXVIII 
Per Cent Passing BLOCK-DESIGN TESTS 
111 
Design Number 
I 
II 
in 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
xrn 
XIV 
XV 
XVI 
XVII 
XVIII 
XIX 
XX 
3 • 
o 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
4 • 
o 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
5 • 
o 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
6 . 
S3 
22 
19 
12 
0 
12 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 • 
»7 
5° 
36 
21 
II 
15 
7 
7 
5 
0 
0 
5 
0 
0 
0 
0 
0 
0 
0 
0 
8 . 
94 
66 
72 
40 
26 
21 
9 
19 
28 
2 
5 
4 
0 
2 
0 
0 
0 
0 
0 
0 
9 • 
99 
79 
89 
44 
42 
34 
2 
19 
21 
8 
3 
3 
4 
7 
5 
7 
7 
6 
0 
2 
IO . 
99 
90 
82 
79 
76 
51 
25 
56 
47 
17 
23 
42 
8 
17 
11 
23 
23 
12 
6 
0 
ii . 
IOO 
98 
93 
85 
85 
69 
44 
57 
64 
33 
33 
39 
23 
26 
30 
23 
45 
22 
12 
8 
12 . 
IOO 
96 
98 
88 
91 
83 
5i 
68 
81 
3° 
38 
49 
29 
55 
44 
48 
69 
35 
9 
0 
13 • 
IOO 
94 
94 
74 
74 
75 
39 
63 
63 
26 
48 
48 
26 
32 
39 
42 
48 
26 
15 
17 
14 . 
IOO 
IOO 
98 
IOO 
9i 
77 
60 
84 
9i 
43 
60 
57 
3i 
57 
46 
53 
77 
52 
33 
25 
IS • 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
88 
90 
88 
57 
57 
88 
40 
7i 
46 
67 
67 
67 
50 
5° 
16 . 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
56 
75 
IOO 
75 
45 
79 
79 
75 
89 
89 
89 
84 
67 
45 
17 • 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
82 
82 
IOO 
IOO 
IOO 
9i 
IOO 
IOO 
IOO 
63 
82 
18 . 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
5° 
IOO 
IOO 
5° 
IOO 
83 
IOO 
83 
83 
IOO 
19 . 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
80 
IOO 
IOO 
IOO 
IOO 
IOO 
80 
IOO 
IOO 
IOO 
IOO 
IOO 
60 
80 
Mental Age Norms (Composite) 
TABLE XXXIX 
Per Cent Passing 112 
INTELLIGENCE MEASUREMENT 
Table XXXVII presents the data for the per cents 
passing at each mental age, the group here being limited 
to those only in the P. S. group whose It Q.’s ranged 
between 86 and 115. 
Table XXXVIII gives the per cents passing at each 
mental age, combining the F. M. with the total P. S. 
group. 
In Table XXXIX. is presented a composite of the data 
in Tables XXXVI, XXXVII and XXXVIII, the arith- 
metic mean being used. It has already been mentioned 
that as a result of this procedure the I. Q. norms receive 
a weight of 3., the norms for the P. S. children under 
86 I. Q. and above 115 I. Q. a weight of 2, and the 
norms of the F. M. group a weight of 1. The figures for 
each of the designs in this table were utilized for the 
final mental age graphs showing per-cents passing at 
each mental age (Graphs 17 to 36). 
A matter which should be observed in connection with 
the composite norms is the fact that the children falling 
in the 13-year (mental age) group, are the only ones 
which do not manifest a consistent superiority over the 
children of the next preceding age. It is true that in 
many instances the difference is no more than 3 or 4 per 
cent in either direction. But not only should this slight 
negative difference not exist, but the 13-year-olds should 
show marked superiority over the 12-year-olds. Biased 
as all devisers of tests are in favor of their own scheme 
of mental examination, the writer might now justifiably 
follow the custom of throwing the blame on the Binet 
tests. In this attempt, however, he is handicapped by 
too many years’ actual experience with the Scale, during BLOCK-DESIGN TESTS 
113 
% Passing 
% Passing 
Mental Age 
Chronological 
Age 
—i——I 
GRAPH 13 
GRAPH 20 
Dtesigip IV | 
Design II 
Age 
Age 
AGE NORMS 
GRAPH 17! 
GRAPH 10 
I 
Desgri III 
Age 
Age 
% Passing 
% Passing 114 
INTELLIGENCE MEASUREMENT 
% Passing 
% Passing 
Mental Age 
_Chronologieal 
Age 
GRAPH 22 
i i 
GRAPH 24 
till' 
Age 
Age 
Djesign iVI 
(Design VIII 
AGE NORMS 
GRAPH 21 
GRAPH 23 
I ? I i 
Design V 
Age 
Age 
Design VII 
% Passing 
% Passing BLOCK-DESIGN TESTS 
115 
% Passing 
% Passing 
Mental Age 
Chronological 
Age 
GRAPH 26 
GRAPH 28 
Design X 
Age 
Age 
Desigh XIJ 
AGE NORMS 
GRAPH 27 
Design IX 
GRAPH 25 
Design XI 
iii i 
Age 
Age 
% Passing 
% Passing 116 
INTELLIGENCE MEASUREMENT 
% Passing 
% Passing 
o 
err 
-x- 
0. 
< 
xc. 
o 
GRAPH 32 
Mental Age 
—-Chronological 
Age 
Design XIV 
Age 
Design XVI 
Age 
AGE NORMS 
iGRAPH 29 
GRAPH! 31 
6esign XIII ' 
i i 
_ Age 
Design XV 
Age 
% Passing 
% Passing BLOCK-DESIGN TESTS 
117 
% Passing 
% Passing 
GRAPH 34. 
GRAPH 36 
iii- 
Mental Age 
.Chronological 
Age 
Design XVIII 
Age 
Design XX 
Age 
AGE NORMS 
grAph 33 
GRAPH 35 
Design XVII 
Age 
Design XIX 
Age 
% Passing 
% Passing 118 
INTELLIGENCE MEASUREMENT 
which period he has developed no little regard for its 
accuracy. The same inadequacy of the 13-year-old 
group, though to a less marked degree, is observable in 
the table giving the chronological age norms. 
(b) Sex Differences (Mental Age Norms) 
Table XL summarizes the data for sex differences 
at ages 6-8, 9-13, and 14-19. This division is merely 
one of convenience, dividing the range of mental ages 
into approximately three equal parts. In this table 
are presented the number of times at the various ages 
for all of the designs that the boys show a greater 
percentage of passes than the girls, in the next row the 
number of times that this is true for girls, and the last 
row the number of times when the per cent passing is 
equal for the sexes. This number of equal per cents 
passing is great because o per cents and 100 per cents 
passing have been included. 
TABLE XL 
Sex Differences 
Mental Ages 
Total 
6-8 
9-i3 
14-19 
Number of instances in which 
per cent of boys passing is 
greater than girls .... 
II 
53 
23 
87 
Number of instances in which 
per cent of girls passing is 
greater than boys .... 
13 
35 
18 
66 
Instances of no difference in 
per cent passing between boys 
and girls 
36 
12 
79 
127 
Total 
60 
100 
120 
280 BLOCK-DESIGN TESTS 
119 
The data of Table XL is summarized more briefly 
and for per cents in Table XLI. It will be evident that 
no marked sex differences are observable here, the boys 
appearing somewhat more superior than the girls. This 
will be corroborated again at a number of other points. 
Sex Differences 
TABLE XLI 
Number 
Percentage of 
Total 
Instances boys superior to girls 
87 
3i-i 
Instances girls superior to boys 
66 
23.6 
Equality 
127 
45-3 
Total 
280 
100.0 
Table XLII presents this evidence again for the first 
ten designs, and for the last ten, and for the total. 
Sex Differences 
TABLE XLII 
Design No. 
Mental Ages 
Total 
6-8 
9-13 
14-19 
I-X 
XI-XX 
I-X 
XI-XX 
I-X 
XI-XX 
I-X 
XI-XX 
Number of instances 
boys superior . 
Per cent 
8 
27% 
3 
IO% 
24 
48% 
29 
58% 
3 
5% 
20 
33% 
35 
25% 
52 
37% 
Number of instances 
girls superior . 
Per cent . . 
13 
43% 
o 
o% 
18 
36% 
Oo H 
7 
12% 
11 
18% 
38 
27% 
28 
20% 
Number of instances 
equal . 
Per cent . . 
9 
30% 
27 
90% 
8 
16% 
4 
8% 
SO 
83% 
29 
49% 
67 
48% 
60 
43% 
Total . . . 
Per cent 
3° 
ioo% 
30 
IOO% 
So 
100% 
SO 
100% 
60 
100% 
60 
100% 
140 
100% 
140 
100% 120 
INTELLIGENCE MEASUREMENT 
In designs I-X, ages 6-8, girls seem superior, with no 
significant sex difference on the last ten designs. Be- 
tween the ages 9-13, boys seem superior throughout. 
Between the ages 14-19 there is a good deal of equality, 
though girls are somewhat superior on the first ten and 
the boys on the last ten designs. In designs XI-XX, 
boys are superior at each of the grouped ages. On de- 
signs I-X girls are superior at each of the grouped ages 
except 9-13. From the table it is clear that in the early 
ages, from 6-8, there is no observable sex difference, 
perhaps girls may be said to be slightly superior, from 
9-13 boys are somewhat superior, and from 14 to 19 
boys are only slightly superior, with marked equality 
between the sexes at this age group. 
To summarize the data for the sexes: In designs I-X, 
ages 6-8, girls are superior; ages 9-13, boys are superior; 
ages 14-18, girls are again superior. In designs XI-XX 
boys are superior at every age group. In the first ten 
designs the girls are superior, in the last ten the boys are 
superior. Perhaps the mechanical, somewhat puzzle- 
like nature of the later designs may help account for 
this difference. Taking the data in Table XL for all the 
designs, there is no significant sex difference from ages 
5-8; between 9-13 and 14-18 boys seem superior. 
Combining all the tests and all the ages, the boys are 
slightly superior. It should be understood by the reader, 
however, that these tables merely show tendencies and 
are not to be interpreted as conclusive evidence for any 
valid argument relative to intelligence differences be- 
tween the sexes. BLOCK-DESIGN TESTS 
121 
(c) Chronological Age Norms 
In obtaining these values we utilized only the P. S. 
cases, discarding all those who were not in the normal 
grade for their chronological age, or not within one 
year of normal grade. This yielded some 241 cases (121 
boys, 120 girls) upon which these norms are based. . 
In Tables XLIII, XLIV, and XLV are presented the 
number and per cents of boys, of girls, and of the total 
number at each age passing each of the designs. The 
range in chronological age is smaller than the range in 
mental age, as would naturally be expected, the lowest 
chronological age falling in the 6-year group and the 
highest in the 17-year group. This yields a range of 
twelve years. 
Attention should be called to the striking similarity 
between the tables for mental age and the succeeding 
tables for chronological age. There are no marked dis- 
crepancies in spite of the fact that the mental age tables 
included reactions from the feeble-minded, which would 
theoretically produce some disturbing effects. 
The adequacy of the sampling and the validity of the 
standardization is also positively indicated by the close 
agreement between the respective tables for mental age 
and chronological age. Although the standardization 
technique for chronological age compels a reduction in the 
number of cases under consideration to 241, an elimina- 
tion amounting to thirty-three per cent, nevertheless the 
figures obtained from this smaller and, in some respects, 
more homogeneous group, agree very closely with the 
figures of the preceding section, based upon mental age 
and on the total 366 cases. 122 
INTELLIGENCE MEASUREMENT 
w 
£ 
55 
O 
S3 
W 
Q 
XX 
m co t*-oo O 
M 
XIX 
ObOoOvOt^OHOcoOO 
CO H lO T}- T}- 0 
M 
l 
o 
o 
o 
8 
13 
20 
IO 
22 
57 
57 
IOO 
IOO 
a 
> 
x 
O O O co co n o O' h g g 
co 'O O O 
M M 
XVI 
o o o oo oncoO'O o 
M CO IO N lo O O 
M M 
> 
O O O *o *o co O Tf-vo N Q Q 
M CN M tJ- co *0 O O 
M M 
XIV 
OOOLO'tr^O^t-^wOO 
H tJ- CM vO rj- io O 
H 
I IIIX 
O O O OO ro K o !*) tN n O Q 
H « co *0 CO 00 o 
M 
XII 
m cn co 0 O 
M M 
X 
OOOOOOOOOvOmOnOO 
CO *0 CN VO *0 
X 
OOOoOMt^OcoOt^OO 
co cn vo co *0 *0 VO O 
M 
a 
OTj-OMOt^OgvOr-OO 
W M CO LOVO oo O co *o O O 
M M M 
vm 
o O co O OwO o o 
CN CN Tt"0 00 *000 O 
M 
vn 
O CO O O Q 
CN CO Tt" *0 rtco O 
> 
OwO o q 
cn co *0*0 O 0 
M M 
> 
O o O' ro N o OwO vo O O 
m covO 00 OvOO 00 OO O O 
M M 
& 
O M o vo *0 co O Ovvo vo O O 
CN oo rt 00 00 00 O O 
M M 
E 
O C- O *000 NO O too O O 
iovo 00 00 00 Ov 0 OvO O O 
M M M M 
« 
*ooo Ng g tog o o 
VO 00 00 00 00 O 0 OvO o 0 
W M M M M 
- 
COVO OQQQQQOOOO 
co 00 OOOOOOOOOOO 
WWHMHMMMW 
No. of 
Cases 
COVO *o O Qv Th vo CN 
M M M M M M HH 
Life 
Age 
vO O' O h CJ co’t *OVO t>» 
MMHHMWMM 
Chronological Age Norms (at or within i Yr. of Grade) 
Per Cent Passing (Boys) 
TABLE XLIII BLOCK-DESIGN TESTS 
123 
No. op 
Design Number 
Age 
Cases 
I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 
xm 
XIV 
XV 
XVI 
xvn 
xvm 
XIX 
XX 
6 
9 
56 
33 
44 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
12 
75 
33 
42 
25 
0 
8 
0 
8 
8 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
8 
18 
100 
72 
72 
49 
33 
22 
17 
22 
28 
6 
6 
0 
0 
0 
0 
0 
0 
0 
0 
0 
9 
ii 
9i 
73 
73 
27 
27 
27 
9 
18 
27 
9 
18 
0 
9 
9 
9 
9 
9 
9 
0 
0 
IO 
12 
100 
92 
67 
75 
75 
67 
8 
42 
25 
17 
O 
17 
8 
8 
8 
8 
8 
8 
0 
0 
ii 
IO 
100 
90 
90 
80 
80 
70 
5° 
5° 
70 
IO 
40 
60 
0 
no 
30 
30 
5° 
10 
0 
0 
12 
12 
100 
100 
100 
92 
83 
92 
33 
58 
67 
17 
58 
58 
33 
17 
25 
42 
58 
33 
17 
8 
13 
13 
100 
92 
85 
92 
77 
69 
39 
69 
69 
3i 
3i 
39 
15 
39 
23 
39 
49 
39 
15 
23 
14 
9 
100 
100 
'1OO 
89 
89 
89 
67 
89 
78 
59 
22 
59 
44 
33 
44 
44 
44 
44 
33 
22 
IS 
8 
100 
88 
100 
100 
75 
88 
63 
75 
75 
63 
5° 
63 
5° 
50 
38 
5° 
5° 
5° 
25 
25 
16 
6 
100 
100 
100 
100 
100 
100 
50 
93 
100 
50 
50 
67 
5° 
67 
97 
50 
97 
97 
33 
17 
Chronological Age Norms (at or within i Yr. of Grade) 
TABLE XLIV 
Per Cent Passing (Girls) 124 
INTELLIGENCE MEASUREMENT 
Life 
No. OF 
Design Number 
Age 
Cases 
I 
II 
in 
IV 
V 
VI 
vn 
vni 
IX 
X 
XI 
xn 
XIII 
XIV 
XV 
XVI 
xvn 
xvm 
XDC 
XX 
6 
15 
47 
20 
27 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
7 
26 
81 
50 
5° 
23 
4 
4 
4 
8 
12 
0 
0 
4 
0 
0 
0 
0 
0 
0 
0 
0 
8 
28 
93 
75 
68 
36 
25 
21 
18 
21 
21 
4 
4 
4 
0 
0 
0 
0 
0 
0 
0 
0 
9 
24 
96 
79 
79 
38 
33 
29 
4 
21 
29 
8 
13 
13 
8 
13 
13 
8 
8 
8 
4 
0 
IO 
28 
100 
89 
79 
75 
68 
57 
25 
43 
39 
25 
21 
25 
11 
29 
18 
14 
25 
11 
4 
0 
ii 
25 
100 
88 
88 
76 
84 
68 
44 
60 
68 
20 
40 
48 
16 
24 
20 
32 
48 
16 
4 
4 
12 
22 
100 
100 
96 
86 
86 
82 
41 
64 
73 
36 
5° 
64 
18 
36 
32 
41 
59 
23 
23 
9 
13 
22 
100 
96 
9i 
9i 
82 
68 
41 
77 
82 
32 
41 
41 
23 
41 
32 
46 
46 
32 
14 
14 
14 
23 
100 
96 
96 
87 
87 
83 
61 
87 
83 
52 
52 
70 
52 
48 
39 
61 
6S 
52 
44 
30 
15 
15 
100 
93 
100 
93 
80 
87 
53 
67 
67 
60 
40 
67 
53 
60 
47 
53 
60 
53 
33 
33 
16 
11 
100 
100 
100 
100 
100 
100 
64 
82 
100 
55 
55 
82 
64 
64 
82 
73 
82 
82 
36 
46 
17 
2 
100 
100 
100 
100 
100 
100 
100 
100 
100 
100 
50 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
IOO 
Chronological Age Norms (at or within i Yr. of Grade) 
Per Cent Passing {Total) 
TABLE XLV BLOCK-DESIGN TESTS 
125 
(d) Sex Differences {Chronological Age Norms) 
Table XLVI analyzes the sex differences in the differ- 
ent age groups for the first ten designs, for the last ten, 
and for the total. 
TABLE XLVI 
Sex Differences 
Design No. 
Chronological Age 
Total 
6-8 
9-13 
14-17 
I-X 
XI-XX 
I-X 
XI-XX 
I-X 
XI-XX 
I-X 
XI-XX 
Number of instances 
boys superior . 
Per cent 
00 
<N 
2 
7% 
28 
56% 
31 
62% 
6 
20% 
27 
90% 
42 
38% 
60 
55% 
Number of instances 
girls superior . 
Per cent 
14 
46% 
I 
3% 
16 
32% 
16 
32% 
14 
47% 
3 
10% 
44 
40% 
20 
18% 
Number of instances 
equal .... 
Per cent 
8 
27% 
27 
90% 
6 
12% 
3 
6% 
10 
33% 
0 
0% 
24 
22% 
30 
27% 
Total 
Per cent 
3° 
100% 
3° 
100% 
So 
100% 
So 
100% 
30 
100% 
30 
100% 
no 
100% 
no 
100% 
It will be observed that girls are superior in designs I X 
at ages 6-8 and 14-16, the boys being superior at ages 
9-13. On the whole, for the first ten designs the girls 
are slightly superior. The boys are superior on designs 
XI-XX at all the age groups. Taking all the designs 
together, girls are superior at the earlier ages, boys be- 
coming superior at about nine and remaining so there- 
after. On the whole, it appears that boys are superior 
in these designs to the girls. These results based on 
chronological age confirm the findings by mental age. 126 
INTELLIGENCE MEASUREMENT 
Further analyses for sex differences have been made 
by means of a tabular comparison of results obtained 
(a) for the mental age (total P. S.) group, (b) for the 
mental age (selected I. Q.’s) group, and (c) for the 
chronological age group, by years below 9, between 9 and 
13, and above 13. These data are not here presented, 
but may be constructed from the tables already given. 
It is evident (a) that for ages below 9, girls are slightly 
superior to the boys, this being especially true for the 
first ten designs. For the next ten designs there is no 
appreciable difference, the same being true for all the 
designs for children below nine years of age. (b) For 
ages 9-13, boys are superior to girls on all the designs 
and much more so on the second set of ten than on the 
first set. And (c) above age 13, boys seem slightly superior 
to girls, but on the first ten designs girls are superior to 
boys, while on the last ten, boys are quite superior to girls. 
Considering merely designs I-X, and allowing for 
errors of sampling, we may say that there are no sig- 
nificant differences between boys and girls, but as regards 
designs XI-XX, with increase in age, boys seem superior 
to girls. Whether this difference is due to a difference 
in analytic synthetic power, or whether it may be largely 
accounted for by specialized mechanics on the part of 
boys, cannot be stated dogmatically. Then, again, 
whether this evidence would change with the addition 
of further samplings cannot be definitely foretold. 
(e) Graphic Presentation of Norms 
With the data then of Tables XXXIX and XLV we 
may plot our curves for per cent passing with increase BLOCK-DESIGN TESTS 
127 
of mental and of chronological age. This has been 
done in Graphs 17 to 36. It should he noted that the 
mental age and chronological age curves overlap, and if no 
key had been presented stating which is which, no one woidd 
have been able to tell them apart. Many have been the 
warnings not to standardize a test on the basis of mental 
age, nevertheless the results are practically identical. 
if) Final Year Scale 
Our final year-location of a test has been determined 
by combining (averaging) the two curves, mental age 
and chronological age. See Table L. Using the 50 
and 75 per cent criteria, the designs are located at the 
ages stated in Table XLVII. Table XLVIII presents 
this material in another form. And Table XLIX gives 
the scores in designs successfully completed at the various 
age levels. Graphs 37 and 38 present the data graphi- 
cally, and we have here added in Graph 39, for purposes 
TABLE XLVII 
(Based on a composite of mental and chronological age norms) 
Year Scale Norms 
Age Value 
Design 
Age Value 
Design 
5°% 
Criterion 
75% 
Criterion 
5°% 
Criterion 
75% 
Criterion 
I 
Yrs. Mo 
6-0 
Yrs. Mo 
6-9 
XI 
Yrs. Mo 
13-6 
Yrs. Mo 
18-0 
II 
7-0 
8-6 
XII 
13-0 
15-3 
III 
7-3 
8-3 
XIII 
1 S-o 
16-3 
IV 
9-3 
10-6 
XIV 
13-6 
16-0 
V 
9-3 
10-3 
XV 
15-0 
16-0 
VI 
10-0 
12-6 
XVI 
13-3 
i5-9 
VII 
13-0 
16-0 
XVII 
11—3 
15-0 
VIII 
10-3 
13-3 
XVIII 
14-0 
15-6 
IX 
10-3 
12-9 
XIX 
15-6 
17-6 
X 
14-0 
16-9 
XX 
16-0 
17-3 128 
INTELLIGENCE MEASUREMENT 
TABLE XLVIII 
Year Scale Norms 
Age 
Design Number 
50% Criterion 
75% Criterion 
6 . . . . 
I 
I 
7 ... . 
II III 
8 ... . 
II III 
g ... . 
IV V 
IO ... . 
VI VIII IX 
IV V 
XI ... 
XVII 
12 ... 
VI IX 
13 • • • • 
VII XI XII XIV XVI 
VIII 
14 ... . 
X XVIII 
15 • • • • 
XIII XV XIX 
XII XVI XVII XVIII 
16 ... 
XX 
VII X XIII XIV XV 
17 ... . 
XIX XX 
18 ... . 
XI 
TABLE XLIX 
Scores to be Expected at the Various Age Levels 
Age 
(50%) 
Score 
(75%) 
Score 
Age 
(50%) 
Score 
(75%) 
Score 
4 
O 
0 
12 
9 
7 
5 
0 
0 
13 
14 
8 
6 
1 
1 
14 
16 
8 
7 
3 
1 
IS 
19 
12 
8 
3 
3 
16 
20 
17 
9 
5 
3 
17 
20 
19 
IO 
8 
5 
18 
20 
20 
XI 
9 
5 
of comparison, the location of these designs on a P. E. 
Scale, the derivation of which is explained in the division 
on “P. E. Scale Norms.’’1 
1 It should be noted that although the original time limits for each 
design were somewhat longer than the later revision, the revision itself 
covers practically the same amount of time in which success may reason- 
ably be expected. The validity of the above-indicated norms are, 
therefore, in no way affected by this change. 129 
BLOCK-DESIGN TESTS 
GRAPH 37 
Age Location of Designs 
(50% Criterion) 
Age 
Age Location of Designs 
(75% Criterion) 
GRAPH 38 
Age 
GRAPH 39 
P. E. Location of Designs 
P, E. Scale 130 
INTELLIGENCE MEASUREMENT 
3. P. E. STANDARDIZATION 
(a) Method 
For a full and detailed explanation of the principles 
underlying the scaling of tests on a P. E. basis and for 
the technique involved, the reader is referred to the work 
of Buckingham, Trabue, and Woody. Here, let it 
suffice to mention that by means of this method, each 
test in the series is weighted, first, depending on the P. E. 
intervals between the separate ages, and second, depend- 
ing on the ratios between the number of passes and 
failures. In Table L are presented the per cents passing 
each design at the various ages from 3 to 19. (This data 
is based on the age norms, mental and chronological, 
smoothed.) In Table LI are presented the differences 
between 50 per cent and the per cent passing a design 
at each age. The data are thus prepared for the use of 
Sheppard’s Tables,1 and in Table LII are accordingly 
presented the P. E. equivalents of the items in Table LI. 
In Table LIII are presented the P. E. intervals between 
consecutive ages, the bottom of the table showing the 
average intervals between consecutive ages. In Table 
LIV are tabulated the distances of each age median 
above the zero of the P. E. scale. The separate age- 
distributions are presented graphically in Graph 40. 
It should be stated that a few minor modifications have 
been made in the application of this method to our prob- 
lem. These changes have been in the direction of elimi- 
nating some of the super-refinements. In theory and 
result the method has been kept intact 
1 See Appendix III. BLOCK-DESIGN TESTS 
131 
Designs 
Age 
(No.) 
3 
4 
5 
6 
7 
8 
9 
10 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
I 
O 
o 
o 
50 
83 
93 
98 
100 
100 
100 
100 
100 
100 
100 
100 
100 
100 
II 
O 
o 
o 
21 
49 
65 
78 
89 
94 
96 
97 
98 
99 
100 
100 
100 
100 
III 
O 
o 
o 
19 
46 
68 
80 
86 
9i 
94 
96 
97 
99 
100 
100 
100 
100 
IV 
O 
o 
o 
6 
20 
34 
50 
68 
79 
85 
88 
93 
97 
100 
100 
100 
100 
V 
O 
o 
o 
o 
10 
25 
40 
70 
79 
83 
86 
88 
94 
100 
100 
100 
100 
VI 
O 
o 
o 
4 
II 
20 
33 
50 
66 
73 
78 
84 
93 
100 
100 
100 
100 
VII 
o 
o 
o 
o 
4 
8 
13 
20 
29 
38 
48 
57 
65 
75 
84 
93 
95 
VIII 
o 
o 
o 
o 
8 
16 
28 
44 
57 
65 
73 
79 
88 
93 
100 
100 
100 
IX 
o 
o 
o 
o 
8 
18 
28 
42 
60 
7i 
78 
85 
93 
100 
100 
100 
100 
X 
o 
o 
o 
o 
0 
3 
9 
17 
24 
29 
36 
46 
55 
67 
82 
100 
100 
Xl 
o 
o 
o 
o 
0 
4 
10 
21 
33 
42 
48 
53 
57 
62 
67 
76 
100 
Xll 
o 
o 
o 
o 
3 
7 
18 
3° 
4i 
48 
56 
64 
73 
84 
100 
100 
100 
XIII 
o 
o 
o 
o 
0 
0 
5 
11 
16 
22 
28 
38 
5° 
7i 
100 
100 
100 
XIV 
o 
o 
o 
o 
0 
2 
10 
19 
28 
37 
46 
54 
64 
74 
85 
93 
100 
XV 
o 
o 
o 
o 
0 
0 
7 
15 
24 
32 
37 
44 
55 
76 
92 
100 
100 
XVI 
o 
o 
o 
o 
0 
0 
8 
17 
28 
37 
46 
56 
65 
78 
88 
96 
100 
XV11 
o 
o 
o 
o 
0 
0 
7 
24 
47 
61 
64 
68 
74 
83 
100 
100 
100 
XVIII 
o 
o 
o 
o 
0 
0 
6 
11 
18 
26 
36 
47 
61 
82 
100 
100 
100 
XIX 
o 
o 
o 
o 
0 
0 
2 
5 
8 
14 
20 
31 
43 
55 
68 
80 
96 
XX 
o 
o 
o 
o 
0 
0 
1 
2 
5 
9 
16 
28 
38 
53 
73 
90 
98 
[Based on Age Norms, Mental and Chronological, — Smoothed’ 
Per Cent Passing Designs 
TABLE L 132 
INTELLIGENCE MEASUREMENT 
Designs 
Age 
(No.) 
3 
4 
s 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
I 
-5° 
-50 
-50 
0 
33 
43 
48 
5° 
5° 
50 
50 
50 
50 
5o 
50 
50 
50 
II 
-5° 
-50 
-50 
— 28 
— 1 
15 
28 
39 
44 
46 
47 
48 
49 
5° 
50 
50 
5° 
III 
-50 
-50 
-50 
-31 
-4 
18 
3° 
36 
41 
44 
46 
47 
49 
50 
50 
5° 
5° 
IV 
-50 
-50 
-50 
-44 
-30 
— 16 
O 
18 
29 
35 
38 
43 
47 
50 
50 
5° 
50 
V 
-5° 
-50 
-5° 
-50 
-40 
-25 
— IO 
20 
29 
33 
36 
38 
44 
50 
50 
5° 
50 
VI 
-50 
-50 
-50 
-46 
-39 
-30 
-17 
0 
16 
23 
28 
34 
43 
5° 
5° 
5o 
50 
VII 
-50 
-50 
-50 
-50 
-46 
-42 
-37 
-3° 
— 21 
— 12 
— 2 
7 
15 
25 
34 
43 
45 
VIII 
-50 
-50 
-50 
-50 
-42 
“34 
— 22 
-6 
7 
15 
23 
29 
38 
43 
50 
5o 
50 
IX 
-50 
-50 
-50 
-50 
-42 
-32 
— 22 
-8 
10 
21 
28 
35 
43 
50 
5° 
50 
50 
X 
-50 
-5° 
-50 
-50 
-50 
-47 
-41 
-33 
— 26 
— 21 
-14 
-4 
5 
17 
32 
5° 
5° 
Xi 
-50 
-50 
-50 
-50 
-50 
-46 
-40 
-29 
-17 
-8 
— 2 
3 
7 
12 
17 
26 
So 
Xil 
-5° 
-50 
-50 
-50 
-47 
-43 
-32 
— 20 
-9 
— 2 
6 
14 
23 
34 
50 
50 
50 
XIII 
-50 
-50 
-50 
-50 
-50 
-50 
-45 
-39 
-34 
-28 
— 22 
— 12 
0 
21 
5° 
50 
50 
XIV 
-50 
-50 
-50 
-50 
-5° 
-48 
-40 
-3i 
— 22 
-13 
-4 
4 
14 
24 
35 
43 
50 
XV 
-50 
-50 
-50 
-50 
-50 
-50 
-43 
-35 
— 26 
-18 
-13 
-6 
5 
26 
42 
50 
5° 
XV1 
-50 
-So 
-50 
-50 
-50 
-50 
-42 
-33 
— 22 
-13 
-4 
6 
15 
28 
38 
46 
5° 
XV11 
-50 
-50 
-50 
-50 
-50 
-50 
-43 
— 26 
-3 
11 
14 
18 
24 
33 
5° 
50 
50 
XVIII 
-5° 
-5° 
-5° 
-50 
-50 
-5° 
-44 
-39 
-32 
-24 
-14 
-3 
11 
32 
5° 
50 
50 
XIX 
-5° 
-50 
-5° 
-50 
-50 
-50 
-48 
-45 
-42 
-36 
-30 
-19 
-7 
5 
18 
30 
46 
XX 
-50 
-50 
-50 
-50 
-50 
-5° 
-49 
-48 
-45 
-41 
“34 
— 21 
— 12 
3 
23 
40 
48 
Difference between 50% and the Per Cent Passing at Each Age 
TABLE LI BLOCK-DESIGN TESTS 
133 
Designs 
Age 
(No.) 
3 
4 
S 
6 
7 
8 
9 
10 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
I 
? 
? 
4.6 
O 
-1.4 
— 2.2 
-3-0 
-4.6 
-? 
_? 
-? 
-? 
-? 
-? 
-? 
-? 
II 
? 
? 
4.6 
1.1 
• O 
- .6 
— 1.1 
-1.8 
-2-3 
— 2.6 
-2.8 
-3-o 
-3-5 
-4.6 
-? 
-? 
-? 
III 
? 
? 
4.6 
i-3 
.1 
- -7 
— 1.2 
— 1.6 
— 2.0 
-2.3 
— 2.6 
— 2.8 
“3-5 
-4.6 
-? 
-? 
-? 
IV 
? 
? 
4.6 
2-3 
1.2 
.6 
O 
- -7 
— 1.2 
-i-5 
-1.7 
— 2.2 
-2.8 
-4.6 
-? 
-? 
-? 
V 
? 
? 
? 
4.6 
1.9 
x .o 
• 4 
- .8 
— 1.2 
— 1.4 
— 1.6 
-1.7 
-2.3 
-4.6 
-? 
-? 
-? 
VI 
? 
? 
4.6 
2.6 
x .8 
1.2 
• 7 
0 
- .6 
~ -9 
— 1.1 
-1.5 
— 2.2 
—4.6 
-? 
-? 
-? 
VII 
? 
? 
? 
4.6 
2.6 
2.1 
i-7 
1.2 
.8 
• 5 
. 1 
- -3 
- .6 
— 1.0 
— 1.5 
— 2.2 
— 2.4 
VIII 
? 
? 
? 
4.6 
2.1 
1-5 
■9 
.2 
- -3 
-6 
~ -9 
— x .2 
-i-7 
— 2.2 
-4.6 
-? 
-? 
IX 
? 
? 
? 
4-6 
2.1 
1.4 
• 9 
•3 
- -4 
- .8 
— 1.1 
— i-5 
— 2.2 
—4.6 
-? 
-? 
-? 
X 
? 
? 
? 
? 
4.6 
2.8 
2.0 
1.4 
1.0 
.8 
• 5 
.1 
— . 2 
- -7 
— 1.4 
—4.6 
-? 
xi 
? 
? 
? 
? 
4.6 
2.6 
1.9 
1.2 
• 7 
• 3 
.1 
— . 1 
- -3 
- -5 
— -7 
— 1.0 
—4.6 
xn 
? 
? 
? 
4.6 
2.8 
2.2 
1.4 
.8 
• 3 
. 1 
— . 2 
— -5 
— .gl 
— 1.5 
—4.6 
— ? 
— ? 
XIII 
? 
? 
? 
? 
? 
4.6 
2.4 
1.8 
i-5 
1.1 
•9 
.5 
0 
- .8 
—4.6 
-? 
-? 
XIV 
? 
? 
? 
? 
4-6 
3-o 
1-9 
i-3 
• 5 
.1 
— . 1 
- -5 
— 1.0 
-1.5 
— 2.2 
—4.6 
XV 
? 
? 
? 
? 
? 
4.6 
2.2 
i-5 
1.0 
• 7 
•s 
.2 
— . 2 
— 1.0 
— 2.1 
—4.6 
-? 
XV1 
? 
? 
? 
? 
? 
4.6 
2.1 
1.4 
■9 
• 5 
. 1 
— .2 
- .6 
— 1.1 
— 1.7 
— 2.6 
—4.6 
Xvn 
? 
? 
? 
? 
? 
4.6 
2.2 
1.0 
. 1 
- -4 
— -5 
- -7 
— 1.0 
— 1.4 
—4.6 
-? 
-? 
XVIII 
? 
? 
? 
? 
? 
4.6 
2-3 
1.8 
1.4 
1.0 
• 5 
. 1 
— .4 
— 1.4 
-4.6 
-? 
-? 
XIX 
? 
? 
? 
? 
? 
4-6 
3.0I 
2.4 
2.1 
1.6 
1.2 
• 7 
.3 
— .2 
— -7 
— 1.2 
— 2.6 
xx! 
? 
? 
? 
? 
? 
4.6 
3-5 
3-o 
2.4 
2.0 
i-5 
.8 
•S 
— .1 
- -9 
-1.9 
-3-0 
P. E. Equivalents of Items in Table LI 
TABLE LII 134 
INTELLIGENCE MEASUREMENT 
Design Number 
Ages 
3-4 
4-5 
5-6 
6-7 
7-8 
8-9 
g-io 
io-ii 
II—12 
12-13 
13-14 
14-15 
15-16 
16-17 
17-18 
18-ig 
I . . 
? 
? 
4.6 
1.4 
.8 
.8 
i.6 
? 
? 
? 
? 
? 
? 
? 
? 
? 
II . . 
? 
? 
3-5 
1.1 
.6 
•S 
•7 
•5 
•3 
.2 
.2 
•S 
1.1 
? 
? 
? 
Ill . . 
? 
? 
3-3 
1.2 
.8 
•5 
•4 
•4 
•3 
•3 
.2 
•7 
1.1 
? 
? 
? 
IV . . 
? 
? 
2-3 
1.1 
.6 
.6 
•7 
•5 
•3 
.2 
•S 
.6 
1.8 
? 
? 
? 
V . . 
? 
? 
? 
2.7 
•9 
.6 
1.2 
•4 
.2 
.2 
.1 
.6 
2-3 
? 
? 
? 
VI . . 
? 
? 
2.0 
.8 
.6 
•5 
•7 
.6 
•3 
.2 
•4 
•7 
2.4 
? 
? 
? 
VII . . 
? 
? 
? 
2.0 
•5 
•4 
•5 
•4 
•3 
•4 
•4 
•3 
•4 
•5 
■7 
.2 
VIII . . 
? 
? 
? 
2-5 
.6 
.6 
•7 
•5 
•3 
•3 
•3 
•5 
•S 
2.4 
? 
? 
IX . . 
? 
? 
? 
2-5 
•7 
•5 
.6 
•7 
•4 
•3 
•4 
•7 
2.4 
? 
? 
? 
lx.. 
? 
? 
? 
? 
x.8 
.8 
.6 
•4 
.2 
•3 
•4 
•3 
•5 
•7 
3-2 
? 
XI . . 
? 
? 
? 
? 
2.0 
•7 
•7 
•S 
•4 
.2 
.2 
.2 
.2 
.2 
•3 
3-6 
XII . . 
? 
? 
? 
i.8 
.6 
.8 
.6 
•S 
.2 
•3 
•3 
•4 
.6 
3-i 
? 
? 
XIII . . 
? 
? 
? 
? 
? 
2.2 
.6 
•3 
•4 
.2 
•4 
•5 
.8 
3-8 
? 
? 
XIV . . 
? 
? 
? 
? 
1.6 
1.1 
.6 
•4 
•4 
•4 
.2 
•4 
•S 
•S 
•7 
2.4 
XV . . 
? 
? 
? 
? 
? 
2.4 
•7 
•5 
•3 
.2 
•3 
•4 
.8 
1.1 
2-5 
? 
XVI . . 
? 
? 
? 
? 
? 
2-5 
•7 
•5 
•4 
■4 
•3 
•4 
•S 
.6 
•9 
2.0 
XVII . . 
? 
? 
? 
? 
? 
2.4 
1.2 
•9 
•5 
.1 
.2 
•3 
•4 
3-2 
? 
? 
XVIII . . 
? 
? 
? 
? 
? 
2-3 
•5 
•4 
•4 
•5 
•4 
•S 
1.0 
3-2 
? 
? 
XIX . . 
? 
? 
? 
? 
? 
1.6 
.6 
•3 
•5 
•4 
•S 
•4 
•S 
•S 
•S 
1.4 
XX . . 
? 
? 
? 
? 
? 
I.X 
•5 
.6 
•4 
•S 
•7 
•3 
.6 
.8 
1.0 
I.X 
Average 
? 
? 
3-i 
i-7 
•9 
1.1 
•7 
•5 
•3 
•3 
•3 
•S 
1.0 
1.6 
1.2 
1.8 
P. E. Intervals between Consecutive Ages 
TABLE LIII BLOCK-DESIGN TESTS 
135 
TABLE LIV 
Distances Above Zero of the Medians of Each Age 
Age 
Above Zero 
Below Next 
Higher Age 
4 
? 
? 
5 
o 
3-1 
6 
3-1 
1-7 
7 
4.8 
•9 
8 
5-7 
1.1 
9 
6.8 
•7 
IO 
7-5 
•5 
ii 
8.o 
•3 
12 
8-3 
•3 
13 
8.6 
•3 
14 
8.9 
•S 
IS 
9-4 
1.0 
16 
10.4 
1.6 
17 
12.0 
1.2 
18 
13.2 
1.8 
19 
15.0 
The reader’s attention is called to two matters of 
importance in the above standardization. First: Any 
age-group which manifested a difference between 50 
per cent and the per cent passing at each age of plus or 
minus 50 per cent (see Table LI), was located on the P. E. 
Scale at 4.6 P. E. above or below the median for that 
grade. It is admitted that 4.6 P. E. is an arbitrary figure, 
but in this the writer has followed the custom of his prede- 
cessors. Second: The basic assumption underlying P. E. 
standardization has always been that distributions of 
mental ability follow the normal curve. Attention has 
already been called to the criticism launched by Boring 
against this hypothesis. We must admit a certain degree of 
error in our standards because of this peculiar inadequacy 
of our standardization technique, and yet we need not 136 
INTELLIGENCE MEASUREMENT 
AgtS 
Distributions to Each Other 
Relation of .Age 
GRAPH 40 
P. E. Scale BLOCK-DESIGN TESTS 
137 
hesitate to use the results thus obtained, if we are at all 
times fully aware of their shortcomings. Until better 
instruments for norm-setting are placed at our disposal, 
we must utilize the best methods we now possess. 
It may not be out of place here to call attention to a 
common fallacy, frequently observed in the writings and 
the methodology of present-day devisers of tests, which 
pertains particularly to the matter of “weighting.” 
The situation is strikingly evident in group testing. For 
example, take one recently devised group-test for mental 
ability.1 It is a booklet containing six exercises. Exer- 
cise One is a list of questions. The answers “Yes-No” 
are tabulated in a column at the right. The child per- 
forming the test is asked to read the questions carefully 
one at a time and draw a line under the right answer to 
each question. This question-exercise consists of forty 
items graded in order of difficulty. (Question i is, “Do 
dogs run?” — Question 40 is, “Are judicial decisions ever 
enforced?”) Exercise Two, however, consists of only 
twenty arithmetic problems, also graded according to 
difficulty. (Example 1 is, “How many are 30 men and 
7 men?” and example 20 is, “A submarine makes 8 miles 
an hour under water and 15 miles on the surface. How 
long will it take to cross a 100-mile channel, if it has to 
go two-fifths of the way under water?”) A time limit of 
five minutes is allowed the pupil for each of these two 
exercises. The unfairness in the scoring lies in the fact 
that in adding up the total score each question success- 
fully answered in Exercise One has equal value with each 
1 Haggerty, “Intelligence Examination,” Delta 2, World Book Co., 
1920. 138 
INTELLIGENCE MEASUREMENT 
question successfully answered in Exercise Two. It is 
true that no attempt has been made to weight these 
exercises. And the impression becomes fixed that no 
weighting is better than one even crudely constructed. 
This was the apparent decision of the committee which 
drafted the Army Tests. 
The reason for mentioning this matter here is to justify 
the writer’s procedure in attempting some sort of weight- 
ing process for each of the designs, and not only as re- 
gards successful performance of each of the designs, but as 
well for the time spent and the number of moves made on 
each design. It is the writer’s contention that some 
rational and statistical basis for weighting is to be pre- 
ferred to no weighting of any sort. 
To come back then to our illustration. In the above- 
mentioned group-test a child may answer twenty ques- 
tions in Exercise One during the five minutes allowed, 
but in Exercise Two, the arithmetic problems, he may 
barely pass eleven. In summating the total score 
achieved, the answers to the questions inevitably have 
twice the importance as compared with the answers to 
the arithmetic problems. In other words, an item in 
the list of arithmetic problems has about half the 
weight of an item in the list of questions. In view of the 
lack of information on this particular matter, there seems 
to be no rational or statistical basis for this apparently 
arbitrary number of items in each exercise. 
It is the writer’s contention, therefore, that some 
reasonable attempt at weighting separate tests in a 
series is justifiable; that there is no escaping some sort 
of weighting; and that between the two evils of no BLOCK-DESIGN TESTS 
139 
weighting at all, and one rationally and statistically 
arrived at, the latter certainly is to be preferred.1 
In standardizing the block designs by the P. E. Scale 
Method, the writer has not followed exactly the orthodox 
procedure of Buckingham, Trabue, and Woody. If we 
keep in mind the fact that educational statistics per- 
taining to mental or pedagogical achievement are in- 
clined to be far less accurate than physical or chemical 
statistics, it seems unnecessary to utilize extra refine- 
ments of standardization in order to obtain satisfactory 
and workable norms. It would, perhaps, be no exaggera- 
tion to state that we have erred as frequently in over- 
refining our statistical procedures as in not refining them 
enough. 
Another matter worthy of note is that in the block- 
design tests the intervals between consecutive ages are 
not equal. The assumption frequently made is that 
increments of mental ability between ages are equal. 
The progress of the intervals for block-design ability is 
indicated in Graph 41. It appears that the differences 
are far more apparent between the ages 4 to n and 14 
to 19 than between the ages n to 14. The elimination 
of a few designs in the middle range, from designs 5 to 
15, might remedy this fault, if such it be. 
The zero point on our P. E. Scale is very easily located 
from the tables of data. It is the age at and below which 
no children pass a given design. 
1 The writer does not wish to be understood as adversely criticizing 
the Haggerty Intelligence Examination. The tests, as such, are excellent, 
but I am convinced that even their author would admit that the norms 
and methods of scoring are open to improvement. 140 
INTELLIGENCE MEASUREMENT 
Design 
(No.) 
Age 
4 
s 
6 
7 
8 
9 
10 
II 
12 
13 
14 
is 
l6 
17 
18 
10 
Final 
P. E. 
Value 
I 
3-i 
34 
3-5 
3-8 
345 
II 
4.2 
4.8 
5-i 
5-7 
5-7 
5-7 
5-7 
5-8 
5-9 
5-9 
545 
III 
44 
4-9 
5-o 
5-6 
5-9 
6.0 
6.0 
6.0 
6.1 
5-9 
5-58 
IV 
54 
6.o 
6-3 
6.8 
6.8 
6.8 
6.8 
6.9 
6.7 
6.6 
6.51 
V 
6.7 
6.7 
7.2 
6.7 
6.8 
6.9 
7.0 
7.2 
7-i 
6.92 
VI 
5-7 
6.6 
6.9 
7-5 
7-5 
74 
74 
7-5 
74 
7.2 
7-11 
VII 
74 
7.8 
8-5 
8-7 
8.8 
8.8 
8-7 
8.6 
8.8 
94 
10.5 
11.0 
12.6 
9.20 
VIII 
6.9 
7.2 
7-7 
7-7 
7-7 
7-7 
7-7 
7-7 
7-7 
8.2 
7.62 
IX 
6.9 
7-i 
7-7 
7-8 
7.6 
7-5 
7-5 
74 
7.2 
7.41 
X 
8-5 
8.8 
8.9 
9.0 
9.1 
9.1 
9.0 
9.2 
9-7 
10.6 
9.19 
XI 
8-3 
8-7 
8-7 
8-7 
8.6 
8-7 
8.8 
9.1 
9.9 
11 -3 
12.2 
9-36 
XII 
7.6 
7-9 
8.2 
8-3 
8-3 
8.4 
8.4 
8.4 
8-5 
8.9 
8.29 
XIII 
9.2 
9-3 
9-5 
94 
9-5 
94 
94 
9.6 
9.41 
XIV 
8-7 
8-7 
8.8 
8.9 
8.8 
8-7 
8.8 
8.9 
94 
10.5 
11.0 
9.20 
XV 
9.0 
9.0 
9.0 
9.0 
9.1 
9.1 
9.2 
94 
9.9 
9.18 
XVI 
8.9 
8.9 
8.9 
8.8 
8-7 
8-7 
8.8 
9-3 
10.3 
10.6 
9.19 
XVII 
9.0 
8-5 
8.1 
7-9 
8.1 
8.2 
8.4 
9.0 
8.40 
XVIII 
9.1 
9-3 
94 
9-3 
9.1 
9.0 
9.0 
9.0 
9-iS 
XIX 
9.8 
9.9 
IO.I 
9.9 
9.8 
9.6 
9-7 
10.2 
II-3 
12.0 
12.4 
10.42 
XX 
10.3 
10.5 
10.4 
10.3 
IO.I 
9-7 
9.9 
10.3 
11.1 
n-3 
12.0 
IQ-53 
Location Above O P. E. of Each Design at Each Age 
TABLE LV BLOCK-DESIGN TESTS 
141 
GRAPH 41 
Location of Age Medians on 
P. E. Scale 
(Showing Size Relation of Intervals) 
P. E. Scale 
Ages 142 
INTELLIGENCE MEASUREMENT 
Table LV may then be constructed from the data of 
Tables LII and LIV, giving the location above zero 
P. E. of each design at each age. In the last column to 
the right (Table LV) are given the final P. E. values of 
each design, obtained by averaging the findings for that 
design at the various age levels. We differ, again, at 
this place in our procedure from that followed by Thorn- 
dike’s students, by not rejecting any of our individual 
P. E. values, and by giving each value equal weight. 
Graph 39 is a pictorial arrangement of the twenty 
designs on the P. E. Scale. 
(b) Time and Move Norms 
As has already been stated, the writer felt in the very 
early stages of the standardization process, that time and 
number of moves were very important diagnostic criteria 
which could not conscientiously be left out of considera- 
tion in the final assignment of a score for a specific per- 
formance. Hoping for some clue whereby the three 
criteria: successful performance, time, and moves, could 
be amalgamated satisfactorily in a single score-value, 
the record of every test made contained a complete 
statement of these three reactions for each design. It 
was difficult in the preliminary stages of the investiga- 
tion to state dogmatically which of the three criteria was 
most and which least important. - But at the conclusion 
of our experimentation sufficient objective evidence had 
been accumulated to answer these questions more or less 
adequately. 
One clue which seemed more worth while developing 
than any other was the relation between the above- BLOCK-DESIGN TESTS 
143 
mentioned three criteria and life age. (Mental age 
would, undoubtedly, have served as well.) If success, 
time, and moves were diagnostic tools of varying im- 
portance, it seemed plausible that these differences would 
become apparent if correlated either with life age or 
with mental age. 
This was therefore done with the following somewhat 
startling results: 
CORRELATIONS 
Life Age and Raw Scores (241 Cases Public School Chil- r P.E. 
dren, “at grade”) +.71, ±.02 
Life Age and Time (Averaged first the individual co- 
efficients and then the indi- 
vidual P. E.’s for each of the 
twenty designs. Note: Only 
those coefficients were used 
where r was at least four times 
the P. E. The results for five 
designs were therefore not 
used. See Table LVII.) +.38, ±.06 
Life Age and Moves (Averaged the individual coeffi- 
cients for r and P. E. as above. 
Note: Only those coefficients 
• were used where r was at least 
twice as large as the P. E. The 
results for six designs were 
therefore not used. See Table 
LVII.) "h.20, ±.07 
Binet Mental Age and Raw Sr ores 
(366 cases. Included are all the 
subjects of this study.) +.82, ±.01 
From these figures it was possible to conclude for this 
test that success, as such, is about twice as important a 
diagnostic criterion as time (ratio 71 to 38), and that 
time is about twice as important as moves (ratio 38 to 
20). In other words, giving moves a value or a weight 144 
INTELLIGENCE MEASUREMENT 
of i, time should, according to the above ratio, receive 
a weight of 2, and success a weight of 4. It is this re- 
lationship that is referred to when the ratios 4:2:1 are 
stated in various sections of this monograph. 
Scientific attitude precludes the existence of bias. 
Nevertheless, it is the rare experimenter who can count 
himself free from all sorts of fixed notions. The writer’s 
conception of the relative importance of time and moves 
squared with the prevalent opinion that moves are more 
important diagnostic-indicators of intelligence than 
time. The poor correlations between “speed” tests 
versus “power” tests helped confirm this belief. Be- 
sides, it had come to be accepted that to attempt the 
combination of such utterly diverse entities as success, 
time, and moves was nothing short of quixotic. 
In presenting the above figures there has been no desire 
to enter into a controversy with common opinion. The 
facts are presented as facts, and as such should receive 
their requisite evaluation. The writer knows of no other 
instance where an attempt has been made by similar 
impersonal methods to determine objectively the weights 
to be accorded the three intelligence-criteria' mentioned 
above, and will await with interest the efforts of others 
in this direction. 
The correlation between life age and the raw scores 
(the factors of time and moves not having been taken 
into consideration) is presented in Table LVI. (All of 
the correlations in this monograph have been determined 
2 xv 
by means of the formula: r— —=====— modified 
\ 2x2 • \ 2y2 
by the writer. See Appendix II.) BLOCK-DESIGN TESTS 
145 
TABLE LVI 
Life Age and Raw Scores Correlation 
Designs 
Completed 
Life Age 
Total 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
IS 
l6 
17 
o 
8 
3 
I 
1 
13 
i 
2 
8 
4 
3 
2 
1 
1 
21 
2 
3 
3 
5 
7 
1 
19 
3 
2 
7 
5 
2 
1 
1 
1 
1 
20 
4 
i 
2 
3 
2 
1 
1 
1 
1 
12 
S 
2 
3 
4 
4 
2 
IS 
b 
I 
3 
2 
3 
4 
2 
1 
2 
18 
7 
I 
2 
1 
3 
2 
3 
1 
3 
16 
8 
2 
1 
1 
1 
2 
1 
8 
9 
1 
1 
2 
1 
1 
2 
1 
1 
10 
IO 
2 
1 
4 
1 
1 
9 
IX 
1 
3 
2 
1 
1 
8 
12 
1 
1 
2 
1 
1 
1 
7 
13 
1 
3 
2 
1 
1 
8 
14 
1 
2 
2 
2 
7 
i.S 
1 
2 
5 
1 
9 
16 
1 
2 
3 
1 
7 
17 
1 
1 
1 
1 
1 
1 
2 
1 
9 
18 
2 
3 
2 
2 
9 
19 
1 
1 
1 
2 
1 
1 
1 
8 
20 
2 
3 
2 
1 
8 
Total 
IS 
26 
28 
24 
28 
25 
22 
22 
23 
IS 
11 
2 
241 
r — + .71 P. E. = ± .02 
The 241 children included in Table LVI were only 
those of the public school group who were located at the 
proper grade for their life age. 
The correlations between life age and time and be- 
tween life age and moves for each of the twenty designs 
is presented in Table LVII, together with their respective 
probable errors. All the correlations are positive, except 
where otherwise indicated. 
In the fourth and eighth columns of the table are pre- 
sented the ratios between the coefficients for time and 146 
INTELLIGENCE MEASUREMENT 
Design 
Number 
Correlation 
Ratio 
Time: Moves 
Design 
Number 
Correlation 
Ratio 
Time: Moves 
Age-Time 
Age-Moves 
Age-Time 
Age-Moves 
r — P. E. 
r — P. E. 
r — P..E. 
r —P. E. 
I . . 
.38 ± .04 
.22 ± .04 
1.7 : 1 
XI . 
.46 + .06 
.18 ± .08 
2.6 : x 
II . . 
45 ± -04 
.26 ± .04 
1.7 : 1 
XII . 
.41 ± .06 
.27 ± .07 
1-5 : 1 
Ill . . 
.38 ± .04 
•17 ± -os 
2.2 : 1 
XIII . 
•59 ± -06 
.23 ± -09 
2.6 : 1 
IV . . 
•S3 ± -04 
•35 ± -OS 
i-5 : 1 
XIV . 
•45 ± .07 
.21 ± .08 
2.0 : 1 
V . . 
.50 ± -04 
.27 + .05 
1.9 : x 
XV . 
.46 ± .07 
.22 ± .08 
2.1 : 1 
VI . . 
•34 ± -OS 
.12 ± .06 
2.8 : 1 
XVI . 
.20 ± .08 
•03 ± .08 
VII . . 
.31 ± -07 
.11 ± .07 
XVII . 
•34 ± .05 
•45 ± .06 
i.2 : 1 
VIII . . 
.16 ± .06 
.00 ± .06 
XVIII . 
.10 ± .09 
.02 ± .09 
IX . . 
•47 ± -05 
•31 ± -05 
1.5 : 1 
XIX . 
.41 ± .10 
•49 ± -09 
0.8 : 1 
X . . 
.31 ± .08 
.08 ± .08 
XX . 
•14 ± .13 
— .10 ± .13 
Average 
.38 ± .06 
.20 + .07 
1.9 to 1 
Life Age with Time and with Moves 
TABLE LVII 
Correlations BLOCK-DESIGN TESTS 
147 
moves for each design. These ratios are finally averaged, 
with the result that time appears a better diagnostic 
criterion than moves to the extent of 2 to i. In aver- 
aging the coefficients for life age and time the results for 
Designs VIII, X, XVI, XVIII and XX were not in- 
cluded, because their coefficients were less than four 
times their P. E.’s. And in averaging the coefficients 
for life age and moves, the results for Designs VII, VIII, 
X, XVIII and XX were not included, because their co- 
efficients were less than twice their respective P. E.’s. 
Consequently in averaging the final ratios for time and 
moves the ratios for Designs VII, VIII, X, XVI, XVIII 
and XX were not used. 
No other methods have been utilized to check the 
validity of this procedure for determining the relative 
weights to be apportioned success, time, and moves. 
However, the method outlined above is objective and 
free from personal bias. 
As regards sex differences for time and moves, there 
were no greater differences apparent than might be 
expected from the expected errors of sampling. 
To go on then to the separate norms for time and for 
moves, in Table LVIII are found the figures for the 
average times (arithmetic mean), and in Table LIX the 
average moves for each design at each chronological age, 
from 6 to 17. Thus for Design I, at age 6, 72 seconds 
are taken for successful completion, as compared with 
22 seconds at age n, and with only 7 seconds at age 17. 
And again, for Design XIX, at age 9, 258 seconds (over 
4 minutes) are necessary for successful completion, as 
compared with 171 seconds at age 14, and only 99 seconds 148 
INTELLIGENCE MEASUREMENT 
Designs 
XX 
lO M O' M O H 
M t^OO 
CN M M M CN M M 
XIX 
00 CN NV)NH MOO O' 
V) O' WOO 
(NMMMMMMM 
XVIII 
CN co M CN rfMOOvO M 
M o 'O 00 
CNCNHMMMWMM 
XVII 
t>-00 vO CN \0 w VO 00 00 
VO M m o M 
MMMMMMMM 
XVI 
m O co <n 
rfiOt^NNfOfO^W 
MMMMMMMMM 
XV 
VO *0 CN O'M M \0 CO 
O' CO O Tj-vO Cl rf O 
MMCNMMMMMM 
XIV 
O' CN O' O <N CN 
M O ’O'O CO CN Tf rf <N 
CSCNMMMMMMM 
XIII 
(N rf CO M M M t'- O' 'Cf 
co tJ-vO O0 CN h 'O N rf 
M M M M M M 
XII 
cow rj- CN M cO O' O' *0 
O cO 'O co Cl 't cO O' O' O' 
CS (N M M M M M 
X 
CO Tf vO IOVO lO o Cl CO 
vOrfMMMMOOO'O'^ 
M M M M M M 
X 
cn co Tf co *0 rJ-vO Q vO CN 
Tt<NlOMCNTtMOOOO 
MMMMMMMMM 
a 
loin W) « O O ■'t 
t'. O' 00 MOiO't'trOtOH 
IIIA 
VO Tf CO'O M lO M CO 
CO VO Tj- CO 
VII 
O0 CN M vO tJ- o WVO OCNVO 
O O' CO O"0 VO VO lOO 
M 
> 
CN OOO CO O' CN O' Tf rf O' VO 
CN lO CN M 
> 
CN M O' O00 O O VO O' M 
O' 0"0 lO'O -<3- CO CO CN M 
a 
Os CN O' CN Tt-00 CO CN 
co co cn co cn m 
a 
O' O t*- cn CO V) lO CO O'VO Tt- O' 
lo N Tt CO Tf Cl CN CN M CN M 
a 
CO CN OO OO CN VO N M VO 00 00 *0 
N N co CO CO CN CN CN M M M 
- 
CN Tt- Tf rt CN 10»00 
C^COCOCNCNCNCNMMMM 
Life 
Age 
vO O' O M CN co rf IOVO 
MMMMMMMM 
Time Norms (Seconds) 
TABLE LVIII BLOCK-DESIGN TESTS 
149 
o V)fO OOO V0 lo 
X 
4 rfCO CO 
CS W COM CO W W 
v 
O O O <M O O' VO »*» o 
NOON CO00 NlOH 
Tf CO CO CO CO CN CN <N CN 
a 
lo O O Tj-vo VO CO CO *0 
> 
X 
Tf co d 6 oo w oo o 
CO CO N CO CM CO W cow 
a 
m o m u) ion Tf o 
5 
ci O 6 Tj* 6 
cocococow W W W W 
M 
O O O N W)W)N «) O 
£ 
ci w 4 d d con 
w cocococow W cow 
ONNOOO»0>ON.O 
X 
W o d VO O O NOO N 
cococow COCOW Cl Cl 
COCO N> M O N" r$* lo 
X 
lorfdw C>» C>* M d M 
cocow cow ci cow CO 
O cc COOO « O 00 O' o 
a 
X 
t>*vo cocod 
MMCICIMMMMM 
O O co O m co co co *0 
X 
N HO0 O O TfvO M 
CICIMMMMMMMMM 
o ioNaa 'too o n o 
§ 
X 
n* do cd co oo n O 
CIMMMMMMMMM 
O O rj* w O' m tt CO O O 
w 
p 
X 
d d d 4 o tj-woo 6 d 
mwmcncicicimcim 
a 
co O O rj- N o N> N- M Cl lo 
C-. 4 *-0 W O' O' N O' N N Tj- 
M M M M 
M 
M O' H Tj- O N M V) 
a 
> 
o vo oo o co oo 0 m 
MM M M 
O w o VO N- rj-vO CO rf W o 
> 
i>» -4- loco ci cd lo cd cd w d 
MM MMMMMMM 
O Ifl O t 1000 ti HO & o 
> 
cdcoMCiciowoO cooo N» 
MMMMMMM M 
O N. O' nt O' O' O COOO O lo 
> 
id cd m o w d ooo d O' 4 
M M M M M 
-t LO CN NION VO CO N tO 
& 
o ci ci M 00 00 00 0 N 
M M M M 
_ 
CO N- CO W co 1C N o w M co O 
cd d d-vd dvo x>* vd o cd to to 
0"0 N O N NOOOO o 
a 
M dvo Lovd lovO rf LO LO 
M 
0 o vo q>vo q co o 
cd LoLOLOLd'd-LOTt-'d-'d-d'Tf 
34 
VO N* CO Qn o m w CO rf N* 
MMMMMMMM 
Move Norms (Moves) 
TABLE LEX 150 
INTELLIGENCE MEASUREMENT 
at age 17. So, too, for moves. For Design I, at age 6, 
8.9 moves are made before success is finally accom- 
plished, as compared with 5.6 moves at age 10, and with 
4.6 moves at age 14. And again, for Design XIX, at 
age 9,42.0 moves (almost 3 moves to each block) are made 
before the design is successfully completed, as compared 
with 28.9 moves at age 14, and only 21 moves at age 17. 
An analysis of sex differences reveals the following: 
For designs I-X, ages 6-8, the tendency is greater 
for boys to give longer times on the same designs, 
although the frequency for giving long reaction times 
is about the same for both groups. For designs I-X, 
ages 9-13, boys more frequently exceed the times of the 
girls (ratio: boys, 31; girls, 18), but the amount of ex- 
cess is about the same (ratio: boys, 15"; girls, 18"). 
For designs I-X, ages 14-16, and for designs XI-XX, 
ages 9-13, no tendency is evident for boys to exceed 
girls in time per design, or vice versa, the excess being 
about the same. And in designs XI-XX, ages 14-16, 
boys more frequently give longer times (ratio: boys, 24; 
girls, 6), but the girls give longer times whenever they 
exceed in time (ratio: boys, 27"; girls, 34")- In general, 
it may be stated that boys tend to give longer reaction 
times more frequently than girls, but when girls take 
longer the excess in time is greater than the excess in 
time for boys. 
As regards sex differences in moves, there are no ap- 
preciable differences except for designs I-IX at ages 6-8, 
and 9-13. In the first instance, the tendency to make a 
greater number of moves is about the same, but the 
excess is greater for boys than for girls; and in the latter BLOCK-DESIGN TESTS 
151 
case, the tendency to make a greater number of moves 
is stronger for boys than for girls, but the excess of moves 
is about the same. 
Tables LX, LXI, and LXII give the correlations be- 
tween time and moves for the four-block, nine-block, and 
sixteen-block designs. The correlations are high, as one 
would expect. 
TABLE LX 
Correlation between Time and Moves 
Moves 
Time 
Total 
1'-3°' 
31 
i'i'-i'3o' 
1'31 '-2' 
2'l *-2'30’ 
4 . . . 
140 
IO 
1 
151 
5- 8 . . . 
192 
90 
8 
3 
I 
294 
9-12 . 
13 
IO 
27 
6 
4 
60 
13-16 . . . 
3 
18 
11 
7 
39 
17-20 . . . 
IO 
8 
6 
24 
21-24 . . . 
6 
2 
7 
15 
25-28 . . . 
1 
1 
2 
29-32 . . . 
1 
1 
2 
4 
33 and over . 
1 
1 
Total 
345 
113 
7i 
32 
29 
590 
(4-block designs) 
r = + .76, ± .01 
Four groups of workers may be segregated from these 
figures by horizontal and vertical divisions of the tables. 
One group which works rapidly and accurately, and con- 
sists almost entirely of those who succeed. A second 
gi'oup which works somewhat too rapidly perhaps, and 
attempts numerous varieties of block-combination. A 
third group which works slowly, makes few moves and 
appears deliberative in procedure. And a fourth group 
which not only works slowly, but also attempts numerous 
combinations, many bordering on the irrational. 152 
INTELLIGENCE MEASUREMENT 
TABLE LXI 
Correlation between Time and Moves 
Moves 
Time 
Total 
I -30 
i'i 
2'l'-2'3o" 
2'3l'-3' 
3'l'-3'3°' 
3'3l'-4' 
9 
4 
I 
5 
10-15 
I 
4 
9 
9 
2 
2 
27 
16-21 
2 
10 
12 
12 
7 
43 
22-27 
I 
3 
3 
6 
4 
2 
19 
28-33 
I 
4 
I 
I 
7 
34-39 
1 
I 
40-45 
I 
1 
Total 
I 
10 
21 
24 
18 
20 
5 
4 
103 
(9-block designs) 
r = + .58, ± .04 
Correlation between Time and Moves 
TABLE LXII 
(16-block designs) 
Moves 
Time 
Total 
31’-1' 
l'3l ’-2' 
2'l'-2'30' 
2'3I '-3' 
3'i'-3'3°’ 
3'3l'-4' 
4'i'-4'30* 
17-20 
3 
I 
I 
I 
6 
21-24 
1 
13 
IO 
6 
2 
32 
25-28 
1 
II 
9 
II 
2 
34 
29-32 
2 
7 
6 
7 
I 
23 
33-36 
3 
8 
8 
4 
23 
37-40 
2 
5 
2 
3 
I 
13 
41-44 
2 
3 
2 
I 
8 
45-48 
1 
3 
I 
5 
49-52 
53-56 
1 
I 
2 
Total 
I 
17 
24 
28 
36 
20 
16 
4 
146 
r = + .70, ± .03 BLOCK-DESIGN TESTS 
153 
(c) Result: The P. E. Scale 
On the basis of these results bearing upon the relation 
between time and moves, and in view of the earlier find- 
ings, the following score-card was devised (Table LXIII). 
The attempt was made to apportion due weight to 
(a) score value, (h) time, and (c) moves in the ratio of 
about 4: 2: i. 
TABLE LXIII 
Score Card 
Design 
P.E. Score 
Excess Time 
Excess Moves 
Number 
Value 
Deduct i Point 
Deduct 2 Points 
Deduct i Point 
I 
II 
III 
3 
5 
6 
21" and over 
31" and over 
21"- 35" 
36" and over 
6 and over 
7 and over 
8 and over 
IV 
7 
31 "-i' 
1' 1 "and over 
10 and over 
V 
7 
36r-i' 5" 
1' 6" and over 
11 and over 
VI 
7 
36r-i* 
1' 1" and over 
12 and over 
VII 
9 
56"-i'io" 
i'ii" and over 
15 and over 
VIII 
8 
4i"- 55" 
56" and over 
10 and over 
IX 
7 
4i"-i'io" 
i'ii" and over 
11 and over 
X 
9 
i/56"-2,io" 
2'n" and over 
22 and over 
XI 
9 
i'36"-2' 
2' 1" and over 
18 and over 
XII 
8 
i'46*,-2,3o" 
2'31" and over 
19 and over 
XIII 
9 
i'3i'-2'3o' 
2'3i" and over 
18 and over 
XIV 
9 
2'26"-2'4o" 
2'41" and over 
32 and over 
XV 
9 
2'26"-2'40" 
2'41" and over 
30 and over 
XVI 
9 
2 21 -2 33 
and over 
31 and over 
XVII 
8 
i,56<'-2,25‘' 
2'26" and over 
30 and over 
XVIII 
9 
2'4I '-3' 0" 
3' 1" and over 
32 and over 
XIX 
IO 
2'4i"-3' 5" 
3' 6" and over 
31 and over 
XX 
ii 
2,4i*’-2'sstf 
2'56" and over 
30 and over 
Maximum Score = 159 Points 
The information in the last three columns of the pre- 
ceding table was obtained by plotting first the norm 
data for each design at each age, both for time and for 
moves. All the curves were then smoothed. After that 
the year-range of the curve was divided into as nearly 154 
INTELLIGENCE MEASUREMENT 
three equal year-divisions as possible. Thus for design 
XI the total year-range for the time-and-life-age curve 
was nine years (age 8 to age 17). All times, then, falling 
within the range of years between 14 and 17 were 
allowed as legitimate. One point of the score value of 
the design, however, was to be deducted if the time 
taken fell within the range of years from n to 14, and 
two points were to be deducted if the time taken fell 
within the earliest range of years, namely, between the 
years 8 and n. The same procedure was utilized for 
determining the deductions for excess time on the other 
designs, except designs I and II for which the method 
pursued for moves was followed. For the one point 
deduction for excess moves the year-range was divided 
into two parts. The range of moves covering the higher 
half of years was regarded as legitimate, whereas the 
range of moves covered by the lower half of years was 
regarded in excess and one point was designated as a 
reasonable deduction from the score value of that design. 
Other methods for arriving at an objective criterion 
for making subtractions for excess time and moves were 
possible.1 For example, instead of the year-range being 
divided into three equal divisions, the score-range might 
have been thus divided. Another method possible 
would have been to take the score-range and divide it 
into four equal parts. Two points would then be de- 
1 It did not seem that any other possible methods possessed any 
superior value over the one actually utilized, and in any event, what- 
ever the procedure for penalizing excess moves and time, the chances 
are very great that no great differences would have resulted in the 
ultimate score assignments to each performance of the block-design 
tests, and in the final standards. BLOCK-DESIGN TESTS 
155 
ducted for the first quarter of the range falling at the 
lowest ages, one point would then be deducted from the 
middle range of 50 per cent, and all times falling within 
the upper range of 25 per cent would have been regarded 
as legitimate. 
Utilizing the scoring instrument thus devised, all the 
tests were then re-scored. The original correlation be- 
tween the Binet Scale and the number of designs suc- 
cessfully completed (already designated as the “raw 
score,” time and moves not being taken into account), 
was + .82, ± .01. The table is presented herewith: 
TABLE LXIV 
Correlation between Binet Mental Age and Raw Block-design 
Scores 
Bind Age 
Raw Scores 
3 
4 
s 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
Total 
o 
3 
7 
14 
14 
3 
1 
1 
43 
I 
7 
9 
9 
2 
2 
1 
1 
I 
32 
2 
5 
5 
7 
7 
3 
3 
30 
3 
4 
6 
6 
5 
1 
1 
2 
1 
26 
4 
i 
7 
6 
S 
2 
1 
I 
1 
24 
S 
I 
3 
9 
6 
5 
1 
1 
1 
27 
6 
i 
5 
4 
4 
4 
3 
2 
I 
24 
7 
4 
6 
6 
3 
1 
I 
21 
8 
2 
3 
3 
1 
1 
1 
11 
9 
i 
1 
2 
4 
I 
1 
2 
12 
IO 
1 
3 
3 
3 
I 
11 
ii 
4 
4 
1 
1 
10 
12 
1 
1 
2 
1 
1 
I 
1 
8 
13 
1 
4 
2 
2 
1 
10 
14 
2 
4 
1 
5 
1 
1 
14 
IS 
1 
I 
4 
1 
2 
1 
10 
16 
1 
2 
4 
I 
1 
9 
17 
1 
3 
I 
2 
1 
I 
1 
1 
11 
18 
1 
1 
3 
1 
3 
2 
11 
19 
2 
2 
1 
2 
1 
1 
2 
11 
20 
1 
1 
3 
3 
1 
2 
11 
Total . . 
3 
7 
14 
3i 
29 
Si 
37 
44 
44 
3i 
20 
17 
11 
11 
7 
4 
5 
366 156 
INTELLIGENCE MEASUREMENT 
Although some of the values in the preceding table 
are scattered, there is a marked consistency in the in- 
crease of raw score with increase of mental age. 
Upon rescoring the 366 tests in order to assign due 
weight to success, time, and moves, the coefficient of 
correlation is not changed to any appreciable amount, 
but there is a marked decrease in the fluctuation, or 
spread, of scores over any given range of years. This is 
more apparent after the elimination of certain designs, 
discussed more in detail in the succeeding section of the 
monograph. The correlation table follows: 
TABLE LXV 
Correlation between Binet Mental Age and Score Points 
Score Points 
Mental Age 
3 
4 
s 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
Total 
o . 
3 
7 
14 
14 
3 
I 
1 
43 
I-IO . 
15 
19 
20 
12 
6 
5 
1 
1 
1 
80 
II- 20 
2 
3 
13 
11 
9 
2 
2 
4 
1 
47 
21- 30 
3 
9 
7 
7 
5 
4 
3 
2 
40 
31- 40 
7 
2 
4 
6 
3 
1 
2 3 
41- 50 
1 
1 
1 
4 
S 
1 
1 
1 
IS 
51- 60 
4 
6 
4 
3 
1 
1 
19 
61- 70 
2 
3 
2 
1 
I 
1 
1 
1 
12 
71- 80 
4 
3 
1 
1 
9 
81- 90 
2 
2 
2 
3 
1 
2 
12 
91-100 
3 
2 
S 
3 
1 
2 
16 
101-110 
1 
3 
2 
2 
8 
111-120 
1 
1 
1 
2 
1 
2 
8 
I21-130 
1 
3 
1 
1 
1 
2 
9 
131-140 
2 
2 
1 
2 
2 
2 
11 
141-150 
1 
2 
1 
2 
1 
7 
ISI-160 
3 
2 
1 
1 
7 
Total . 
3 
7 
14 
31 
29 
Si 
37 
44 
44 
3i 
20 
17 
11 
11 
7 
4 
5 
366 
f — + -83, ± .01 BLOCK-DESIGN TESTS 
157 
In order to appreciate the significance of this coeffcient, 
the following list of correlations between the Stanford- 
Binet test and other intelligence tests is presented: 
Block-design Test and Binet Test . . + .83 
Army Alpha and Binet Test,1 . + .80 to + .90 
Army Beta and Binet Test,1 . . . + .73 
Stanford-Binet and Stanford-Binet (repeated tests),1 -j- .94 to + .97 
Stanford-Binet Entire and Stanford-Binet Abbreviated (2 tests per 
year)1 + .92 
Each Army Performance Test and Stanford-Binet1: 
1. Ship Test 
2. Manikin and Feature Profile Test 
3. Cube Imitation Test 
4. Cube Construction Test 
5. Form Board Test 
6. Reproducing Designs Test 
7. Digit-Symbol Test 
8. Maze Test 
9. Picture Arrangement Test 
10. Picture Completion Test 
Lowest Correlation, +.48 
Highest Correlation, +-78 
Abbreviated Army Performance Test (5 Tests) and Stanford Binet,1 
+ -84 
Stanford-Binet and Seguin Form Board,2 . . -f- .55 
Porteus and Stanford-Binet2 
Boys . . . + .21 
Girls . . . + .60 
Healy’s 3 Form Boards (Mare and Foal, Construction Test A, and 
Construction Test B) and Stanford-Binet Mental Age,3 . + .45 
Porteus Mental Age and Stanford-Binet Mental Age 3 . . . + .79 
Army Alpha 
Teachers Estimate 
Class Standing 
and Ferguson Form Boards4 
+ .5i 
+ -So 
+ .56 
Grade Location and Form Board Ability,4 + .80 
1 C. S. Yoakum and R. M. Yerkes:“ Army Mental Tests” (New York, Holt, 1920), p. 20 
* S. D. Porteus: “Porteus Tests—The Vineland Revision” (Vineland, 1919), p. 28. 
19, 20. 
’Elizabeth L. S. Ross: “Vocational Tests for Mental Defectives: Studies in Mental 
Inefficiency” (1921), 2: i-t>. 
* G. O. Ferguson, Jr.: “A Series of Form Boards,” J. of Exp. Psychol., 1920, 3: p. 37- 158 
INTELLIGENCE MEASUREMENT 
Inter-Test Correlations 1 
TABLE LXVI 
(Table Rearranged) 
Army 
Thurstone 
Pressey 
Indiana 
Survey 
Otis 
Army 
+ .60 
+ .36 
+ .36 
+ •57 
Thurstone 
+ .60 
+ .25 
+ -25 
+ 46 
Pressey .... 
+ -36 
+ -25 
+ .22 
+ -44 
Indiana Survey . 
+ -36 
+ .25 
+ .22 
+ -34 
Otis 
+ -57 
-f- .46 
+ -44 
+ -34 
Pintner’s Non-Language Group-Test and Stanford-Binet I. Q.,2 -f .66. 
A cursory survey of the stragglers in the upper right- 
hand corner of the table (LXV) reveals children who ob- 
tain high Binet scores, but do poorly in these tests. 
These are generally children who are retarded mentally 
or are feeble-minded. There seems to be evidence that 
children of inferior endowment do poorer work with 
these tests than children of superior endowment but of 
the same mental age. So, too, the stragglers at the lower 
left-hand corner of the table are children who are foreign 
born, the language-handicapped, such as the Portuguese, 
Italians, Japanese, and Chinese, who do poorly with the 
Binet, yet obtain good scores on the designs. 
The following are the median scores at each mental 
age. These medians were determined from a table of 
1 J. A. Clement: “ Use of Mental Tests as a Supplementary Method for Making School 
Adjustments in Colleges.” Educ. Adminislr. and Superv., 1920, 6: p. 441. 
2 R. Pintner: “A Non-Language Group Intelligence Scale. ” /. of Applied Psychol 
1919, 3: 199-214, p. 214. BLOCK-DESIGN TESTS 
159 
original data, no grouping of scores beyond the one unit 
being made for scores 1 to 15. Beginning with score 16, 
however, the frequency intervals were 5 score-points. 
The median values in Table LXVII are, therefore, inter- 
polated only from age ten up. The left half of the table 
presents actual values, and the right-hand portion the 
medians obtained from the smooth curve of Graph 42. 
TABLE LXVII 
Actual Medians 
Smooth Curve Medians 
Age 
Score Points 
Age 
Score Points 
3, 4, 5 
o 
3> 4i S • • • • 
0 
6 
' i 
6 
I 
7 
5 
7 
S 
8 
IS 
8 
9 
9 
13 
9 
17 
IO 
29 
10 
29 
ii 
48 
11 
4i 
12 
63 
12 
ss 
13 
S3 
13 
71 
14 
92 
14 
88 
is 
118 
is 
104 
16 
114 
16 
118 
17 
143 
17 
133 
18 
138 
18 
143 
19 
132 
19 
152 
20 
159 
20 
159 
Median Scores at Each Mental Age 
Graph 42 is the curve showing the increase of score 
with mental age. The dots represent the median scores 
at each age. The deviations between the curve and the 
actual medians are explained largely on the basis of 
idiosyncracies in the age-groups tested. Thus at age 
thirteen, the difference is quite striking. But by referring 160 
INTELLIGENCE MEASUREMENT 
back to the table showing the correlation between Binet 
age and life age (Table XIII) it will be observed that at 
thirteen the median mental age of the group examined 
(33 —16 boys and 17 girls) was about twelve years, a 
-GRAPH—42- 
J n c rea se_of_Sco re_Po i n ts_wi th_ Age. 
Block - design Score Points 
Binet Mental Age 
retardation of approximately one year. Referring back 
to the curve (Graph 42) for the performance of the 12- 
year-mental-age group, it will be observed that this 
group attains scores superior, on the average, to the 
12-year standard, but inferior to the 13-year standard. 
The explanation is practically the same for the deviations 
at the other ages. BLOCK-DESIGN TESTS 
161 
There was a twofold motive in further work to make 
the block designs a reliable and a serviceable test: In 
the first place, it was deemed wise to reduce the time 
for giving the test as much as possible without a sacrifice 
of reliability; and, on the other hand, there were a few 
designs which, if eliminated, would tend to decrease the 
scatter of scores over a given range of mental ages. It 
was for these reasons that further analyses were made, 
in order to determine which designs could be sacrificed 
in order to bring the above desirable conditions to pass. 
Space prohibits an extended discussion of the technique 
of elimination, but the main features of the revision are 
presented in the following section. 
4- FINAL REVISION 
(a) Eliminations 
In reducing the number of designs it was recognized 
that the most desirable procedure to follow would be 
that which would result in the greatest reduction of 
scores for those of progressively poorer mental capacities, 
without affecting the scores of those of higher mental 
development. A general leveling of scores, without a 
compensating increase in the diagnostic importance of a 
unit score, as a rule, decreases the actual diagnostic value 
of any measuring scheme. The designs, therefore, 
which were considered for elimination were those falling 
within the middle range, namely, designs VII, XI, XIII, 
XIV, XV, XVI, and XVII. On the basis of various 
criteria which were utilized, those designs could more 
easily be sacrificed than the others. 162 
INTELLIGENCE MEASUREMENT 
Three elimination schemes were tried: 
(а) the elimination of designs VII, XI, XIII, XVI, 
and XVII; 
(б) the elimination of designs XI, XIII, XIV, XV, 
and XVII; and 
(c) the elimination of designs XI, XIII, and XVII. 
The final eliminations to be effected were to be those 
which would (a) most effectively reduce the scatter or 
range of scores from ages 3 to 19, (b) that would save 
time with least sacrifice of diagnostic efficiency, (c) that 
would result in a higher coefficient of correlation between 
block-design score and Binet mental age, and (d) one 
that would show an increased reliability of final score 
achieved. 
Elimination Method (a). Thus elimination method 
(a) permitted a maximum score attainment of 115. The 
correlation beween the number of points lost (from the 
original score using the twenty designs) and Binet age 
was + .63 d The number of cases in which the score 
was affected was 140 or 38 per cent. Analyzing the 
results of this re-scoring method more closely, it becomes 
apparent that taking each mental age there has been a 
greater ratio of reduction in the scores of the lower ages 
(73 per cent) and a smaller ratio of reduction in the 
scores of the upper ages (27 per cent) — although the 
absolute values show a gradual increase in points lost 
with increase of age. The changed scores make for a 
1 This coefficient may also be interpreted as the correlation between 
these five designs taken alone and Binet mental age. This is a fair 
criterion of the reliability of the block-design tests as a whole, if thes,. 
five designs are the poorest. BLOCK-DESIGN TESTS 
163 
greater differentiation between the lower and the higher 
mental ages. Although the extremes of score were 
from 5 to 159, the latter score being 31 times the 
former, the extremes of per cent lost were from 8 to 41, 
only 5 times the former instead of 31. 
Elimination Method (b). Rescoring the tests on the 
basis of the eliminations by method (b) the maximum 
score attainable is 115, the same as by method (a). Here 
again the correlation between block-design scores and 
Binet mental age was -f .85 ± .01. In this instance, 
however, the scores at the lower ages were affected to 
the same extent as by method (a), but the scores at the 
higher ages were reduced in greater proportion than was 
the case with method (a), largely due to the limitation 
of designs eliminated to those above design X. Com- 
paring the two methods, it was found that in 46 per cent 
of the cases, method (a) yielded higher scores than 
method (b), in 24 per cent of the cases method (b) yielded 
higher scores than method (a), and in 30 per cent of the 
cases, the scores by both methods were exactly the same. 
Elimination Method (c). Based on the results of 
methods (a) and (b), method (c) is a compromise, only 
those designs being cast for elimination which were 
common to methods (a) and (b). By this method the 
maximum score attainable is 133, 26 less than when all 
the twenty designs are used. The correlation between 
block-design score points and Binet mental age is .84 
± .01. A survey of the correlation table (Table LXVIII) 
reveals a somewhat greater consolidation, or a reduction 
in the scatter, of the tabulated scores about the mean 
trend as compared with the original correlation table 164 
INTELLIGENCE MEASUREMENT 
(Table LXV) which presents the scores based upon the 
use of the total twenty designs. 
TABLE LXVIII 
Correlation between Binet Mental Age and Score Points 
(Elimination Method (c)) 
Binet Mental Age 
Score Points 
3 
4 
s 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
IS 
l6 
17 
18 
19 
Total 
o 
3 
7 
14 
14 
3 
I 
1 
43 
I- IO 
IS 
19 
20 
12 
6 
S 
1 
1 
1 
80 
II- 20 
2 
3 
13 
11 
9 
2 
2 
4 
1 
47 
21- 30 
3 
IO 
7 
9 
s 
4 
3 
2 
43 
31- 40 
6 
2 
3 
7 
4 
1 
23 
41- 5° 
1 
1 
1 
6 
9 
3 
3 
2 
26 
SI- 60 
1 
4 
5 
3 
I 
I 
I 
16 
61- 70 
1 
1 
3 
4 
3 
1 
I 
1 
15 
71- 80 
2 
2 
2 
5 
3 
2 
16 
0 
O' 
\ 
M 
00 
1 
3 
2 
4 
I 
11 
91-100 
1 
3 
2 
I 
1 
2 
10 
101-110 
1 
2 
1 
2 
3 
3 
3 
3 
18 
111-120 
1 
I 
2 
1 
1 
1 
7 
121-130 
1 
1 
3 
2 
1 
8 
131 
and over 
1 
1 
1 
3 
Total . 
3 
7 
14 
31 
29 
Si 
37 
44 
44 
3i 
20 
17 
11 
11 
7 
4 
S 
366 
r = + .84 ± .01 
A comparison of the mental ratings resulting from 
this new array of designs with those in which all the 
designs were included, and with those in which elimina- 
tions (a) and (b) were made, revealed that the original 
determination of reducing the scatter of scores, of saving 
time without a sacrifice of diagnostic efficiency, of in- 
creasing jthe validity of the final score achieved, and 
of increasing the correlation between block-design scores 
and Binet mental age, had, to a degree been accom- BLOCK-DESIGN TESTS 
165 
plished. The superiority of elimination method (c) is 
again made manifest from the following table, which 
shows what per cent the quartile deviation is of the 
maximum score (the score-range) at each age, for each 
of the elimination methods. 
TABLE LXIX 
Per Cent that Q. D. is of Score Range 
Age 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
IS 
16 
17 
18 
19 
No designs eliminated . 
2 
2 
6 
6 
14 
IS 
19 
25 
16 
24 
17 
6 
5 
6 
Elimination Method (a) 
3 
3 
8 
9 
14 
IS 
16 
3i 
IS 
22 
21 
7 
7 
8 
Elimination Method (b) 
3 
3 
8 
8 
14 
13 
16 
22 
13 
25 
24 
8 
8 
9 
Elimination Method (c) 
3 
3 
7 
7 
13 
13 
i7 
22 
15 
22 
20 
9 
9 
8 
b 
a 
b 
a 
a 
Method Preferred 
any 
any 
c 
c 
c 
or 
or 
or 
b 
or 
c 
a 
a 
or 
f 
6 
c 
c 
c 
The directions for the block-design test, the methods 
of scoring, and the norms, to which Chapter II of Part B 
has been exclusively devoted, are based upon the results 
obtained after rescoring the test blanks, designs XI, 
XIII, and XVII being eliminated. The designs, after 
this final revision, have been renumbered as already 
explained in the introduction to this chapter, each de- 
sign now being designated by an Arabic instead of a 
Roman numeral. 
(b) Sex Differences 
On the basis of the changes in scoring above indicated, 
a second analysis was made to determine sex differences. 166 
INTELLIGENCE MEASUREMENT 
This attempt was not as thorough or as complete as the 
first, indications very early pointing toward no change in 
the original findings. There was no reason to expect 
any shifts in the comparative performances of the sexes, 
since all efforts with the designs were in the direction of 
refining the test procedure and of improving the method 
for placing a specific intelligence-valuation upon any 
given response. 
The block-design test as it now stands is comparatively 
free from the disturbing factor of sex for the first ten 
designs and for ages below thirteen or fourteen. For 
the last seven designs and for ages above thirteen, boys 
seem slightly superior to girls. The reason for this dif- 
ference at the upper ages and for the more difficult 
designs is not immediately apparent. Attention has 
already been directed toward reasonable explanations. 
(See pp. 118-121, and pp. 125-126.) 
Possibly introspective evidence might throw consid- 
erable light upon the matter. At any rate, the differences 
between the sexes are not so great as to invalidate the 
results which one might obtain, nor is a compensating 
formula necessary to correct any error which might be 
theoretically assumed. For all practical purposes sex 
differences may be disregarded. 
(c) Final Norms 
The final norms, with a suggested procedure for giving 
and scoring the block-design tests are presented com- 
pletely in Chapter II (Part B). The writer has assembled 
all of this material in one chapter, in order to facilitate 
the use of the designs and to assist the interpretation of BLOCK-DESIGN TESTS 
167 
results derived therefrom. The longer one uses the block 
design tests, the more is one convinced of the superiority 
of the P. E. method of scoring and interpretation over 
the year-scale method. By means of the former, finer 
gradations are possible, resulting in finer intelligence 
differentiations. It is therefore recommended that the 
P. E. method be used in preference to the year-scale 
method. CHAPTER V 
The Results 
I. DO THE BLOCK DESIGNS MEASURE INTELLIGENCE? 
To answer this question, one must necessarily first 
define intelligence. Perhaps the easiest way out of the 
difficulty is to state that this test measures very largely 
the same kind of mental processes that are measured by 
the Binet scale. And if the Binet scale measures intelli- 
gence, so do the block designs, as is evident from the 
high correlation between the two. 
To some, this reply may appear an evasion of the issue 
and quite unsatisfactory. In that case we must review 
the current definitions of intelligence. These fall prac- 
tically into two types, (a) those expressed by Ebbinghaus, 
Ziehen, and Meumann, and (b) those expressed by Binet, 
Stern, and Terman. According to the first group, 
“Intelligenz ist Kombinationsgabe”— intelligence is the 
ability to “put two and two together,” the ability to 
combine, to synthesize. Whenever, for purposes of 
adaptation or problem solution, we are called upon to 
bind together, or to relate, two or more experiences 
which have, in our own lives, never before been tied up, 
we are utilizing “intelligence” factors in the process. 
The more efficient this combination in actual practice, 
or the less open it is to error and misdirection, the more 
effective has been the functioning of this “intelligence 
168 THE RESULTS 
169 
machinery.” There is no question but that “intelli- 
gence” is dependent upon a large mass of materials which 
have been acquired through experience and stored away 
ready to be called upon whenever occasion demands its 
use, but “intelligence” as such is neither “experience” 
nor “information” but “combinative power” — the 
ability typified, for example, in the mechanics of syllogis- 
tic reasoning. 
According to the second group, intelligence is the 
capacity of an individual to adapt himself to new situa- 
tions. Whenever we are confronted with problems, 
questions, situations of one sort or another, which call 
for new modes of behavior, an adequate solution of the 
difficulty, if not accidental, is the result of the operation 
of “intelligence.” Whether “intelligence” has been 
utilized or not — and if used, to what extent— may be 
determined by appraising the result. What “intelli- 
gence” does is the matter of chief importance. Omy by 
a knowledge of the range of possible accomplishment and 
by our ability to measure differences in this capacity can 
we make practical application of the functioning of intel- 
ligence in such fields as education, delinquency, demc- 
tiveness, and industry. 
It is apparent upon careful analysis that neither of 
these definitions really touches rock-bottom. Severe in 
the standards by which definitions of those we examine 
are judged, we ourselves indulge in an infantile reaction 
for which we merit some condemnation. As mature, 
thinking people our definitions should certainly be 
“better than in terms of use.” To define intelligence as 
“adaptation to new situations” is but little superior to 170 
that of an immature young’s ter who defined “soldier,” 
“to fight.” We wish to know what intelligence is, not 
what it does. Although the explanation of intelligence 
as “combinative ability” falls short of a complete 
definition, it does introduce us, however, more intimately 
to the basic processes underlying “intelligence-activity.” 
Psychologically considered, “adaptation” is a most 
complex activity, and intelligence cannot be defined as 
adaptation, because we are not here dealing with those 
elements which condition adaptation. 
The reader’s attention, at this point, may well be 
turned to our earlier consideration of the processes of 
analysis and synthesis. We noted there that these men- 
tal activities were of the greatest importance in the 
growth and development of hierarchies of mental 
functioning. No matter where our cross-section was 
made, whether at perception, ideation, judgment, reason- 
ing — there we found these phenomena, analysis and 
synthesis, explaining to a large extent the compounding 
and the unifying of processes and of mental material. 
We noted then that our ability to analyze a presented 
situation, is as important as our ability to synthesize 
details into a unity. Ebbinghaus, Ziehen, and Meu- 
mann overemphasize the importance of “ Kombinations- 
fahigkeit,” making slight if any mention of “analytic 
ability.” To that extent they fall short of a satisfactory 
definition of intelligence. To illustrate, suppose one is 
suddenly, and for the first time, confronted with this 
problem: Devise an instrument which will assist you 
in overcoming the effects of gravity. Immediately, 
numerous ideas come to one’s mind. Perhaps you think 
INTELLIGENCE MEASUREMENT THE RESULTS 
171 
of balloons, elevators, aeroplanes, feathers, birds, your 
body weight, electronic forces, etc., etc. The goal to be 
attained continually thrusts itself into your conscious- 
ness, often working havoc with what seems a perfect 
plan. Conditions of all sorts are considered, weighed, 
and measured. Handicaps of all varieties are met with 
and either they master you, or you master them. Be- 
fore you have proceeded very far upon your program 
of action, you have been dealing with a host of details — 
you have been comparing, discriminating, “analyzing,” 
“combining,” judging. Suppose now, some definite 
solution finally comes to you. Let us assume you have 
decided upon some intricate electrical mechanism. 
This decision would never have been reached had various 
details not been synthesized into what appeared, after 
a good deal of checking of experiments, a logical, practi- 
cal plan. 
Intelligent acts of all sorts require both an analysis 
of the situation which confronts one, a critical inquiry 
into methods of solving the problem, and a final synthe- 
sizing of details into a consistent whole. Our definition 
of intelligence as “adaptation” fails to take into ac- 
count the higher syntheses and analyses of the thinker, 
the scientist, the generalizer, the discoverer of laws. 
What factors of “adaptation” are there present in the 
propounding of a theory of heredity, of a doctrine of 
evolution, of a “periodic law,” of an electronic theory, 
of a cosmic hypothesis? Nevertheless, such syntheses 
are often the results of years of painstaking labor, 
critical search, and the keenest of insight. Few, if any, 
will deny that these are most decidedly the results of 172 
INTELLIGENCE MEASUREMENT 
the highest type of intellectual functioning. It seems 
clear that the definition of intelligence as “adaptation” 
breaks down most emphatically at just this point. 
Intelligence more adequately defined would be ex- 
pressed as the ability of an individual to analyze and 
synthesize. Ability in this direction varies as does 
physical height. And there can be no intelligent adap- 
tion of any sort which is not conditioned upon these 
fundamental activities. Analysis and synthesis are the 
mechanics of intellectual behavior — adaptation to 
changing situations is but one of the many results. 
To return now to our original proposition, do the 
block designs measure intelligence? It may be stated 
in reply that there seems to be no reasonable doubt, 
substantiation having been obtained through introspec- 
tions, that these tests require first, the breaking up of 
each design presented into logical units, and second, a 
reasoned manipulation of the blocks to reconstruct the 
original design from these separate parts. The results 
of this activity, it is presumed, yield a fair index of this 
analytic-synthetic power which we have termed “in- 
telligence.” 
2. VALIDITY 
To measure the validity of any newly devised test of 
intelligence is not a simple matter. It devolves upon 
the standardizer to present evidence that the new in- 
telligence scale measures this inadequately defined 
entity “intelligence” with approximately the same 
degree of accuracy as those standards or “measuring 
rods” now commonly accepted and in current use. THE RESULTS 
173 
In the following sections the writer will limit his dis- 
cussion to ten criteria, although admittedly, these are 
neither exhaustive nor of equal importance: 
(1) The mental processes employed; 
(2) Increased in score from year to year; 
(3) Correspondence of median mental ages; 
(4) Correlations between mental ages and intelli- 
gence quotients; 
(5) Correlations with teachers’ estimates of intelli- 
gence, and with school standing; 
(6) Conformance of intelligence-quotient distribu- 
tion with normal probability; 
(7) Correlations with vocabulary; Trabue B and C 
and Military Test; 
(8) The probable error of a block-design mental age; 
(9) The segregation of the feeble-minded; 
(10) Percentage ratios of agreement and disagreement 
with established standards of intelligence. 
(1) Mental Processes Employed 
In devising and standardizing this test the writer did 
not approach the problem with any bias of “faculty 
psychology.” The idea still seems prevalent, though 
not as much now as in the immediate past, that in order 
to possess an adequate measuring instrument for intelli- 
gence, the device must contain separate tests for each 
mental “function”: sensation, perception, association, 
imagination, memory, judgment, reasoning, etc. On 
the other hand, it has been amply demonstrated that 
the only intelligence scales worth the name draw service 
freely from all “functions.” Binet has pointed out that 174 
INTELLIGENCE MEASUREMENT 
all “intelligent operations” involve the functioning of 
three primary activities: first, attention to the problem 
presented; second, a conscious attempt on the part of 
the subject to consummate an adequate adaptation to 
the situation; and third, the exercise of auto-criticism in 
order to determine how efficiently the specific “adap- 
tation” has solved the problem. Put in somewhat 
different words,1 “Binet’s conception of intelligence em- 
phasizes three characteristics of the thought process: 
(1) its tendency to take and maintain a definite direction, 
(2) the capacity to make adaptations for the purpose of 
attaining a desired end, and (3) the power of auto- 
criticism.” (p. 147.) 
A cursory examination of the demands made upon the 
mental operations of the person tested with the block 
designs will clearly reveal that attention, adaptation, and 
auto-criticism are all involved in the successful accom- 
plishment of each task. That point in the graded series 
of designs at which a child will begin failing to achieve 
further success, will be a rough measure of the develop- 
ment of his ability to attend, to adapt, and to critically 
survey his general plan of performance and his ultimate 
accomplishment. In his discussion of the ‘patience test’ 
in the 1908 scale, and these words might as well apply 
to the block-design tests, Binet states:2 
“ It is a game, but at the same time a work of the intelli- 
gence. When one analyzes the operation it is found to 
1 L. M. Terman: “The Stanford Revision and Extension of the Binet- 
Simon Scale for Measuring Intelligence” (Warwick & York, 1917; 179 p.). 
2 “The Development of Intelligence in Children,” Publication No. 
II (Vineland, 1916). THE RESULTS 
175 
be composed of the following elements: (i) Conscious- 
ness of the end to be attained, that is to say, a figure to 
be produced; this end must be understood, and kept in 
mind; (2) the trying of various combinations under the 
influence of this directing idea, which often unconsciously 
determines the kind of attempt which should be made; 
(3) judging the combination formed, comparing it with 
the model, and deciding if it resembles the other.” (p. 
*95 •) 
If “ intelligence” involves the following mental opera- 
tions: analyzing, combining, comparing, deliberating, 
completing, discriminating, judging, criticising, and 
deciding, then the block-design tests may, with justice, 
be said to call upon the functioning of intelligence and 
to that extent they are a measure of that mental capacity. 
(2) Increase in Score from Year to Year 
As regards the second criterion, reference to Graph 6 
and to the various tables of Chapter IV will clearly reveal 
that this requisite is satisfied. 
By itself, this evidence would be wholly inconclusive, 
for the reason that growth in height and in weight also 
show rising increments with every year of increasing 
life age, yet these values are not diagnostic of mental 
growth. It is only in relation to other standard criteria 
that the evidence of yearly increments has any validity. 
A slight diversion from the main theme of this section 
may not be out of place. 
A matter worthy of note is the lack of consistence in 
the variability of one mental age (Binet) in terms of the 
other mental age (block-design) at various age levels 
(see Table LXX). Thus up to Binet-age 7, and after 176 
INTELLIGENCE MEASUREMENT 
Binet-age 16, the variability in comparable block-design 
age is slight, but from Binet-age 7 variability increases, 
reaching a maximum at Binet-ages 10 and n, and 
decreasing thereafter to Binet-age 17. 
Binet-Age and Block-Design Age 
TABLE LXX 
Binet-Age 
Block-Design Age 
3 
4 
5 
6 
7 
8 
9 
IO 
II 
12 
i3 
14 
15 
16 
17 
18 
19 
Total 
Below 
5 
3 
7 
i4 
14 
3 
i 
I 
43 
6 
• 
IO 
IO 
IO 
2 
3 
3 
I 
i 
40 
7 
• 
2 
7 
9 
7 
2 
i 
I 
29 
8 
. 
4 
3 
4 
IO 
4 
2 
2 
I 
3° 
9 
• 
i 
3 
14 
6 
7 
I 
4 
2 
3» 
IO 
• 
2 
6 
5 
8 
5 
2 
3 
2 
33 
u 
# 
6 
2 
4 
9 
4 
I 
i 
27 
12 
# 
I 
i 
2 
6 
8 
3 
4 
2 
I 
28 
13 
. 
I 
3 
7 
5 
3 
I 
I 
i 
22 
14 
. 
2 
3 
2 
7 
4 
2 
20 
IS 
. 
2 
3 
5 
3 
4 
I 
18 
16 
. 
I 
2 
i 
I 
I 
2 
i 
3 
12 
17 
I 
2 
4 
1 
3 
2 
i 
14 
18 
• 
i 
2 
3 
19 
i 
2 
i 
4 
20 
• 
2 
2 
I 
5 
Total . 
3 
7 
14 
3i 
2Q 
5i 
37 
44 
44 
3i 
20 
17 
ii 
II 
7 
4 
5 
366 
(Note: Age io means 10-7 to. 11-6, etc.) 
Rather than regarding this condition a handicap, 
invalidating the tests as a differentiating mechanism for 
diagnosing feeble-mindedness, it appears, on the con- 
trary, to possess distinct advantages. Too frequently 
do the Binet tests leave us uncertain as to defmitemen- 
tal classification after obtaining a quotient of 73 or 76. 
Other evidence in the case, educational, social, biological, THE RESULTS 
177 
industrial, medical, is either meager or inconclusive. We 
wonder whether the child’s superiority in memory, for 
example, may not account for a higher quotient than he 
probably actually possesses. At other times, we are at a 
loss to account for exceptional success in one or more of 
the tests in higher ages, unless it be explained on the 
basis of previous familiarity. It is at such times that an 
additional differentiating mechanism, such as the block- 
design tests, may be of pronounced value in forming a 
more definite decision as to further social and educational 
handling. 
Suppose, for example, we have just concluded the 
examination of a child whose life age is 15 years, and who 
obtains a Binet mental age of n. The I. Q. in this 
instance would be 74. If then the block-design tests are 
given, on the basis of Table LXX, this Binet n-year-old 
may theoretically obtain a mental rating anywhere be- 
tween 6 years and 17 years on the block-design tests — 
a possible divergence of five years in either direction. 
The value of this apparent disagreement will be self- 
evident to psychoclinicians who are daily confronted 
with the need for rapid, yet accurate, prognostic diag- 
noses. In the above-mentioned instance, an I. Q. of 50 
on the block-design tests coupled with a Binet I. Q. of 
74 and a rather negative history of self-dependence 
might be of unquestioned assistance in outlining a 
rational plan for further care and direction of a subject 
under examination. The same value, of course, would 
attach to a block-design test-result in the case of a child 
with a Binet I. Q. of 74 and with a block-design I. Q. 
of 150. 178 
INTELLIGENCE MEASUREMENT 
In view of a later return to this same matter, the 
diagnostic importance of this divergence will not be 
stressed any further at this point. 
(3) Correspondence of Median Mental Ages 
At each life age do the median mental ages obtained 
by the block-design tests correspond with the median 
mental ages obtained by the Binet tests? This question 
is an important one, and the extent of correspondence 
or deviation should measure very largely the validity 
of the newly devised tests. 
In the following table this comparison is presented: 
Correspondence of Median Mental Ages 
TABLE LXXI 
Lite 
Age 
Yrs. 
No. OF 
Cases 
Median 
Binet Age 
Yrs.-Mos. 
Median Block- 
Design Age 
Yrs.-Mos. 
Difference 
Between Medians 
(Mos.) 
Average of 
Two Medians 
Yrs.-Mos. 
6 . . 
i6 
6- 1 
5~ 3 
10 
5- 8 
7 • • 
27 
7- 5 
6— 8 
9 
7-V2- 
8 . . 
28 
8- 0 
8- 2 
2 
8-1 
g . . 
27 
9- 0 
8-11 
I 
8-1i34 
IO . 
33 
9- 8 
10- 3 
7 
9-11J4 
ii . 
30 
10- 6 
11- 6 
12 
n- 0 
12 . 
29 
II-IO 
12- s 
7 
12- 1 y2 
13 • • 
32 
11- 5 
12-6 
13 
II-IlJ'S} 
14 • • 
28 
13- 9 
13- 6 
3 
13- 73^ 
IS • • 
19 
13- 3 
14- 0 
9 
13- 7xA 
16 . 
16 
IS- 6 
13-10 
20 
14- 8 
Average—8.5 
Four important items are worthy of note: In the first 
place, the average deviation of the median Binet ages 
from the life ages at each year is 6 months; second, the 
average deviation of the median block-design ages from THE RESULTS 
179 
the life ages at each year is 8.8 months; third, the 
average deviation between the two intelligence-test me- 
dians is S}/2 months, and finally, the arithmetic mean of 
the two medians for each life age results in a more accurate 
approximation of what may he the “true” mental age than 
either median taken alone. 
We have, perhaps, in our early enthusiasm over the 
diagnostic accuracy of the Binet scale overlooked the 
importance and the need for calling to our assistance 
supplementary information which should aid us in arriv- 
ing more accurately at a positive diagnosis. The further 
our studies upon the fallibility of intelligence ratios 
continue 1 the more does it become apparent that, at 
least for the determination of mental deficiency, a Binet 
I. Q. alone is a hazardous symptom upon which to base 
a definite diagnosis of feeble-mindedness. Many and 
frequent have been the criticisms, sometimes mild, at 
other times venomous, that the accuracy of the Binet 
result was impaired by the intercipient factors of school- 
ing and linguistic facility. It may, consequently, not 
be a mistaken procedure to utilize both a language and 
a performance test in the determination of mental level 
■— the performance test to compensate for the over- 
emphasis in the Binet scale of certain capacities not 
highly correlated with intelligence per se, the Binet scale 
to compensate for the inevitable easy-spread of ability 
characteristic of practically all performance intelligence- 
tests. 
1 Florence Mateer: “The Diagnostic Fallibility of Intelligence 
Ratios,” Ped. Sem., 1918, 25:369-392. 
E. A. Doll: “The Growth of Intelligence,” Psychol. Monographs, 
1921, Vol. 29. No. 2,130 p. 180 
INTELLIGENCE MEASUREMENT 
After comparing the Binet age medians with the block- 
design age medians for each life age (Table LXXI), 
it may be sufficient to remark, in conclusion, that the 
approximation between the Binet and the block-design 
medians is remarkably close, especially when we con- 
sider that the block-design tests are free of [the “language 
factor” and of the influence of schooling. 
(4) Correlation between Mental Ages and Intelligence 
Quotients 
One of the greatest handicaps experienced in standard- 
ization is to select a standard of comparison! which is 
absolute. All existing standards are, unquestionably, 
affected by a variety of disturbing factors, frequently 
difficult to determine, and always difficult to discount. 
As in the year-scale standardization, the writer may 
have erred in selecting the results of Binet testing as a 
criterion of accurate mental age. That procedure, how- 
ever, was necessary because we have, as yet, no other 
equally accurate measuring stick — one which has 
attained a similar degree of general confidence. 
For the same reason, the Binet results are again 
utilized to check the validity, in the present instance, 
of the block-design ages. 
It may be of interest, first, to state the separate cor- 
relations of the two mental ages with life age. Con- 
formance with life age is, apparently, greater with the 
Binet than with the block-design tests. 
1. The correlation between Binet age and life age is 
-f .80 (P. E. ± .01) (291 public school cases). THE RESULTS 
181 
2. The correlation between block-design age and life 
age is + .66 (P. E. ± .02) (291 public school 
cases). 
Segregating the results for the total 366 cases, for the 
291. public school cases, and for the 75 feeble-minded the 
correlation between Binet age and block-design age 
follows: 
3. The correlation between Binet age and block- 
design age is -f .82 (P. E. ± .01) (366 cases). 
4. The correlation between Binet age and block- 
design age is + .81 (P. E. ± .01) 291 public 
school cases). 
5. The correlation between Binet age and block- 
design age is + .67 (P. E. ± .05) (75 feeble- 
minded cases). 
The lower correlation between Binet and block-design 
ages for the feeble-minded is sufficiently great to require 
some comment. 
The application of the tests to the feeble-minded was 
purposely divided, in point of time: the first group of 
feeble-minded cases (28) were examined at Vineland, 
the summer of 1917; the second group (47) at the 
Sonoma State Home (Eldridge, Cal.), were tested during 
the spring of 1918. Almost one year later, because of 
accumulated experience with the block-design tests the 
outstanding deviations in performance of some of the 
feeble-minded could be more intelligently interpreted. 
Dr. George Ordahl, the psychologist of the Sonoma 
State Home, remarked during the period of experimenta- 182 
INTELLIGENCE MEASUREMENT 
tion that the block-design tests seemed to measure 
functional efficiency to a far greater degree than did the 
Binet tests. Looking back to the writer’s personal 
knowledge of the cases at Vineland this remark was 
corroborated. It appears that many feeble-minded 
actually work at a higher level of complexity and ef- 
ficiency than one would expect on the basis of Binet 
mental age. For the reason that the Binet possibly 
underestimates the work-capacity of certain timid or 
retiring or inexpressive types of defectives, or for the 
reason that the block-design tests possibly place less 
emphasis upon verbal expression and more upon per- 
formance, it seems that in certain instances the feeble- 
minded obtain inconsistent scores on the two scales, 
yet their ratings by the block-design tests are a fairer 
index of their functional efficiency in various occupations 
than the Binet. 
This is a matter which can well afford further in- 
vestigation. There still remain unchartered territories 
without number awaiting exploration by those interested 
in determining individual differences among the feeble- 
minded as well as the differences between the normal 
and the feeble-minded. 
As regards the correlation between the I. Q.’s of the 
Binet and the block-design tests, the results again are 
segregated for the total 366 cases examined, for the 291 
school children, and for the 75 feeble-minded. These 
follow: 
6. The correlation between Binet I. Q. and block- 
design I. Q. is + .80 (P. E. ± .01) (366 cases). 
The table is herewith presented: THE RESULTS 
183 
TABLE LXXII 
Binet I. Q. and Block-design I. Q. 
Binet I. Q. 
Total . 
Block-Design I. Q. 
Osdn Go to m O O OsCa 4** Go 
ooooooooooooooo 
M 
M 
O 
M 
M 
m Go Go 
GJ 
o 
M 
4^ 
M H -P>- 
4* 
0 
H 
ON 
M H to Ca Os H 
Cn 
O 
M 
M H M 4*- 10 HI 
Os 
o 
to 
On 
to wCoOo-f*. 00HCO h 
*o 
O 
Ca 
M 
M -vj OsO M Os O M 
00 
o 
68 
t0HCnOOOtOj0.HMM 
o 
o 
00 
Go 
M to to M 
w Go Go 00 Go o O O Go to 
8 
4^ 
O 
m m Go *vj to Ca to 
o 
to 
mm tn C/i Cn io m to to 
o 
Os 
M to H M M 
Go 
O 
Go 
M M M 
o 
Go 
Os 
Os 
HHK)-fs^^-fSK)tOH(OtO 
m Go toGiCasO to Os 00-£* m 'O 00 O Go 
H 
o 
$ 
(Note: I. Q. of 50 means 46-55, etc.) 
7. The correlation between Binet I. Q. and block- 
design I. Q. is + .58 (P. E. ± .03) (291 school 
children). 
8. The correlation between Binet I. Q. and block- 
design I. Q. is + .67 (P. E. ± .05) (75 feeble- 
minded cases). 
The correlations of the two I. Q.’s, both for the total 
366 cases and for the 75 feeble-minded are equal to the 
comparable correlations of the two mental ages men- 
tioned above. In the case of the 291 school children 
there is a marked difference, however. Whereas the 
correlation between Binet age and block-design age 
is + .81, the correlation between Binet I. Q. and block- 184 
INTELLIGENCE MEASUREMENT 
design I. Q. is only -f- .58. It is difficult to explain this 
discrepancy, both tables having been checked for ac- 
curacy on three different occasions. The only plausible 
explanation at this time is the greater range of the mental 
age table as compared with the I. Q. table. The latter 
has fewer class-intervals, I. Q.’s having been taken in 
ranges of ten each. 
In this connection may also be presented the individual 
deviations in I. Q. between the Binet and the block- 
design tests. No one would expect exact correspondence, 
yet a high percentage of agreement should be demanded. 
In the following tables, segregated for the 291 public 
school children and for the 75 feeble-minded, this cor- 
respondence is presented. 
TABLE LXXIII 
Correspondence of I. Q.’s 
(201 P. S. Cases) 
Freqtjencx 
I. Q. 
B. D. I. Q. 
Higher 
B. D. I. Q. 
Lower 
Total 
Same 
i-5 
27 
29 
7 
56 
6-10 
35 
22 
57 
11-15 
20 
28 
48 
16-20 
25 
22 
47 
21-25 •••#••• 
16 
XI 
27 
26-30 
12 
5 
17 
31-35 
6 
6 
12 
36-40 
3 
2 
5 
41-45 
5 
3 
8 
46-50 
3 
1 
4 
51-55 
2 
2 
56-60 
1 
1 
Median I. Q. Difference . 
15 
13 
14 THE RESULTS 
185 
From the above table it is evident that 50 per cent of 
the cases show no greater deviation than 14 I. Q. be- 
tween the two tests. It is also clear that there are 
almost as many lower deviations as higher: 
The total number higher — 155 cases (53%) 
The total number lower — 129 cases (44%) 
The total number the same — 7 cases (3%) 
If anything, the block-design tests err in the direction 
of leniency rather than severity of mental age estima- 
tion. 
The closeness of correspondence is again apparent 
from the following analysis: 
Total deviations no greater than 5 I. Q. 63 cases (22%) 
“ “ “ “ “ 10I.Q. 120 cases (41%) 
“ “ “ “ “ 15 I. Q. 168 cases (58%) 
“ “ “ 20 I. Q. 215 cases (74%) 
“ “ “ “ “ 25I.Q. 242 cases (83%) 
“ “ “ “ “ 301. Q. 259 cases (89%) 
“ “ “ 35 I- Q- 271 cases (93%) 
For the feeble-minded, the data runs parallel,1 except 
that to a certain extent the figures are much more 
significant in comparison with the same group of data 
for the 291 P. S. cases, and from the point of view of the 
diagnostic efficiency of the block-design tests. So in 
Table LXXIV the correspondence of I. Q.’s for the 75 
feeble-minded cases is presented: 
1 It should be stated that all block-design zero scores were given a 
mental age rating of 5 years 3 months. This inaccuracy increases the 
I. Q. deviations. But this was purposely done in order artificially to 
increase the differences between the two I. Q.’s wherever possible. The 
comparisons throughout are, therefore, quite_conservative. 186 
INTELLIGENCE MEASUREMENT 
Correspondence of I. Q.’s 
TABLE LXXIV 
(75 F. M. Cases) 
*J 
Frequency 
I. Q. 
B. D. I. Q. 
Higher 
B. D. I. Q. 
Lower 
Total 
Same 
i- s 
15 
13 
3 
28 
6-10 
S 
13 
18 
11-15 
6 
3 
9 
16-20 
2 
3 
5 
21-25 
1 
2 
3 
26-30 
1 
3 
4 
31-35 
2 
2 
4 
36-40 
1 
1 
Median I. Q. Difference . 
6 
8 
7 
It is clear from this table that 50 per cent of the total 
feeble-minded examined show no greater deviation than 
7 I. Q. between the two tests. This similarity of results 
indeed merits special emphasis. It will also be noted 
that whereas, for the average school child, there is a 
strong tendency to secure a somewhat higher score on 
the block-design tests, this is reversed for the feeble- 
minded. The latter group tends to secure lower scores. 
This is evident from Table LXXIV, and also from the 
following totals: 
The total number higher — 32 cases (43%) 
The total number lower — 40 cases (53%) 
The total number the same — 3 cases (4%) 
This evidence is in harmony with the remark pre- 
viously made, that the block-design tests assist in the THE RESULTS 
187 
differentiation of the feeble-minded from the border- 
zone or the normal case. 
Although the above-mentioned differences exist be- 
tween the two I. Q.’s, yet correspondence is higher for 
the feeble-minded than for the public school group: 
Total deviations no greater than 5 I. Q. 31 cases (41%) 
“ “ “ “ “ 101. Q. 49 cases (65%) 
“ “ “ “ “ 15 I. Q. 58 cases (77%) 
“ “ “ “ “ 201. Q. 63 cases (84%) 
“ “ “ “ “ 251. Q. 66 cases (88%) 
“ “ “ “ “ 301-Q. 70 cases (93%) 
In conclusion, it may be stated that the correlations be- 
tween the two test methods, considering their marked dif- 
ference in character, are high enough to guarantee frequent 
correspondence between their mental ages and I. Q.’s. 
(5) Correlations with Teachers' Estimates and with School 
Standing 
The search for the “fountain of youth” presented few 
if any greater difficulties than the search for criteria by 
means of which to weigh the validity of measuring instru- 
ments for intelligence. It is comparatively easy to devise 
tests, to develop an efficient technique for application, to 
establish norms, and to obtain results which may possess 
some psychological, educational or social significance. 
But to find a stable criterion for establishing validity 
appears almost hopeless. 
It has been customary to rely upon teachers’ estimates 
of intelligence to check the validity of one’s intelligence- 
test schema. It is valuable to utilize this “common- 
sense” check, even though high correlations between 
teachers’ judgments and test results cannot be expected, 188 
INTELLIGENCE MEASUREMENT 
and in spite of the fact that there are some very serious 
forces invalidating such judgments. It is clear that 
the same high I. Q. receives a lower estimate by the 
teacher if a child is in upper grades rather than in the 
lower grades, because of the elimination of poorer pupils 
in the upper elementary grades. Thus an I. Q. of 90 is 
more likely to receive an estimate of average or above 
average in the lower grades, whereas in the upper grades 
or in the high school the same I. Q. will more probably 
receive an estimate of below average or inferior. Other 
writers have already indicated other factors, having no 
bearing upon or relation to intelligence, which interfere 
with the accuracy of judgment on the part of teachers. 
School marks, also valuable criteria with which to 
check the results of a newly devised test, are also ineffi- 
cient to an extent, because they are generally crude, are 
limited to a rather narrow range, contain spurious ele- 
ments such as neatness, order, and so on, are often 
given for disciplinary reasons, or as bait for an educa- 
tional spurt, and are not based upon uniform standards. 
However, there is a corroborative value in teachers’ 
estimates and in school standing which is worth men- 
tioning. 
9. The correlation between teachers’ estimates of 
intelligence and Binet I. Q. is + .47 (P. E. ± .03) 
(291 school children). 
10. The correlation between teacher’s estimates of 
intelligence and block-design I. Q. is + .23 (P. E. 
± .04) (291 school children). The table is here- 
with presented. THE RESULTS 
189 
TABLE LXXV 
Teachers’ Estimates and Block-design I. Q. 
Total 
Block-Design I. Q.1 
Ostia W u h QC 0\Ca Cw 
ooooooooooooooo 
-t* 
to to 
■f* 
M 
M 
to M Oo M M M to 
ca 
ca 
to 
M 
H to to Go OCa On to m 
On 
M 
Co 
H 
M to to to to 
h H to Ca Ca Go h On O m vO Ca h m 
>1 
On 
00 
h Os-f>- *0 00-2 O OCMb H 
00 
to 
to 
Oo Oo Oo Go C/i m Oo m 
O 
Oj 
H H M 
0 
to 
O 
M 
H H H H 
MC*» NUiMO K> GOO -f» M M 
3 
> - 
Teachers’ Estimates 
> (30 signifies scores between 26 to 33, etc.i 
r = + .23, ± .04 
Although the correlation between block-design age 
and Binet age is + .82, teachers’ estimates of intelligence 
correlate only one half as much with the block-design 
I. Q.’s as with the Binet I. Q.’s. The reader may recall 
that one of the original objections to the Binet scale was 
that it measured school training. Only to a limited 
extent has this been denied, the explanation having been 
made that the tests measure intelligence through the 
medium of knowledge only partly influenced by school 
training. It has been admitted, true, that practically all 
children are exposed to these educational influences, but 
the ultimate difference in achievement is explainable on 190 
INTELLIGENCE MEASUREMENT 
the basis of differences in endowment. However this 
may be, the results of the block-design test would perhaps 
tend to show that there is more to this charge than we 
have been inclined to admit. It will, no doubt, be con- 
ceded without much question that the block-design tests 
are less affected by school training than the Binet. 
Regarding the correlations between school standing 
(school marks) and block-design I. Q. the following are 
the results: 
n. Block-design I. Q. and Reading: + .18, P. E. 
dz .04 (276 cases). 
12. Block-design I. Q. and Language: -f- .20, P. E 
± .04 (259 cases). 
13. Block-design I. Q. and Household Arts: + .22 
P. E. ± .09 (48 cases: 44 girls, 4 boys). 
14. Block-design I. Q. and Drawing + .25 P. E. 
± .04 (258 cases). 
15. Block-design I. Q. and Arithmetic: + .31, P. E. 
± .04 (251 cases). 
16. Block-design I. Q. and Manual Training: + .36, 
P. E. ± .08 (58 cases: 56 boys, 2 girls). 
It will be observed that block-design results correlate 
least with reading and language, and most with manual 
training and arithmetic. When discussing sex differences 
in an earlier section of this monograph, attention was 
called to the slight superiority of boys over girls at the 
higher ages. It was mentioned then, that perhaps the 
mechanical nature of some of the higher designs gave 
boys a slight advantage. The evidence here is, to an 
extent, a corroboration of this view. This condition THE RESULTS 
191 
does not point necessarily to a weakness in the test 
scheme. It will be conceded by those who analyze the 
activity that success in manual training involves the 
utilization of intelligence in planning one’s work, in 
criticising one’s progress through the various stages of 
accomplishment, and in holding the goal to be achieved 
in mind and in attaining it. It would possibly be gen- 
erally admitted that efficiency in manual training draws 
no less upon “intelligence” than do reading and 
language. 
It may also be of interest to compare the average of 
the correlations between reading, language and arith- 
metic, the “mind” subjects on the one hand, and house- 
hold arts, drawing, and manual training, the “hand” 
subjects on the other. The averages of the two groups 
are -f .23 for the first subjects, and + .28 for the second. 
Again we find corroboration of the contention that the 
block-design tests are actually tests of performance, more 
free of the language factor than many of the tests, neces- 
sarily dependent upon language, now in common use. 
The need for the application of such a test as this in 
combination with others, in order to estimate accurately 
a child’s intelligence, appears self-evident. 
When the teachers were requested to fill out the ques- 
tionnaire they were asked to answer this question for 
each child examined: “If this child were given a mental 
test involving chiefly the use of language, or the ability 
to understand and handle language symbols (as con- 
trasted with a test requiring silent observation and 
performance) would you expect him (her) to pass; very- 
low, low, below average, average, above average, high, 192 
INTELLIGENCE MEASUREMENT 
very high?” It was expected that the replies to this 
question would bring to light those cases where undue 
superiority or undue inferiority in language understand- 
ing and expression might affect the results of a mental 
test dependent upon language symbols for comprehension 
and success. The correlation between block-design I. Q. 
and these estimates by the teachers follows: 
17. Block-design I. Q. and teachers’ estimates of 
language vs. performance: + .24, P. E. ± .04 
(291 cases). 
Analyzing the table of data it is found that 6 per cent 
of cases possessing I. Q.’s of 106 and over were estimated 
by the teachers likely to obtain very low, low, or below 
average scores on a “language” intelligence test, and at 
the other extreme 10 per cent of cases possessing I. Q.’s 
of 95 or under were estimated by the teachers likely to 
obtain above average, high, or very high scores on a 
“language” intelligence test. In other words, according 
to the judgment of teachers, it would appear that a 
total of 16 per cent, or one sixth of all children in the 
average public school, are likely to be misrated if judged 
by a “language” test alone. This proportion is probably 
too high. At any rate, the data is offered for what it is 
worth. 
By way of summary, it may be remarked that not only 
do the block-design tests show a reasonable correlation 
with school standing and teachers’ estimates of intelli- 
gence, but the emphasis upon performance as opposed to 
verbal impression or expression is a desirable feature of 
the test. THE RESULTS 
193 
(6) Conformance of Intelligence Quotient Distribution 
with Normal Probability 
A very necessary index in weighing the validity of 
any standardized test is to determine the extent to which 
an actually found distribution conforms to its theoretical 
distribution. 
The assumption that the distribution of intelligence 
follows normal probability is recognized as an arbitrary 
one, but it is utilized merely as a working hypothesis. 
If not this, what else? Until further investigation gives 
us more light on this problem we must continue to grope, 
more or less, in the dark. 
In the following table are presented the I. Q.-range 
distributions for the Binet and the block-design tests. 
The respective percentage values are compared with 
what one should theoretically expect. 
Attention is again called to the “spread” of ability 
greater for the block-design tests than for the Binet, 
previously mentioned. It is apparent that ‘ ‘ intelligence ’ ’ 
measured by the Binet test manifests a lesser diveristy 
than the block-design test. Which of the two is more 
truly representative it is difficult to state dogmatically. 
Perhaps an average of the two approaches more nearly 
the truth. It may be of interest to mention a note con- 
tained in a letter to the writer from W. A. McCall in 
which he remarks “that the distribution of Reading 
Quotients,” obtained from his recently completed reading 
scale, “conforms more closely to your I. Q.’s than 
Terman’s.” 
Whatever the true situation regarding the general 
character of the distribution of intelligence, the fre- 194 
INTELLIGENCE MEASUREMENT 
26 
36 
46 
56 
66 
76 
86 
96 
106 
Il6 
126 
136 
146 
156 
166 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
35 
45 
55 
65 
75 
85 
95 
105 
ns 
125 
135 
145 
155 
165 
175 
Stanford Binet Ob- 
tained 
Theoretical Expec- 
,i-7 
5-5 
16.5 
22.7 
28.2 
13-8 
8.3 
2.1 
1.0 
tation .... 
.16 
1.6 
8-5 
23.42 
32.64 
23.42 
8.5 
1.6 
.16 
Block-deisgn Ob- 
tained 
Theoretical Expec- 
.034 
.034 
1.4 
6-5 
6.2 
14.4 
i5-i 
18.9 
14.4 
10.0 
5-2 
5-2 
.07 
1.0 
•034 
tation (Median 
at 99) ... 
•49 
1.28 
2.78 
5-21 
8.67 
12.05 
14.66 
15-3° 
13.84 
10.69 
7.25 
4.11 
2.08 
.88 
•33 
Intelligence Quotient Ranges 
TABLE LXXVI THE RESULTS 
195 
quencies of the block-design I. Q.’s conform more closely 
to theoretical expectation. Thus the average deviation 
from theoretical expectation for the Binet I. Q. ranges is 
3.3 per cent per I. Q. group. The average deviation for 
the block-design tests is only 1.4 per cent per I. Q. 
group. 
In conclusion, the evidence of correspondence between 
the empirical and the theoretical distributions testifies 
to a fair degree of validity of block-design I. Q. 
(7) Correlations with Vocabulary, Trabue B and C, and 
Military Test 
Mention has already been made of the correlations 
between block-design and Binet test results. The data 
of the Stanford-Binet vocabulary, the Trabue Language 
Scales B and C, and the military test were also utilized 
to verify the accuracy with which the block-designs 
estimate intelligence. These criteria were especially 
chosen for the reason that, besides the inevitable differ- 
ences to be expected from the application of two intelli- 
gence scales, additional disturbing factors of language 
and group testing were added in order to exaggerate the 
inherent discrepancies. It was also the intention to 
obtain some information which would throw light upon 
the much mooted questions, “Does the Binet test 
exaggerate the importance of language in contradistinc- 
tion to performance?” and “Are there specialized capaci- 
ties of ‘doing’ which are as indicative of intelligence as 
those concerned with ‘talking’ and ‘information’?” This 
problem, however, can only be barely touched upon at 
this point. 196 
In the following tables are presented, first, the correla- 
tions between Stanford-Binet mental age and Stanford- 
Binet vocabulary score, and second, between block- 
design score points and Stanford-Binet vocabulary score: 
INTELLIGENCE MEASUREMENT 
TABLE LXXVII 
Correlation between Binet and Vocabulary 
Vocabulary Score* 
Binet Mental Age 
Total 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
o- 4 
4 
4 
8 
5- 9 
3 
7 
4 
I 
I 
16 
10-14 
6 
4 
9 
1 
I 
21 
iS-19 
10 
19 
6 
1 
36 
20-24 
11 
16 
13 
3 
43 
25-29 
3 
11 
13 
2 
2 
3i 
30-34 
2 
11 
12 
5 
3 
33 
35-39 
I 
3 
11 
4 
1 
1 
1 
22 
40-44 
I 
10 
7 
4 
1 
23 
45-49 
I 
I 
6 
5 
4 
1 
18 
50-54 
2 
6 
4 
7 
4 
2 
I 
26 
55-59 
2 
2 
2 
2 
8 
60-64 
1 
1 
1 
2 
2 
2 
9 
65-69 
1 
2 
3 
2 
8 
70-74 
2 
I 
1 
1 
5 
75-79 
1 
3 
4 
80-84 
85-89 
1 
1 
90-94 
I 
1 
2 
Total 
13 
25 
36 
44 
43 
30 
20 
17 
11 
II 
7 
4 
5 
314 
r — + .91, P. E. ± .007 
* These class-intervals, although not the best, were used in order to correspond with 
Terman’s. 
It may be worth remarking at this point that of the 
three children who achieved the highest scores on the 
vocabulary test, two were inmates of the institutions for 
the feeble-minded! On the block-design test, however, 
their mental incapacity is evident, one achieving a score THE RESULTS 
197 
between 21-30, the other a score between 71 to 80. The 
Binet ages of the two fell, for the first, between 14-7 
and 15-6, and for the second, between 15-7 and 16-6. 
Referring to Table LXXVII, the correlation ratio 
+ .91 is the same as that found by Terman in his analysis 
Correlation between Block-design and Vocabulary 
TABLE LXXVIII 
Block-design Score Points 
6l 
81 
Score 
I 
II 
21 
31 
41 
51 
71 
91 
IOI 
III 
121 
131 
Total 
O 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
IO 
20 
30 
40 
So 
60 
70 
80 
90 
ICO 
no 
120 
130 
o- 4 • 
35 
18 
4 
3 
60 
5“ 9 • 
2 
9 
2 
1 
1 
I 
16 
10-14 • 
5 
10 
5 
I 
21 
15-19 . 
14 
10 
8 
3 
I 
36 
20-24 . 
1 
14 
14 
3 
4 
3 
1 
1 
I 
1 
43 
25-29 • 
5 
6 
8 
2 
3 
5 
2 
31 
30-34 • 
5 
2 
4 
4 
5 
2 
5 
2 
3 
1 
33 
35-39 • 
2 
1 
2 
2 
2 
2 
3 
3 
1 
2 
I 
1 
22 
40-44 . 
2 
4 
4 
2 
2 
1 
2 
1 
1 
2 
1 
I 
23 
45-49 • 
2 
2 
1 
5 
3 
2 
I 
I 
1 
18 
50-54 • 
1 
2 
3 
3 
1 
3 
2 
3 
4 
2 
2 
26 
55-59 • 
I 
I 
1 
1 
2 
2 
8 
60-64 • 
1 
1 
1 
1 
2 
2 
1 
9 
65-69 . 
1 
2 
1 
4 
8 
70-74 • 
2 
1 
2 
5 
75-79 • 
80—84 • 
2 
1 
1 
4 
85-89 . 
1 
1 
90-94 • 
1 
1 
2 
Total . 
43 
80 
47 
43 
23 
26 
16 
15 
16 
10 
10 
18 
7 
8 
3 
365 
r = + -77, P. E. ± .02 
of the records of 631 school children,1 wherein mental 
age and vocabulary score were correlated. Based upon 
statistical analysis, not personal opinion, the vocabulary 
1L. M. Terman: JThe Intelligence of School Children” (1919), p. 310. 198 
INTELLIGENCE MEAS 
test stands out clearly as the best single test in the whole 
Binet series. The correlation ratio + .91 is to a certain 
extent spurious because vocabulary score entered into 
the estimation of mental age and to that extent weights 
the Binet mental age in its favor. In view of this condi- 
tion the correlation between Binet mental age and block- 
design mental age (+ .84) is not so much lower than one 
would conclude off-hand. Then, again, reference to 
Table LXXVIII and to Terman’s Table 411 reveals 
clearly that the variability of a block-design score in 
terms of Binet mental age is not so great, when we 
observe that the vocabulary test presents approximately 
the same degree of variability, and in spite of the fact 
that the vocabulary aided in the determination of Binet 
mental age. For 482 miscellaneous adults — hoboes, 
prisoners, delinquents and business men — Terman 
found the correlation between mental age and vocabulary 
to be + .81, three points lower than the correlation be- 
tween the Binet and the block-design tests. 
It is quite surprising to note the correspondence be- 
tween efficiency in the block-design tests and in vocab- 
ulary, the former apparently concerned with hand- 
manipulations, the latter with language, supposedly 
affected by schooling and experience. In the past we 
have been inclined to look to performance tests as 
“fillers-in” for the assumed inadequacies of the Binet 
tests. The high correlation between the two types of 
examination leads one to the conclusion that both 
systems call upon somewhat similar mental processes — 
processes involved in the normal functioning of intelli- 
1L. M. Terman: “The Intelligence of School Children” (19x9), p. 3x0 THE RESULTS 
199 
gence. So that, although the two methods of expressing 
this mental power differ radically in character, the men- 
tal manipulations making for successful achievement are 
fundamentally the same. 
An analysis of the reactions of the feeble-minded to the 
two test systems reveals roughly three rather distinct 
groups. On the one hand there are what Binet has 
termed the “loquacious types.” These are the feeble- 
minded who have an easy facility with language, and 
who, because of their loquaciousness and ability to 
speak with apparent intelligence on many subjects, give 
to the lay mind the impression of average mental capac- 
ity, a sort of general ability and “intelligence.” These 
aments secure high scores in the vocabulary test, but 
their performance in the block-design tests is strikingly 
low. Then again, there are a number of others, con- 
siderably backward in speech expression and in language 
ability — what some have designated “ the silent type.” 
The character of their actual daily activity belies their 
mental rating on the Binet scale. Low in their achieve- 
ments on this intelligence test, they are nevertheless 
capable of considerable rather intelligent effort if taught 
to do something, and are placed upon their own initiative 
which will involve no greater than a few minor adapta- 
tions. These mental deficients although markedly un- 
intelligent on a test involving the understanding and the 
use of language, nevertheless are capable of a con- 
siderable amount of useful and complex effort on the 
institution grounds. Those who have actually worked 
with the feeble-minded in their institutions will readily 
recall numerous instances which are corroborative of 200 
INTELLIGENCE MEAS 
the above remarks. Finally, there are those aments 
who manifest the same degree of intelligence-develop- 
ment by both tests. This group, of the three, is ap- 
parently the largest. 
It appears that our earlier notion that language 
capacity and performance were two somewhat mutually 
exclusive abilities was to a large extent erroneous. 
Granted a certain level of intelligence-development, 
the vocabulary test or the Binet scale are, in most cases, 
no less effective measures of that level than a reliable 
performance test itself, no matter how carefully or 
efficiently devised or standardized. But, in case of doubt, 
both tests may be given to advantage, averaging the 
results of the two. 
What has already been said regarding the relation 
between the diagnostic efficiency of a language test and 
a performance test holds true for such a language test 
as Trabue B and C. Devised originally to measure 
pedagogical achievement in language, it was found very 
early to be also diagnostic of intelligence-development. 
It is again surprising to note the relatively close cor- 
respondence in scores between this language and the 
block-design tests. See table on the next page. 
The correlation of: + .57 between these two test 
schemes is indicative of a certain amount of common 
mental activity characteristic to both, irrespective of 
outward differences in the physical form of the tests 
themselves. 
An analysis of the regression of the block design on 
Trabue score may be of interest. From the table it 
is evident that as Trabue score increases, the increase THE RESULTS 
201 
in block-design score is relatively slight. When, however, 
the middle range of Trabue scores are reached the in- 
crease in one is paralleled by similar increases in the 
TABLE LXXIX 
Correlation between Trabue B and C and Block-design Scores 
Trabue 
Score 
B AND C 
O 
I 
TO 
IO 
II 
TO 
20 
21 
TO 
30 
O O M 
41 
TO 
SO 
SI 
TO 
60 
6l 
TO 
70 
71 
TO 
80 
81 
TO 
90 
91 
TO 
IOO 
101 
TO 
no 
III 
TO 
120 
121 
TO 
130 
131 
and 
over 
Total 
o- I . . 
7 
18 
5 
1 
I 
32 
2- 3 • • 
1 
I 
4- 5 • • 
1 
1 
I 
3 
6- 7 . . 
1 
2 
1 
4 
8- 9 . . 
3 
1 
4 
I 
9 
io-ii . . 
1 
8 
2 
I 
12 
12-13 • • 
7 
1 
5 
2 
1 
1 
17 
14-15 . . 
4 
2 
6 
16-17 • • 
4 
3 
3 
I 
2 
1 
1 
1 
16 
18-19 • • 
1 
2 
5 
2 
I 
1 
2 
14 
20-21 . . 
3 
4 
8 
2 
3 
1 
I 
2 
1 
25 
22-23 . . 
I 
4 
3 
2 
5 
I 
3 
1 
2 
3 
1 
26 
24-25 . . 
2 
1 
1 
2 
4 
2 
3 
3 
1 
1 
1 
21 
26-27 . . 
5 
4 
5 
3 
4 
I 
3 
3 
2 
3 
I 
34 
28-29 • • 
X 
1 
2 
4 
1 
2 
2 
2 
3 
18 
30-31 • • 
I 
3 
2 
1 
2 
3 
2 
2 
16 
32-33 • • 
1 
1 
2 
4 
34-35 • • 
I 
1 
4 
1 
2 
I 
10 
36-37 • • 
1 
1 
1 
I 
4 
38-39 • • 
1 
1 
Total . 
9 
55 
32 
37 
21 
25 
14 
15 
13 
10 
8 
16 
7 
8 
3 
273 
other, except that the higher the Trabue score the 
greater the variability in terms of block-design score. 
So vice versa, the lower the block-design score the greater 
the variability in terms of Trabue score. This condition 
may be interpreted as indicating that at the lower ages 
facility in language is rather low, so that block-design 
scores are higher at any given age. On the other hand, 
r = + .57, P. E. ± .03 202 
INTELLIGENCE MEASUREMENT 
the reverse is true for the higher ages: Trabue scores 
here seem to possess higher diagnostic efficiency. 
A number of the children who were included among 
those tested for block-design ability had been given the 
military test when it was in its early stages of standard- 
ization. This again is a test in which the “language 
factor” plays no insignificant part, yet is a recognized 
instrument for intelligence estimation. The cases which 
could be included in this analysis were limited, but the 
results may be of interest. The table follows: 
TABLE LXXX 
Correlation between Military and Block-design Scores 
Block-design Scores 
Military 
Test 
I 
II 
21 
31 
41 
SI 
6l 
71 
81 
91 
IOI 
III 
121 
131 
Total 
Score 
O 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
TO 
and 
IO 
20 
3° 
40 
So 
60 
70 
80 
go 
IOO 
no 
120 
130 
over 
o- 19 
2 
9 
3 
5 
1 
20 
20- 39 
2 
4 
4 
10 
40- 59 
1 
5 
5 
1 
I 
1 
14 
60- 79 
1 
3 
I 
I 
1 
1 
8 
80- 99 
2 
1 
3 
2 
1 
9 
100-119 
2 
1 
1 
I 
1 
1 
7 
120-139 
3 
3 
2 
2 
I 
11 
140-159 
2 
3 
6 
1 
2 
4 
1 
19 
160-179 
1 
2 
5 
3 
2 
2 
1 
1 
17 
180-199 
i 
1 
2 
2 
I 
2 
1 
10 
200-219 
1 
1 
2 
2 
3 
3 
1 
13 
220-239 
1 
2 
I 
I 
2 
1 
8 
240-259 
1 
1 
2 
2 
2 
8 
260-279 
2 
2 
3 
7 
280-299 
1 
2 
3 
300-319 
1 
1 
320-339 
1 
1 
340-359 
360-379 
1 
1 
Total 
2 
18 
20 
27 
11 
16 
10 
10 
12 
4 
5 
15 
7 
7 
3 
167 
r — + .71, P. E. ± .02 203 
THE RESULTS 
The correlation + .71, between the military test and 
the block-design test, although surprisingly high to those 
accustomed to regard “performance” and “linguistic 
ability” as separate and distinct capacities, is neverthe- 
less to be expected in light of the fact that both test 
schemes aim to measure intelligence. 
In the following tabular arrangement the correlations 
of the block-design test with the three tests in which 
“language” plays an important role are given: 
1. Block-design test and Binet Vocabulary . + .77, P. E. ± .02 
2. Block-design test and Trabue B and C . + .57, P. E. ± .03 
3. Block-design test and Military . . . + .71, P. E. ± .02 
In order to determine whether the correlations between 
the block-design test and the three tests designated as 
involving the use of language might have been higher 
but for the interference of this “language” factor, the 
scores of the Binet vocabulary and the military test were 
correlated, both having the “language factor” in com- 
mon. It is presumed that if these latter two tests show 
no greater correlation than either test with the block- 
designs, that other factors than language facility enter 
to lower the correlation from -f- 1.00. 
The correlation between Binet vocabulary and mili- 
tary test is + .87, P. E. dh .02 (167 cases). 
It is, consequently, apparent that other disturbing 
factors than “language” are operative tending to reduce 
the correlations between these three tests. The cor- 
relations between the block-design and any one of the 
three other tests is not very appreciably lower than the 
correlations between any two random “language” in- 
telligence tests. 204 
INTELLIGENCE MEASUREMENT 
This brings us to our original problem, “Does the Binet 
test exaggerate the importance of language in contra- 
distinction to performance?” If such a condition does 
exist, its importance has been greatly overemphasized 
in the past. And to our other question, “Are there 
specialized capacities of ‘doing’ which are as indicative 
of intelligence as those concerned with ‘talking’ and 
‘information’?” a rational reply based upon our statisti- 
cal data would include the remark that there are no 
such compartment-like functions, and that facility in 
one direction is highly correlated with facility in the 
other. 
From the point of view of the validity of the proposed 
test-scheme, the block-design tests, the above-mentioned 
correlations between this performance test and typical 
language-intelligence tests bear out the contention that 
the block designs measure intelligence rather effectively. 
(8) The Probable Error of a Block-design Mental Age 
The consistency with which a newly-devised measur- 
ing instrument estimates presented values may be re- 
garded a fair index of its validity. Extreme variability 
and haphazard deviations from normal expectation may 
be interpreted as indicating lack of efficiency in evalu- 
ating quantitative differences. On the other hand, re- 
peated identity of determined values for any given 
objective quantity argues for proficiency of the measur- 
ing tool. It is, therefore, regarded important to de- 
termine to what extent, and with what probability, 
extreme deviations of significant magnitude may be 
expected. THE RESULTS 
205 
The probable error (P. E.) is the statistical device 
whereby such consistency may be computed. 
In his study of vocabulary, Terman found1 the prob- 
able error of a mental age based upon vocabulary score 
alone to be 9.6 months (631 children). In other words, 
based on vocabulary alone, mental age thus determined 
will not deviate from the mental age derived from 
applying the entire Stanford-Binet scale more than g}/2 
months in 50 per cent of cases. The table of ratios 
follows: 
Deviation 
Per Cent of Cases 
9)/2 mos 
5o 
12 mos 
40 
18 mos 
24 mos 
10 
36 mos 
r = + .91 
A difference in mental age as great as three years may be 
expected in only one case out of ioo, and a difference of 
two years in only i out of io. Or, put differently, taking 
any obtained score, the chances that it is within one year 
correct (one year above or one year below) are 60 that 
it is, to 40 that it is not. The chances that the score is 
within two years of the correct mental age are 90 to 10, 
and within three years, 99 to 1. 
For adults the vocabulary test did not function as 
efficiently. The probable error of a mental age based 
1Terman, Lewis M., Kohs, S. C., and others: “The Vocabulary 
Test as a Measure of Intelligence,” Journal of Educ. Psychol., October, 
19x8 206 
INTELLIGENCE MEASUREMENT 
upon the vocabulary score with this group of cases 
was 12 mos. The table of ratios follows: 
Deviation 
Per Cent of Cases 
12 mos 
So 
18 mos 
3i 
24 mos 
18 
36 mos 
4-3 
r = + .81 
A divergence greater than one year between mental 
age as determined by the vocabulary alone and that of 
the Binet scale applied as a whole was to be expected 
in 50 cases out of 100. A two years’ divergence or mbre 
had only 18 chances out of 100 in its favor, and the chance 
that a mental age was within three years correct was 
95.7 to 4-3- 
In the light of this information it may be of interest 
to present the probable error of a mental age derived 
from the application of the block-design tests. 
The data of the table on the opposite page were secured 
frohi the figures of Table LXX (p. 176). 
Although the median quartile deviation is approxi- 
mately two months lower than the average (arith. mean) 
quartile deviation, the latter, although less favorable 
to the block-design tests, will be utilized in this 
analysis. 
The data of Table LXXXI indicate that the probable 
error of a block-design mental age in terms of Stanford- 
Binet mental age is about 16 months. In other words, 
th'e chances are that a mental age based upon block- 
design performance will not be incorrect more than 16 THE RESULTS 
207 
Block-design Age IYks.) 
Below 
6 
6 
7 
8 
9 
IO 
II 
12 
13 
14 
is 
l6 
17 
18 
19 
20 
No. of Cases 
43 
40 
29 
30 
38 
33 
27 
28 
22 
20 
18 
12 
14 
3 
4 
5 
Median Binet 
Age * . . 
64 
90 
98 
108 
120 
129 
133 
138 
144 
149 
181 
186 
181 
191 
202 
Qi • • • 
56 
78 
88 
93 
96 
104 
108 
121 
130 
126 
137 
138 
177 
160 
181 
195 
Q* . . . 
73 
102 
109 
120 
I23 
136 
138 
150 
i57 
164 
165 
217 
209 
204 
229 
207 
Quartile Devi- 
ation . 
8-5 
12.0 
10.5 
13-5 
13-5 
16.0 
15.0 
i4-5 
13-5 
19.0 
14.0 
39-5 
16.0 
22.0 
24.0 
6.0 
Median Binet Ages for Each Block-design Age 
* The figures in the body of the table are in terms of months. 
Average Quartile Deviation . . 16.1 mos. 
Median Quartile Deviation . . 14.25 mos. 
TABLE LXXXI 208 
INTELLIGENCE MEASUREMENT 
months in at least 50 per cent of the cases examined. 
The table of ratios follows: 
Deviation 
Per Cent of Cases1 
12 mos 
61 
16 mos 
50 
18 mos 
45 
24 mos 
3i 
30 mos 
36 mos 
13 
42 mos 
8 
48 mos 
4 
r = + .84 
A difference in mental age as great as four years may 
be expected in only 4 cases out of 100, a difference of 
three or more years in only 13 cases out of 100, and a 
difference of two years or less may be expected in 69 cases 
out of 100. 
Based upon this criterion alone the block-design test 
appears to have about 56 per cent the diagnostic power 
possessed by the Binet vocabulary. 
(9) The Segregation of the Feeble-minded 
Although at the present time the writer has no evidence 
to adduce other than his experience coupled with a 
certain insight into the general condition of feeble- 
mindedness, it seems reasonable to assume that feeble- 
mindedness is not an arbitrary psychological and 
1 These results have been derived through the use of Sheppard’s 
table of values of the normal probability integral modified for interpo- 
lated terms and presented in Table XC in Appendix III. Because of 
the interpolations this table may be found to possess greater utility than 
Thorndike’s “Mental and Social Measurements” (2d ed., p. 200) or 
Buckingham’s “Spelling Ability,” p. 35 and p. 116. THE RESULTS 
209 
statistical designation which fluctuates and changes as 
do our moral standards. After years of effort in this 
field one cannot help but be led to the conclusion that 
mental feebleness is merely one of the surface indications 
of general physiological incompetence. This notion is 
expressed as follows by Cabot: 
“Our best social diagnoses, such as idiocy or feeble- 
mindedness, do not refer to the mind only. They refer 
to the body just as much. Feeble-mindedness is a state- 
ment about the child’s body, his brain, his voracious 
appetite, the diseases to which he is likely to succumb, 
his extraordinary susceptibility to cold, and his poor 
chances of growing up. One says a great deal about 
the physical side of a child, as soon as one pronounces 
the word ‘feeble-minded.’”1 
It is just this aspect of the general problem which has 
been overlooked by those whose only basis for the term 
“feeble-mindedness” has been the “normal curve of 
distribution.” Mental deficiency is a general, disordered, 
physiological condition, which transcends such simplicity 
of definition or understanding. 
It has frequently been argued that because the results 
of an intelligence test yield, what appears to the eye, 
a normal distribution curve, this in itself is complete 
proof that human intelligence is a perfectly-graded, 
homogeneous entity. The writer, at this time, merely 
wishes to call to the reader’s attention the important 
discussion by Boring2 in which he points to the fact that 
1 Richard C. Cabot: “Social Work,” (Boston: Houghton, Mifflin Co., 
1919; 188 p.), pp. 107-108. 
2 “The Logic of the Normal Law of Error in Mental Measurement,” 
Amer. J. of Psychol., 1920; 31:1-33. See especially pp. 12, 13, and 15. 210 
INTELLIGENCE MEASUREMENT 
whereas Merriman’s frequently quoted table of shots 
aimed at a target is generally utilized to illustrate the 
functioning of the normal law to errors, nevertheless 
“Pearson showed that the distribution of shots at a 
target, given by Merriman, is best represented by the 
sum of normal curves.” For the same reason there is 
room for belief that possibly the curve for human in- 
telligence, which in reality is not “normal” but skewed, 
may be the composite of two (perhaps more) separate 
curves, perhaps “normal,” perhaps not, each represent- 
ing measurements of somewhat distinctively separate 
groups. 
Any test devised to measure intelligence has a specific 
bearing upon the general problem of the clinical differ- 
entiation of the feeble-minded. The present test has 
been purposely devised to be of especial assistance in 
this general direction. After wrestling with various 
problems of clinical psychology for a number of years, 
one of the pressing outstanding questions appeared to be 
that of the borderzone case. A number of mental ex- 
aminers apparently are content with designating a child 
“borderzone intelligence,” and allowing the matter to 
rest there. This is especially true of those who have 
been given to a rather arbitrary ultilization of the Binet 
scale, chopping off cases into groups on the basis of I. Q. 
alone. So, in spite of the fact that any determined 
I. Q. may be in error 2 or more points in 50 per cent of the 
cases, if Johnny Smith is 79 I. Q. he is a “borderzone 
case,” but if it happens to be 81, he is just dull normal! 
Clinical psychology, to gain substantial recognition, 
must take itself more seriously! Binet I. Q. is merely THE RESULTS 
211 
one of the minutiae of an adequate diagnostic syllabus. 
And a final summation of information from the psycho- 
logical, educational, social, medical, vocational, and 
biological fields is considerably more than can be epito- 
mized in a brief label of one or two words. 
The writer is making a plea, not for the abandonment 
of intelligence classifications as such, but rather that the 
psycho-clinician dictate his classification, and not allow 
the classification to master and dictate to him. There 
are frequent occasions when established classifications 
fail to fit a specific case. That is the time when the 
efficient examiner manifests his mettle and his intelligence 
by freeing himself from any previous systematized 
procedure and analysis, and arrives at the truth by other 
channels and other criteria. 
Looking at the matter from a social and practical 
point of view, those who engage the services of trained 
clinical psychologists do not look for any half-baked 
theories or any speculative conclusions about certain 
individuals or families who are distinct social problems. 
They require definite, practicable, intelligent recommen- 
dations, based upon a thorough and scientific analysis 
of the factors involved. Shall this child be sent to an 
institution for the feeble-minded? Can Mary, aged 
nineteen, be held responsible for her acts? What shall 
we do with Johnny, the recidivist, father insane, mother 
out working? Shall the Jones family, consisting of step- 
father, mother, and eight children, be broken up? Ought 
we to sterilize William? Shall we place Mrs. Smith as 
a domestic? Shall Tom be sent to the insane asylum or 
the penitentiary? What can we do for the Thompson 212 
INTELLIGENCE MEASUREMENT 
family, a typical instance of continued dependency 
running over a considerable period of years? And so on, 
ad infinitum. All along the line the life, happiness, and 
futures of our fellow human beings are being placed in 
the balance, and we aid in tipping the balance, up or 
down. Terms such as “borderzone intelligence” based 
upon the Binet test mean little if anything in writing out 
a prescription for action necessary to be taken in each 
of the above-mentioned instances. The social worker 
who is to handle a case wishes to know whether there is 
reason to hope for a moderate degree of success at social 
rehabilitation, or whether hope of success is unthinkable 
in the light of existing handicaps and social forces. To 
him a person is normal or not, well or not, dead or alive. 
One who is feeble-minded should not be handled as nor- 
mal, he who is normal should not be handled as feeble- 
minded. For the feeble-minded the road-directions point 
one way, for those who are normal they point in the 
opposite. There exists no borderzone. 
Whatever theories we may hold regarding the develop- 
ment, the distribution, the varieties and classifications 
of intelligence, a person presented for examination is 
or is not feeble-minded. Our determination of this fact 
may take on various degrees of expertness. In standard- 
izing the block-design tests the writer was motivated by 
a desire to devise an additional tool which might assist 
in an intelligent determination of whether a person was 
or was not feeble-minded.1 Among ourselves we may 
1 As used here, the term “feeble-minded” is understood to be based 
upon a thorough analysis of all phases of a person’s past and present 
history taken from all diagnostic angles, and not upon the Binet test 
alone. THE RESULTS 
213 
create all sorts of fantastic notions and classifications 
about which we may pleasantly wrangle, such for 
example as the “borderzone group,” some of us believing 
that that group represents the overlap between normals 
and feeble-minded, and others of us maintaining that that 
group is a distinct, clear-cut entity, — but to the prac- 
tical worker engaged in curing the ills of humanity 
these “fantastic notions” mean next to nothing. 
What has been said may appear a rather unique and 
veiled return to an earlier contention regarding the 
“borderline case”1 which some may have expected the 
writer to have abandoned after some hoped-for increase 
in maturity and knowledge! The chief purpose, however, 
in the present instance was to emphasize the importance 
of “differentiability” which a good test of intelligence 
should possess. For a very adequate discussion of the 
borderzone question the reader is referred to Miner’s 
monograph “Deficiency and Delinquency.”2 
Five cases have been selected from the writer’s most 
recent clinical experience to illustrate the assistance 
which the block-design tests may render. This material 
was written on August 3, 1921, and the five cases listed 
below represent the last five consecutive examinations 
in which the block designs were used. 
1 Kohs, S. C.: The Practicability of the Binet Scale and the Question 
of the Borderline Case. Bull. No. 3, 1915, Research Dept. Chic. House 
of Correction, p. 23. 
2 Miner, J. B.: “ Deficiency and Delinquency” (Baltimore, Warwick 
& York, 19x8; 335 p.). 214 
INTELLIGENCE MEASUREME: 
Name 
Tests Used 
Date Examined 
I. 
Irving T 
(a) 
Illinois Examination II, 
Form i 
July 28, 1921 
(b) 
Stanford-Binet 
(c) 
Kohs Block-designs 
2. 
Edna U 
(a) 
Stanford-Binet 
July 27, 1921 
0b) 
Kohs Ethical Discrimi- 
nation1 
(c) 
Kohs Block-designs 
3* 
Chas. V 
(a) 
Stanford-Binet 
July 21, 1921 
(b) 
Kohs Block-designs 
4- 
Frank W 
(a) 
Stanford-B i n e t (by 
Miss K. Donald) 
July 14, 1921 
(b) 
Kohs Block-designs 
5- 
Kenneth X.. 
(a) 
Stanford-Binet 
July 13, 1921 
(b) 
Kohs Block-designs 
KEY TO ILLUSTRATIVE CASES 
Case No. i. At the time of the examination Irving 
was 17 years 10 months old. Born in Minnesota, of 
American-born parents, German-English descent, reached 
the seventh grade, now plumber’s helper earning $5 a 
day, has a small bank savings. Father died little over 
two years ago, was a lumber piler. Three other children, 
older, one boy, two girls. Mother has no influence over 
Irving. Lives in rented two-story house. Home fairly 
furnished, clean, and orderly. Irving well clothed. 
History of delinquency may be tabulated as follows: 
1 Kohs, S. C.: “An Ethical Discrimination Test.” J. of Delin- 
quency, 1922, Vol. 7, pp. 1-15. Copies of this test with complete in- 
structions and scoring material may be secured from the C. H. 
Stoeltirar Co . t.ot.7 Carroll Ave.. Chicago. Illinois THE RESULTS 
215 
Date 
Delinquency 
Disposition 
Oct. 13, 1917 
Stole sample case containing gums, 
candies, cookies from auto. Sample 
case found. Contents gone. Impli- 
cated with three other boys. 
Cautioned and released. 
Sept. 19, 1918 
Stole box of crackers from Cracker 
Co. Irving admitted theft. Claimed 
he was hungry. Box unopened when 
found. 
Ordered to return box, apologize and 
work to pay damages. Cracker Com- 
pany satisfied with apology after box 
was returned. Warned that if he ap- 
peared in Court again might be sent to 
one of the institutions. 
June 9, 1919 
Maliciously abusing another boy. 
Advised to desist and reminded of the 
State Training School. 
July 26, 1919 
Larceny of automobile. Captured 
after running machine into telephone 
pole and front of a grocery. 
Placed on probation with a Big Brother 
who arranged for boy’s employment. 
Damages to be paid. 
Jan. 7, 1920 
Stole two chickens. Three other boys 
implicated. 
Severely lectured. 
Nov. 7, 1920 
“Shooting craps” on street. 
Attention of parent called to this matter. 
Mar. 10, 1921 
School attendance officer reports Ir- 
ving will not attend evening school. 
Father dead, mother can do nothing 
with boy. 
No specific action taken. 
July 27, 1921 
Larceny of one auto on July 17, con- 
fessed to another on July 4. On 
July 18 stripped accessories from two 
other machines. 
Disposition now pending. 216 
INTELLIGENCE MEASUREMENT 
On the Illinois Examination II, which the writer has 
adapted for individual testing, Irving obtained a total 
score for the general intelligence tests (7) of 67 points. 
This is equivalent to a mental age of 11 years o months. 
His I. Q. comes to 69 per cent. On the Stanford-Binet, 
with a basal year of 9, he obtains an intelligence rating 
of 12 years 4 months, giving him an I. Q. of 77 per cent. 
On the block-design test, seven out of thirteen designs 
attempted are successfully completed, yielding a score 
of 35 points which is equivalent to a mental age of 10 
years n months. His I. Q. here is 68 per cent, within 
one point of the Illinois Examination. 
Irving, on the basis of the Binet test, is a borderzone 
case. On the two other tests he falls below the 70 per 
cent dividing line. Taking a composite, or an average 
of the three estimates, his I. Q. becomes 71, still border- 
zone, which was the intelligence classification finally set 
down. The complete social analysis of the case is in the 
process of being made, but the psychological report, at 
the present stage reads that “if continued social in- 
capacity is manifested in the future, this boy may be 
classified as feeble-minded and as such committed to the 
State Institution for the Feeble-minded.” 
Case No. 2. Edna is a nice-appearing girl, 15 years and 
11 months old at the time of examination, and rather 
over-developed physically for her age. Born in Oregon 
of American-born parents, Irish-English descent. 
Reached the seventh grade. Mother died of tuberculosis 
soon after Edna was born. Father thought dead, but 
only recently traced to a small town in Oregon where he 
is employed as a mill-worker (general labor). Edna has THE RESULTS 
217 
a brother about four years older, about whom little is 
known. She first became notorious about a year ago 
when charges of contributing to the delinquency of a 
minor were brought against the principal of a small town 
school which she was attending. The principal was 
almost lynched at the hands of the inhabitants, although 
acquitted of the charges by a jury. After this episode 
she was brought to Portland and placed with an aunt 
who is rather irresponsible. Excerpts of the report from 
the Woman’s Protective Division read as follows: 
“Sat. July 16, Edna was sent to a grocery store at 
Sts., to make some purchases. D waited on her. 
She loitered in the store looking at a book and finally 
D told her she owed him io cents and asked her to 
come into the back room. She went in and D had 
relations with her. She says she went to the store 
between i and 2 and left between 2 and 3. 
“ She dared not go home so started to walk. On 
st. she was overtaken by Ed who was driving an 
automobile. (Ed is a juvenile who has previously 
been before the Court for immorality.) He asked her 
where she was going and she replied to Q (a small 
town approximately 20 miles distant). He offered to 
take her there; she got into the machine with him, he 
drove her to Q out Road and had relations with 
her in the woods. Then took her back to Q at about 
10 p.m. 
“She stayed alone at Hotel, room 6, registered as 
(fictitious name) and paid 75 cents for her 
room. She says she had a little money when she left 
home. 
“Ed gave her his name and address when he left 
her. In the morning she started to walk back to Port- 
land, had no supper or breakfast. She walked all the 218 
INTELLIGENCE MEASUREMENT 
way back to Portland to , arriving there about 3 or 
4 Sunday p.m. 
“George saw her standing on the street corner 
across from St. He and Ed took her in a Ford 
for a ride, went out past Road, both boys had rela- 
tions with her, first Ed, then George. George had rela- 
tions with her twice at this time. She thinks she was 
out with the boys about two hours ...” And so the 
story unravels, involving more boys the farther it goes. 
The girl was not actively in search of these experiences 
but seemed a rather obvious mark to the unscrupulous. 
When this information reached the press it appeared 
under the following headlines: 
“GIRL, 15, FOUND IN SHACK, 20 men suspects 
arrested, but only 5 are held — police are of opinion 
runaway child is weak-minded — physician takes 
charge.” 
After a short period of observation Mrs. Lola G. Bald- 
win, head of the Woman’s Protective Division, declared 
the girl utterly irresponsible. 
By the Stanford-Binet test, with a basal year of 8 
years, Edna manifested an intelligence equal to 11 years 
5 months. With a life age of 15 years n months her 
I. Q. is 72 per cent — borderzone. Given the block 
designs she succeeded in passing only one, the first, of 
the six designs attempted. Her score on this test 
amounted to 1 point, this being equivalent to a mental 
age of 5 years 7 months. This indeed, is far from the 
girl’s actual intelligence level, but it possesses diagnostic 
significance, especially in relation to our “borderzone” 
problem. On the Ethical Discrimination Test the 
percentage efficiency in each exercise was as follows: THE RESULTS 
219 
I. 
Social Relations 
• 90% 
2. 
Moral Judgment 
■ 8o% 
3- 
Proverbs 
• 6o% 
4- 
Definitions of Moral Terms 
• 53% 
5- 
Conduct Evaluation 
• 5o% 
6. 
Moral Problems 
• 90% 
Average 
• 7i% 
On the basis of tentative norms this average of 71 
per cent is equivalent to the performance of about a 12x/i 
year-old. 
In the light of this history, her motives, and her general 
record, the girl was declared feeble-minded, unable 
because of marked retardation in intelligence to manage 
herself and her affairs with the ordinary prudence com- 
mon to other girls of her life age. The further disposition 
of the case is now pending. 
Case No. 3. Charles is the duller-looking one of the 
two boys left with a maternal aunt after the father died 
five years ago, having been killed by a railroad train, 
and the mother had been committed to State Institution 
for the Feeble-minded two and a half years ago. Mrs. 
M brought Charles to court one day (Dec. 2, 1920), 
claiming the boy was feeble-minded just like his mother, 
that she was willing to keep the other boy, but that 
Charles was a hopeless case and consequently the state 
should undertake the care of the child. At the time of 
the first examination Charles was 7 years n months 
and tested, by the Stanford-Binet, showed an intelligence 
of 6 years 6 months, his I. Q. being 82 per cent, and 
classifiable as dull-normal. Although a petition in feeble- 
mindedness had been duly filed in this case, this was 
canceled and the boy turned over to the Boys’ and Girls’ 220 
INTELLIGENCE MEASUREMENT 
Aid Society for observation, education and treatment. 
Charles was born in Portland of German-American 
parentage, the father only being foreign-born. The 
child’s report card for three months showed “good” 
marks in all subjects except “application” for the second 
month. Charles is affected with ptosis, giving one a poor 
impression of his intelligence. On April 12, 1921, we 
unearthed the fact that a quack “psycho-analyst,” had 
“examined” the boy back in 1918, had adjudged him 
feeble-minded, a vacancy for the boy had been made at 
the feeble-minded institution, and in 1919 when the boy 
was about to be sent, his aunt experienced a change of 
heart. She claims Charles is unreliable, can remember 
nothing, frequently fails to come home from school or 
after being sent upon errands, and that he has been two 
years in the first grade. There is a sister of Charles’ 
eleven years old staying with grandparents in eastern 
Oregon who are very poor. When Mrs. M’s home was 
visited it was found to be a four-room affair, rather neat. 
Mr. M was found in bed where he has been confined for 
many years with articular rheumatism. The sources 
of income of the M family are distributed as follows: 
“$20 a month from Mr. M’s lodge, sick-benefit; $30 
from the county for the care of Charles and his brother, 
and the money paid by three men boarders. Of this 
money $100 must be paid every three months in pay- 
ment for the purchase of this home. Mrs. M has three 
daughters, aged 18,16 and 8. The two eldest are in high 
school and must sleep at a neighbor’s for lack of room. 
The boarders occupy a tent in the yard. After Charles 
was at the Boys’ and Girls’ Aid Society for four months, THE RESULTS 
221 
he was reported by the Superintendent as being feeble- 
minded and unplaceable. Another mental examination 
was, therefore, arranged. On July 21, 1921, Charles 
was again examined. He was now 8 years 6 months and 
on the Stanford-Binet obtained a mental age of 7 years 
o months. Again his I. Q. was 82, and was again classi- 
fiable as dull normal. It was then decided to give him 
the block-design tests. Although on the basis of life age 
he should have secured a score of 14 points, and on the 
basis of mental age his block-design score should have 
been at least 6 points, he failed to perform any of the 
designs correctly, in spite of continued explanations and 
demonstrations. His intelligence age here was below 
5 years 3 months, yielding an I. Q. under 62. However, 
he was sent back to the Aid Society for further observa- 
tion and treatment. In the meantime his intelligence 
has been set down as dull normal, but possibly poten- 
tially feeble-minded. 
Case 4. Frank W. first came to the attention of the 
court when a neighbor reported on December 14, 1918, 
that Frank, n, and his sister of 4 had been left with a 
maternal grandmother, a widow, the mother having 
died recently, and the father having deserted, his where- 
abouts not being known. The family also was reported 
to the local Associated Charities as being in destitute 
circumstances. It was learned later that Frank’s father 
was rather nomadic in tendency, and in 1914 had 
deserted the family for good after the second child had 
been born. On September 2, 1919, it was reported to 
us that the grandmother was abusing and unmercifully 
beating Frank. On September 8, the grandmother was 222 
INTELLIGENCE MEASUREMENT 
visited. She claimed Frank was unruly and disobedient, 
that she does punish him, there being no other way of 
getting along with him; denied most emphatically that 
she had ever punished him to an extent that might be 
deemed cruel or excessive. She was found living in a 
rented home, her income being derived from little sew- 
ings and from keeping a boarder. For some intangible 
reasons she has been ostracised by her neighbors. Al- 
though Frank did not appear quite normal to the visitor, 
his sister seemed a happy, healthy child, neat, apparently 
well cared for, and devoted to her grandmother. At 
the time of this visit Frank was attending the regular 
schools, was in the 4th grade, and the teachers gave a 
good report of his conduct in school. Four months later 
we find Frank in the Etna School (ungraded) with a 
petition for feeble-mindedness filed by the Public Wel- 
fare Bureau. He was examined July 14, 1921. His life 
age was 13 years 4 months, and on the Stanford-Binet he 
secured a mental age ranking of 8 years 9 months. His 
I. Q. was 66. On the block-design test, of six designs 
attempted two were successfully completed, scoring 
3 points on the first design and 4 points on the third 
making a total of 7 points. He was utterly lost beyond 
the third design. His mental age ranking here was 
7 years 3 months, with an I. Q. of 55 per cent. The 
grandmother admitted that the boy was feeble-minded 
but was prone to argue about the causation. Disposition 
of the case is now pending. 
Case 5. Kenneth X. first came to our attention June 
20, 1921, when Miss Ida M. Manley, principal of the 
Etna School (ungraded) filed a petition in feeble-minded- THE RESULTS 
223 
ness. This was accompanied by a memorandum which 
contained the following information. Mother until 
recently a janitress in one of the schools, father died 
two years ago, said to have had locomotor ataxia. Ken- 
neth has been in special class for three years (third 
grade). Has habit of taking everything loose about 
the school. Is exceedingly clever in making up stories 
to cover his guilt. Repeated scoldings, warnings, and 
punishments have no effect. Kenneth’s mother has had 
three other children, one died because of premature 
birth, one was born paralyzed, and the other died at six 
years of age of a “natural disease,” as the mother put it. 
With a basal year of six Kenneth obtained a mental age 
of 8 years io months. His life age at the time of ex- 
amination was n years 6 months, giving him an I. Q. 
of 77 per cent, classifiable as borderzone. On the block- 
design tests, of ten designs attempted only three were 
successfully completed, and after design six he appeared 
hopelessly baffled. His total score was n, i point on 
design i, 5 on design 4, and 5 on 6. This performance 
is equivalent to an intelligence age of 8 years o months, 
yielding an I. Q. of 70 per cent. Other elements in the 
situation made it appear more reasonable to hold up 
proceedings on the commitment for another year, pend- 
ing further observation and treatment. 
The cases cited have not been specially selected, but 
have been taken in consecutive order. The limitations 
of space have made it necessary to omit much social 
and psychological information which is pertinent. The 
chief object has been to indicate wherein the block- 
design tests have been of assistance; consequently their 224 
INTELLIGENCE MEASUREMENT 
importance may appear exaggerated from the bare 
perusal of the material presented. It is expected that the 
reader will understand the correct proportion of emphasis 
placed upon block-design performance. 
In conclusion, the block-design tests, even though it 
should be granted that they fail to measure intelligence 
as efficiently as other standard methods, nevertheless 
are found valid because they assist in the differentiation 
of the borderzone group, some of whom are normal and 
some feeble-minded. 
(10) Percentage Ratios of Agreement and Disagreement 
with Established Standards of Intelligence 
In this section an analysis will be attempted to in- 
dicate in quantitative terms the actual amount of diverg- 
ence between the mental age and I. Q. estimates of the 
block-design test and the Binet. 
(a) The Method of Direct Comparison: Taking Table 
LXX (p. 176) and analyzing it for agreement and diver- 
gence of mental ages, the table on p. 225 is obtained. 
It is apparent that the block-design test is inclined to 
give somewhat higher mental ages, in general, than the 
Binet. Interpreted in a slightly different fashion, the 
following tabular analysis is obtained. 
Exact correspondence and within i yr. = 53.8% 
“ “ “ “ 2yrs. =75-9% 
“ “ “ “ 3yrs. =89.1% 
“ “ “ “ 4yrs. =93-7% 
“ “ “ “ 5 yrs. = 98.4% 
In other words, in practically 90 per cent of the cases 
examined the two mental ages were the same or showed 
no difference greater than 3 years in either direction. THE RESULTS 
225 
Per Cent 
Exact 
Corre- 
SPONDENCE 
Binet Age Per Cent Higher 
Binet Age Per Cent Lower 
i Yr. 
2 Yr. 
3 Yr. 
4 Yr. 
S Yr. 
6 Yr. 
7 Yr. 
1 Yr. 
2 Yr. 
3 Yr. 
4 Yr. 
S Yr. 
6 Yr. 
20 .$ . . 
18.0 
9-3 
55 
1.6 
2-5 
•5 
•S 
IS-3 
12.8 
7-7 
3° 
2.2 
•S 
Total —37.9% 
Total — 41.5% 
Total 
99-9% 
Mental Age Divergences 
TABLE LXXXII 226 
INTELLIGENCE MEASUREMENT 
This substantially corroborates the findings discussed 
under the heading, “The Probable Error of a Block- 
design Mental Age.” 
In order to appreciate the true significance of this 
divergence the discrepancies between two Binet tests 
of the same individual will be stated. 
The following has been obtained from Ter man’s table1 
showing the agreement between the earlier and later 
tests of 428 children by the Stanford-Binet. (Correla- 
tion, r = + .93.) 
TABLE LXXXIII 
I. Q. Divergences 
Per Cent 
Exact 
Corre- 
spondence 
Second I. Q. Points 
Higher (%) 
Second I. Q. Points 
Lower (%) 
5 
IO 
is 
20 
25 
30 
35 
5 
IO 
is 
20 
25 
30 
35 
40 
45 
30.0 . . 
25.0 
11.8 
3-o 
1.9 
•7 
.2 
14.2 
8.6 
2.6 
•9 
.2 
. 2 
Total — 42.6% 
Total — 26.7% 
Total 
99-3% 
Although the basis of comparison is not entirely 
equivalent, some idea may be obtained of the reliability 
of the block-design tests if compared with the discrep- 
ancies found upon measuring the same individual with 
the same measuring scale on two different occasions, the 
I. Q. in this instance being assumed to remain fairly 
constant. (Although the following observation is some- 
what aside, it may be of interest to call attention to the 
fact that the positive discrepancies of I. Q.’s obtained 
from the second Binet were more than one and one-half 
1L. M. Terman: “The Intelligence of School Children,” p. 143 
(Table 26). THE RESULTS 
227 
times as frequent as the lower ones.1 It will be observed 
that exact correspondence occurs in 30 per cent of the 
cases, and the other deviations maybe tabulated as follows: 
Exact correspondence 
or within 
5 I- Q. 
= 69.2% 
CC CC 
CC 
cc 
IO I. Q. 
= 89.6% 
cc cc 
CC 
cc 
15 1. Q. 
= 95-2% 
cc cc 
cc 
cc 
20 I. Q. 
= 98-0% 
cc cc 
cc 
cc 
25 I. Q. 
= 98.9% 
It should be borne in mind, however, that at different 
life ages, I. Q. changes of the above magnitudes will 
possess different equivalent age values. 
These figures serve as a fairer basis of comparison in 
determining the discrepancies between I. Q. as deter- 
mined by the Binet and the block-design tests. (Again 
the comparison is not a fair one in view of the existing 
controversy over the constancy of the I. Q. The writer 
has been unable to find material which would be exactly 
comparable.) 
Taking the date of Table LXXII (p. 183) the follow- 
ing agreement and divergence of I. Q. are found: 
TABLE LXXXIV 
I. Q. Divergences 
Per Cent 
Exact Cor- 
respondence 2 
Binet I. Q. Points Higher 
Binet I. Q. Points Lower 
IO 
20 
3° 
40 
SO 
IO 
20 
30 
4° 
So 
23-5 • • 
20.8 
9.0 
4.6 
2-5 
•3 
18.0 
ii.8 
5-5 
2.7 
1.4 
Total —37.2% 
Total — 39.4% 
Total 
100.1% 
1 For additional interpretations of this condition see E. A. Doll: 
“The Growth of Intelligence,” Psychological Monographs, Vol. 20. No. 2. 
1921, 130 p., especially Chap. III. 
s Frequency interval is io I. Q. 228 
INTELLIGENCE MEASUREMENT 
Or presented in another form: 
Exact correspondence 
or within 
io I. Q. 
= 62.3% 
ii ii 
ii 
u 
20 I. Q. 
= 83-1% 
ii a 
a 
ii 
30 I. Q. 
= 93-2% 
it a 
u 
ii 
40 I. Q. 
= 98-4% 
A better balance between the per cent of negative and 
positive divergencies is observable here, and also a greater 
spread of variability than is the case with I. Q.’s derived 
from consecutive Binet testings. 
(b) *.The Method of Critical Ninths: A determination 
of discrepancy may be obtained by an analysis of a dif- 
ferent sort. Every table presenting the relation between 
the frequencies of two variables may be divided into nine 
parts, Qi and Q3 for both serving as the dividing lines. 
Qi and Q3 divide any distribution into three portions low, 
middle, and high. Consequently nine groups are possible, 
thus: 
Variable (i) 
c 
Low 
h C 
Middle 
is 
High 
« Q3 
Li H2 
(icritical cases) 
Mx H2 
Hi H2 
Qs 
lRIABLE 
Middle 
O 
LiM2 
Mx M2 
Hi M2 
Qi 
> * 
o 
Li L2 
Mx L2 
HxL2 
(critical cases) 
c 
h C 
>3 
For two tests which supposedly are expected to meas- 
ure the same trait, Li H2 and Hi L2 may be regarded as 
the critical sectors in which as small a proportion as THE RESULTS 
229 
possible of cases should be found. Every case found 
within these limits is a clear argument against the validity 
of a newly devised instrument, when measured against 
one which has already been established (assuming that 
the already-established instrument is absolutely reliable). 
Applying this criterion of validity to the data of Table 
LXX, the following percentages are obtained: 
Variable (i) Binet Age 
Variable (2) Block-design Age 
Critical Cases 
Li H2 = o (0%) 
HxL2= 2 (.5%) 
Total = 0.5% 
Correspondence 
Lx L2 - 61 (16.7%) 
Mi M2 =129 (35.3%) 
Hi H2 = 71 (19.4%) 
Total = 71.4% 
In order to make these values comprehensible in terms 
of other correlations, the percentage of critical cases for 
the Binet and Vocabulary1 and for Army Alpha and 
Stanford-Binet Age2 will be presented: 
Variable (1) Binet Vocabulary 
Variable (2) (631 cases) Binet Age 
Critical Cases 
Lx H2 = o 
Hi L2 = o 
Total = 0% 
1L. M. Terman: “The Intelligence of School Children,” p. 3x0. 
2 R. M. Yerkes: “Psychological Examining in the Army,” (Memoirs, 
Nat. Acad, of Sciences, vol. 15, 1921, 890 p.), p. 621. 230 
INTELLIGENCE MEASUREMENT 
Correspondence 
Li L2 = 145 (23.0%) 
Mi M2 = 244 (38.7%) 
Hx H2 = 113 (17.9%) 
Total = 79-6% 
Variable (1) Stantord-Binet Mental Age 
Variable (2) Alpha Raw Score (653 cases) 
Critical Cases 
Li H2 = o 
Hi La = 1 (.15%) 
Total = 0.15% 
Correspondence 
Li L2 = 104 (15.9%) 
Mi M2 =273 (41.8%) 
HiH2= 99 (iS-2%) 
Total = 72.9% 
It is apparent that a close correspondence exists be- 
tween the evaluations of intelligence (in terms of Binet 
mental age) on the part of the vocabulary test, the army 
alpha, and the block designs. 
Finally, the same analysis is presented for Binet I. Q. 
and Block-design I. Q. (data of Table LXXII, p. 183). 
Variable (1) Binet I. Q. 
Variable (2) Block-design I. Q. 
Critical Cases 
U H2 = 2 (.5%) 
Hi L2 = o 
Total = 0.5% 
Correspondence 
Li L2 = 73 (19.9%) 
Mi M2 = 131 (35.8%) 
Hi H2 = 51 (13.9%) 
Total = 69.6% THE RESULTS 
231 
P. S. /B= Boys 
Cases |G= Gjfis 
• • - F. M. Cases 
Life Age - 9 Yrs. 
Life Age - 14 Yrs. 
I. Q. Discrepancies 
GRAPH 43 
Binet I. Q. • 
Binet I. Q.~ 
IB. D. I. Q. 
Bmet I. Q. 
B. D. I. Q. 
Binet I. Q. 
B. D. I. Q. 
B. D. I. Q. 232 
INTELLIGENCE MEASUREMENT 
(c) Graphic Analysis: For a graphic presentation of 
discrepancies the life ages of 14 and 9 have been selected 
— age 14 because this life age had the largest single 
number of feeble-minded below age 17 (see Table I) and 
age 9 purely at random. An analysis of Graph 43 indi- 
cates the existence of a number of conditions: 
(1) A mild process of compensation is operative, some 
who have low I. Q. on the Binet, obtain high I. Q. on 
the block designs and vice versa (especially true of the 
9 year-olds); 
(2) Low Binet I. Q. are often coupled with still lower 
B. D. I. Q., and high Binet I. Q. are often found in con- 
junction with still higher B. D. I. Q. 
(3) The larger proportion, however, manifest little, 
if any, discrepancy between the two I. Q. 
It will be observed that the range of I. Q. in the block- 
design tests is considerably increased. This has its 
disadvantages, but from a clinical point of view this char- 
acteristic is a desirable one, because of its bearing upon 
the differentiation of the inferior and the superior. 
Summarizing this discussion of discrepancy, it may be 
stated that although the results of the block-design test 
do not tally exactly with those of other measures of intel- 
ligence, nevertheless, agreement is close enough to grant 
the block designs a fair degree of validity, the instances of 
disagreement being in themselves sufficiently crucial to 
require a psychological analysis apart from the tests 
themselves. 
This concludes the discussion of validity. A number 
of criteria have been utilized, each differing in weight and THE RESULTS 
233 
in general importance. In reality the only effective acid 
test is the pragmatic one. If the tests will be found to 
work, that is all that the most critical ones of us demand. 
The array of evidence just presented seems to indicate 
not only that the tests measure intelligence, but that this 
is accomplished with a fair degree of accuracy. On the 
other hand, one should bear in mind Stern’s caution:1 
“Psychological tests must not be overestimated, as if 
they were complete and automatically operative meas- 
ures of mind. At most, they are the psychographic 
minimum that gives us a first orientation concerning 
individuals about whom nothing else is known, and they 
are of service to complement and to render comparable 
and objectively gradable other observations — psycho- 
logical, pedagogical, medical — not to replace these.” 
3. DIAGNOSTIC VALUE OF THE TESTS 
It has been intimated a number of times by writers of 
varying degrees of expertness and reliability that an 
estimate of intelligence based upon the use of a single 
measuring instrument is inclined to be less accurate than 
one based upon the application of a number of such 
diagnostic tools. In fact, a frequent failure upon the 
part of numerous psycho-clinicists is to disregard other 
important criteria for the proper diagnosis of intelligence 
or of mental deficiency and to rest content with the 
results of a single test, somewhat mechanically evaluated. 
This is especially true of feeble-mindedness. No diagno- 
sis of this condition is adequate which has not included 
1 “ The Psychological Methods of Testing Intelligence ” (Warwick 
and York, 1914), p. 12. 234 
INTELLIGENCE MEASUREMENT 
weighing the evidence in other fields than the psycho- 
logical. Thus a verdict of feeble-mindedness which is 
not supported by evidence of vocational impotence, of 
educational failure, of social incompetence, of biological 
taint, is, except in rare and exceptional instances, quite 
weak and untenable. 
The issue also has been raised whether we have not 
overemphasized the verbalistic tests with the inevitable 
injustice to those who may be laboring under a language 
handicap. Without desiring at this point to enter any 
evidence for or against the reasonableness of this con- 
tention, other than that already presented in this mono- 
graph, it does seem wise to utilize tests which measure 
intelligence through “performance” as well as through 
“language.” The combined results of an inquiry in 
both these directions seem to indicate a closer approxi- 
mation of what is the actual mental age of a subject, than 
if either is used alone. 
On the other hand, it is plainly evident that no “per- 
formance” test yet devised measures intelligence as 
adequately or with as high a coefficient of efficiency as 
the Binet or two or three other “language” tests. Of 
course, the standards upon which our judgments of 
efficiency have been based may be unsatisfactory, e.g., 
school progress, teachers’ estimates, school marks, etc. 
At any rate, looking at the matter from a practical point 
of view, few, if any, clinical psychologists would be free 
to abandon our so-called “language” intelligence tests 
for the exclusive use of “performance” tests in classifying 
children and in making diagnoses of mental deficiency. 
At present, performance tests are of chief importance as THE RESULTS 
235 
corroborative and supplementary sources of information. 
This probably will hold true for some time to come. 
4. SERVICEABILITY 
In his “Stanford Revision of the Binet-Simon Scale” 
(Warwick and York, 1917) Terman states,1 that “to 
be widely serviceable a test should demand only the sim- 
plest material or apparatus, should require at most but 
a few minutes of time, and should lend itself well to uni- 
formity of procedure in application and scoring.” The 
writer has attempted to satisfy these demands in stand- 
ardizing the block-design tests. Those who utilize the 
tests will find after a little practice that there can be but 
little variation in the findings of two examiners, and that 
the only chance for difference is in the recording of the 
number of moves made. 
The special value of the block-design tests lies in the 
fact that valid results may be obtained independently of 
the “language factor.” Neither deafness nor lack of 
language-understanding should be disqualifications in 
the proper performance of the test. The block designs 
may therefore be utilized in the study of racial differences, 
in determining the mental capacities of the deaf and of 
those suffering from various other language handicaps. 
As regards the borderzone problem, it appears that this 
test will aid in a better differentiation of the group of 
cases falling in this category. The writer maintains that 
feeble-mindedness is not an arbitrary statistical designa- 
tion, but is rather a clearly demarked physiological entity 
quite distinct from normality, statistical psychologists 
1P. iso- 236 
INTELLIGENCE MEASUREMENT 
notwithstanding. Years of experience with this type of 
defect has fixed the notion in the writer’s mind that 
feeble-mindedness is indicative not only of mental mal- 
functioning, but also of physiological mal-functioning 
possibly of endocrine character. The results of fur- 
ther research, however, can be the only tests of the truth 
of one’s statements at this time. CHAPTER VI 
Supplemental Observations 
1. Average Mental Age of Adults 
2. Increasing Divergence versus Parallel Progress of 
Mental Development 
3. A Performance Intelligence Scale 
I. AVERAGE MENTAL AGE OF ADULTS 
Of importance in interpreting the results of this newly 
devised mental test is the recently raised question regard- 
ing the average mental age of adults. The current prac- 
tice of regarding 16 years as the age when intelligence- 
maturity is attained, and the age characteristic of the 
American population at large, has been adhered to in 
the standardization of the block-design tests and in the 
interpretation of scores derived therefrom. 
The results of army testing have thrown some question 
upon the tenability of this standard, and although 
previous to the testing in the army criticism of the 16- 
year criterion emanated from certain quarters,1 no great 
importance was attached to these attacks, clinical psy- 
chologists continuing the practice of regarding 16 years 
as the intelligence of the average adult. The results of 
army testing, due to the overwhelmingly large numbers 
examined, are likely to receive greater recognition and 
1 See controversy between J. E. W. Wallin and S. C. Kohs in Journal 
of Amer. Institute of Criminal Law and Criminology, 1916, vol. 6 and 7. 
237 238 
INTELLIGENCE MEASUREMENT 
may be regarded by some as unalterably conclusive. 
The army tests indicated that the average mental age 
of adults, especially utilizing the figures of Group X, a 
supposedly random sampling of 653 men, is 13 34 years.1 
The attempt will here be made to present reasons why 
we should exercise caution in accepting this level as 
average, advising instead the continued use of the 
16-year standard until further experimentation has been 
carried on to decide the issue finally. The reasons for 
questioning the 1334 estimate will be listed seriatim, 
and have not been arranged in order of importance but 
rather as they suggested themselves to the writer. 
(1) It is advantageous in measuring intelligence to 
utilize a tool which will not present adaptive difficulties 
for the person examined. Thus familiarity, previous 
experience, specialized imagery, the peculiar mechanics 
of the test itself may make it easier for some to obtain 
satisfactory scores to whom the technique of the test is 
adapted, and, on the other hand, more difficult for those 
to whom the test procedure and its attack are strange 
and unfamiliar. The army test, together with the con- 
ditions under which it was taken, in and of itself requires 
“an adaptation to a new situation” which is quite com- 
plex. All subjects will not adapt themselves similarly. 
This condition introduces a spurious factor likely to 
underweight the performance of those below average in 
mental ability, with the inevitable result that the general 
average is reduced. An ideal test of intelligence measures 
“ability to adapt oneself to a new situation,” but is not 
1 R. M. Yerkes: “Psychological Examining in the Army,” Memoirs 
National Acad, of Sciences, pp. 195, 790. SUPPLEMENTAL OBSERVATIONS 
239 
itself a matter to which “adaptation” is required. In 
this respect the army tests may be said to fall short, 
a correcting formula being necessary to compensate for 
this “drag” upon sub-average ability, when determining 
the average capacity of a group examined. 
(2) A matter deserving serious consideration at this 
time when group testing has deservedly gained such great 
popularity, both for analyses of intelligence level and of 
pedagogical achievement, is what the writer has termed 
the “ theory of progressive score reductionA tacit 
assumption generally made in group examining is that 
ability manifested in a group-test will very closely cor- 
respond to the same level of ability attained in an in- 
dividual examination. Regression tables and correlation 
coefficients are presented as evidence bearing out this 
contention. A close analysis of the situation will, 
however, reveal the existence of this condition: Whereas 
a high score in a reliable group intelligence test is un- 
questionably indicative of that mental level, because 
superior scores cannot be obtained by accident or 
haphazard, the same does not hold true for low scores. 
One hardly dare state that a low score is ipso facto the 
inevitable performance of an inferior mentality. Any 
number of factors may have entered to reduce this score. 
The chances are that the lower the examinee’s intelligence 
the greater are the number of these “reducing” factors; 
and vice versa, the higher the intelligence, the lower the 
number. The actual situation may be pictured graphi- 
cally. 
To make this graph clear, let us assume that we have 
applied the Binet tests to a large number of subjects and 240 
INTELLIGENCE MEASUREMENT 
we select eleven whose intelligences are respectively, 
6, 8, io, 12, 14, 16, 18, 20, 22, 24, 26.1 The median 
mental age here will be observed to be 16. Let us also 
suppose that this large group, in which these eleven are 
included, have been given Army Alpha. It is the writer’s 
contention that the lower the actual mental ability of the 
subject examined, to that extent will his score in the 
group test deviate from his true mental age. According 
to Graph 44, the subject testing 26 on one test will, 
supposedly, test exactly the same on the group test. 
For the other ages. 
a 
24 Binet will possibly measure 23 
a 
20 Binet will possibly measure 18^ 
a 
16 Binet will possibly measure 13^ 
a 
12 Binet will possibly measure 83^ 
an 
8 Binet will possibly measure 3^ 
GRAPH 44 
Age Reduction 
Individual Test 
(Binet) 
Group TesJ,(Army Alpha)' 
'Aver./ 
Aver. 
The median performer who on the Binet obtains an 
intelligence rating of 16, may on the group test, because 
of this phenomenon of progressive score reduction, ob- 
tain an intelligence rating of barely 14. (The material 
1 The writer is aware that the Stanford-Binet cannot yield such high 
mental ages except through the predictive use of the I. Q. But for the 
purposes of this presentation, this deficiency will be overlooked. SUPPLEMENTAL OBSERVATIONS 
241 
of the graph has been made to conform with the possible 
condition of the figures obtained from the application 
of Army Alpha.) It should be noted that the data of 
Graph 44 would yield a correlation coefficient of + 1.00, 
yet it would not reveal the increasing inaccuracy of the 
group intelligence examination with the decrease in the 
mental ability which it has been devised to measure. 
(3) It cannot be denied that the Army Alpha over- 
weights reading ability. Those who have difficulty in 
reading, or in translating the printed word into more 
familiar imagery, may be expected to obtain lower 
scores than on an individual test like the Binet. Evi- 
dence of this was clearly revealed by the fact that going 
from Army Alpha to the Combined Scale did not yield 
the same results in terms of Combined Scale scores, as 
going from Army Beta to the Combined Scale. In the 
Beta test (performance) those possessing the mental 
ability had a more satisfactory opportunity to manifest 
it than with Alpha. So that in the case of Alpha both the 
dull normals and inferiors, together with those laboring 
under language handicaps of whatever form, tended to 
slide toward the lower end of the frequency distribution. 
Attention, in this connection, is called to the recent 
experience of Whipple 1 with three pupils who obtained 
a mental age from one to three years lower on the 
National Intelligence Tests than on the Stanford-Binet. 
Quoting: 
“These three cases strongly suggest, what would be 
a priori intelligible, that pupils who have special difficulty 
1 G. M. Whipple: “The National Intelligence Tests,” Journal of 
Educ. Research, 1921, 4:18-31. 242 
INTELLIGENCE MEASUREMENT 
in reading will suffer a decided reduction in mentai age 
rating by a group intelligence test when compared with 
their rating by the individual and oral examination of 
the Binet, though it remains possible that the former 
rating may be the more significant in predicting school 
progress.” (P. 31.) 
(4) The assumption that the draft represented a fair 
cross-section of the American population is admittedly 
unwarranted. The frequency tables from which the 
average intelligence of the American citizen is deduced 
does not include the figures for officers of all grades. 
It should also be recalled that thousands of professional 
men, and those engaged in essential industries were 
exempted from service and were consequently free of 
the draft. If we can regard a man more intelligent be- 
cause he has taken on family responsibilities and has 
been exempted because he is engaged in caring for those 
dependent upon him, then this is another very large 
and important group whose range of ability is not 
adequately represented in the total results. 
(5) It is a recognized fact in psychological testing- 
technique that the physical conditions under which a 
subject is working may have a very profound effect 
upon the result achieved. It perhaps will not be ques- 
tioned that the experimental conditions at the various 
draft camps were with few exceptions very far from 
ideal. It was recognized that the failure of the War 
Department to provide special buildings for psycho- 
logical examinations proved a very serious handicap, 
and the facilities which were extended interfered con- 
siderably with the effectiveness of the work. Among SUPPLEMENTAL OBSERVATIONS 
243 
the factors which might be expected to affect the results 
were the following: 
(a) Examinations followed at varying intervals after 
inoculation for typhoid, influenza, etc. at various camps; 
(b) The same degree of variation was characteristic 
for the time of examination after arrival; 
(c) In some camps men were examined with a full 
equipment of apparel including the heavy top-coat, in 
others men were in their shirt sleeves; 
(d) Sitting on the floor, tailor-fashion, some on mats, 
some against posts or the wall for support, others with- 
out mats or back-supports, may have had some influence 
upon the results; 
(e) The use of beaver-boards for hand-rests may have 
had a varying influence upon efficiency; 
(f) The preexamining conditions, physical and mental, 
may possibly have been a factor which should be con- 
sidered ; 
(g) The light, air, comfort, and physical properties 
of the various buildings which served as examination 
centers were variable quantities which also may have 
some bearing upon the interpretations of the final 
averages. 
It might be well to state before continuing, lest the 
writer be misunderstood, that these remarks are not 
made in criticism of the splendid work which was ac- 
complished by the Psychological Division of the Army, 
but an attempt is being made to interpret the statistical 
evidence that the average mental age of adults is 13J4 
years. In view of the difficulties and handicaps which 
were inevitable and insurmountable, we should be 244 
INTELLIGENCE MEASUREMENT 
cautious in carrying over this result to the field of clinical 
psychology, overturning standards which have been 
current practice for a good many years. Let us first 
check these averages for scientific validity. 
(6) A necessary element in all group testing is “speed.” 
Experimentation with the army tests has thus far re- 
vealed that “speed” and“intelligence” are fairly well 
correlated, and that doubling the time in Army Alpha, 
for example, does not materially change final rankings. 
It should be borne in mind, however, that possibly 
“speed” has been overweighted in the army tests. In 
fact it is admitted that “assuming that we are dealing 
with an unselected group, Table LXXIX shows that 
some limit between double and single time would prob- 
ably be more suitable.” 1 There is considerable question 
now regarding the relative values of “speed” versus 
“power ” tests. There are many who insist that “speed” 
should be made subordinate to “power.” In view of 
the possible overemphasis upon speed in the Army Alpha 
tests, together with the difficulty of discounting it ac- 
curately, perhaps we had better await further experi- 
mentation before accepting the intelligence-average as 
found. 
(7) For a number of years it has been the practice of 
clinical psychologists to subdivide the feeble-minded 
into three groups: idiots, imbeciles, and morons. The 
mental age limits for these groups are: idiots, from below 
age one to age two; imbeciles, ages three to seven; 
and morons, ages eight to twelve. According to the 
1 R. M. Yerkes: “Psychological Examining in the United States 
Army,” p. 420. SUPPLEMENTAL OBSERVATIONS 
245 
data of the army examinations, if all those testing less 
than twelve are designated feeble-minded, then 30.3 per 
cent would be so classified. This, of course, is absurd 
and unthinkable. We have been ready to admit that 
approximately the lowest two per cent of the population 
is mentally unfit to manage itself and its affairs with 
ordinary prudence. On this basis the army examina- 
tions indicated that those testing below eight amounted 
to 2.1 per cent. To reverse our reasoning and to contend 
that any one with a mental age of eight or over is men- 
tally fit to manage himself and his affairs with ordinary 
prudence is to lead to another absurdity belying the 
facts of our daily experience. 
We are therefore confronted with two horns of a 
dilemma, from which there seems no clear-cut escape. 
If it is true that years is the average mental age of 
adults, and if it is true that 8 years is the line of demarca- 
tion for those who are feeble-minded, then we should be 
prepared to empty our feeble-minded institutions of at 
least one-fourth of their present populations. We should 
also proceed immediately to change the I. Q. classifica- 
tions of intelligence. Instead of an I. Q. of 70 or 75 
being indicative of feeble-mindedness (utilizing 16 years 
as the devisor for adults), the I. Q. of 60 should be 
adopted (13% years being the highest divisor possible). 
Similar revisions should be made for the other groups. 
The moron feeble-minded, then, has been a pure figment 
of the imagination! The statistical result of the army 
intelligence tests veritably “knocks the props from 
under” the customary 2 per cent criterion, the I. Q. 
of 70 as indicative of feeble-mindedness, it annihilates 246 
INTELLIGENCE MEASUREMENT 
the moron group, and weakens in its entirety the psycho- 
logical criterion of feeble-mindedness. On the basis of 
army findings many may be designated “normal” men- 
tally whose social, pedagogical, industrial, and hereditary 
history clearly indicates “feeble-mindedness.” Whereas, 
heretofore, the psychological criterion has been recog- 
nized as generally the most valuable of them all, it may 
now become the least significant. Engaged daily and 
for years in the handling of social misfits, the writer will 
be slow to abandon established standards until the newer 
ones are more carefully checked both for reliability and 
practicability. It may be true that in the army seven 
to ten-year-olds functioned more or less efficiently, and 
that comparatively low intelligences on the army tests 
reported successful living at-large, yet clinical psycho- 
logists will recall few, if any cases, testing seven to ten 
years on the Binet who manifest such successful adapta- 
tions to the complexities of their environment. It is 
true, of course, that because of the nature of our work we 
manage to learn only about the unsuccessful morons. 
Much more satisfactory evidence must be presented, 
however, to convince one that the successful moron 
requires no supervision and direction, and actually 
guides his affairs with ordinary prudence. 
(8) Because of the constant need for substitutes for 
the Binet test on account of previous examinations, 
possible coaching, etc., the writer has had more than two 
years’ experience applying group tests, such as the Army 
Alpha, the Haggerty, the Illinois Examination, the 
National Intelligence Tests, and so on, to individual 
subjects. It has been amazing to find, after the pre- 247 
SUPPLEMENTAL OBSERVATIONS 
scribed instructions had been read, the frequency with 
which additional explanations had to be given before 
the subject could proceed intelligently. There have 
been occasions where a whole test — for example, the 
disarranged sentences (true and false), of Army Alpha — 
had been entirely misunderstood. In this instance all 
items were underlined “false.” The experimenter then 
explained the problem more thoroughly, the subject this 
time placing on record a truer representation of his 
degree of mental ability. Such procedure in group 
testing is, of course, impossible. Set directions are pre- 
scribed. If they are understood, well and good; if not, 
the matter cannot be helped. No questions can be enter- 
tained. It is a credit to all the group tests now in use 
that the directions are remarkably clear and under- 
standable. But in every group of two hundred, a few 
will be found who will not quite get the idea, and when 
averaging results these records give a false weight to the 
figures. 
(9) An adequate treatise dealing with the psychology 
of the crowd would be a valuable asset assisting in the 
interpretation of the army test results. As yet such an 
analysis is lacking. We can only speculate upon the 
nature of an individual’s mental composition when 
handled merely as one in a large group. If we were to 
contrast individual psychological examining with group 
testing, it would not be unfair, perhaps, to state that the 
circumstance of the crowd is not conducive in all cases 
to maximum mental effort. There are a host of subtle 
factors brought into play which it has not yet been 
possible for scientific psychology to catch hold of. Some 248 
INTELLIGENCE MEASUREMENT 
instincts such as rivalry may make for extraordinary 
exertion and increased efficiency; on the other hand, 
there are other counteracting instincts which might just 
as likely lead to decreased efficiency. In what direction 
the total balance lies, whether favorable or unfavorable, 
cannot be dogmatically stated. It is natural to expect 
that under the best conditions one cannot exceed one’s 
native ability. On the other hand, native ability may 
not become manifest under certain restricted conditions. 
(io) The most important check upon the results of 
the army testings were the Stanford-Binet ages of 653 
draftees from nine different camps. This group has pre- 
viously been mentioned, and was designated in the army 
statistics as Group X. The supposition was made that 
this is a random sampling and is typically representative. 
There are a number of reasons why this sampling should 
be questioned. These follow: 
(a) It is significant that with a possible maximum 
score of 414 in Army Alpha (weighted) no one of this 
group received a higher score than 360, and with a possi- 
ble maximum of 212 (unweighted) no score was higher 
than 180. (P. 779-780.)* 
(b) No member of Group X had a schooling record 
beyond four years of college. It is admitted that the 
upper range, both for mental ability and for schooling, 
is not here represented. (P. 779.) 
(c) Men of foreign birth had been eliminated. (P. 780.) 
(d) The total group (633) included a number of 
illiterate men. (p. 781.) 
1 These page references are to R. M. Yerkes: “Psychological Exam- 
ining in the United States Army.” SUPPLEMENTAL OBSERVATIONS 
249 
(e) Group X failed to include men who were selected 
as officers or for prospective officer-material. And be- 
cause of the operation of the draft it was inevitable that 
many men, because of physical or mental handicaps, were 
thrown in the discard and never reached a training camp. 
To what extent a normal distribution is disturbed by 
these selective processes is a matter still to be deter- 
mined. 
(/) This group is admitted defective as a sample on 
p. 384. “In the first place, the group chosen in any given 
camp cannot be thought of as typical of the camp; and 
in the second place, there was the selection involved in 
the choice of camps.” 
(g) The attempt was not made to set down first the 
earmarks of a satisfactory sampling and then adhere 
closely to the prescription. No effort was made for a 
proportionate selection, covering the whole range of 
mental ability. It was felt, rather, that the heterogeneity 
of the group was a sufficient guarantee of the adequacy 
of the sampling. (P. 779.) 
Whatever averages are obtained from Group X must 
be interpreted with the above facts in mind. 
(n) The pragmatic test has supported the 16-year 
criterion. The calculation of the I. Q.’s of adults and 
the classifications inevitably resulting from the use of 
this standard have met with rather general satisfaction 
among clinical psychologists. The utilization of test 
statistics gathered in the army for the interpretation of 
mental capacity is well illustrated in the following report1 
1 From the Survey of Saturday, Oct. 30, 1920 (Vol. XLV., No. 5), pp. 
147-148. 250 
INTELLIGENCE MEASUREMENT 
which is quoted in full. We may naturally expect very 
strange generalizations such as are here propounded: 
“Prisoners vs. ‘Men Generally’ 
“One of the most significant contributions made to 
the science of penology since Dr. Charles Goring’s monu- 
mental report on the criminal type, seven years ago, is 
the recent report of the Mental Survey of Penitentiary 
Prisoners in Illinois. Dr. Goring’s report completely 
repudiated the existence of a uniform physical criminal 
type, and established to be an illusion the doctrine which 
for a previous quarter of a century had done an incal- 
culable damage to penal reform. 
“This new mental survey, under the direction of Dr. 
Herman Adler, the criminologist, dispels the existence of 
a uniform mental criminal type. The basis of comparison 
in the Goring report was the physical characteristics of 
law-abiding citizens such as college students, soldiers, 
hospital patients, and the like; the basis of comparison 
in the Adler report is the result of the group mental tests 
applied to the United States Draft Army, comprising 
some 1,700,000 men of draft age from all sections and 
classes and racial groups in the United States. The 
report asserts that the result of the army test is an index 
of the average mental age of the people of this country. 
“In the Illinois survey the conclusions drawn were on 
the basis of 1,650 accurate records of prisoners examined 
by army tests. Four and one-half per cent were in the 
lowest group — four per cent in the highest. In the 
penitentiary the inferior group was 16 per cent — in 
the draft army, 2 5 per cent. The striking fact is there- 
fore revealed, that the penitentiary has fewer men of 
inferior development than the draft army, and that it has 
more men of superior mental development. 
“The report further shows: Relatively few inferior 
men, relatively many superior men in the crimes of fraud SUPPLEMENTAL OBSERVATIONS 
251 
and crimes against property; the reverse in case of sex 
crimes; the short-termers an average group; the long- 
termers often either superior or inferior with a larger 
percentage of inferior. Those prisoners who had 
served previous terms had half as many inferior types, 
and nearly twice as many superior types as those prison- 
ers without previous records of arrest. 
“Among the reformatory prisoners the comparative 
results are much the same. The average age is lower and 
accounts for the existence of fewer superior men in the 
reformatory than in the draft army. 
“If the analogy is correct that the American draft 
army is an index of the country, it is evident from this 
report that as a group, the prison population is not 
inferior to men generally.” 
In contrast to this analysis, in which it is demonstrated 
practically that penitentiary prisoners in Illinois are 
superior to men at large, are the findings of Goring,1 
of Fernald, Hayes, and Dawley,2 of the NewYork Prison 
Survey Committee,3 of Miner,4 of Williams,5 and of 
Healy.6 The testimony of this group cannot very 
easily be controverted. 
1C. Goring: “The English Convict” (abridged edition), London: 
His Majesty’s Stationery Office, 1919, 275 pp. 
2 Mabel R. Fernald, Mary H. S. Hayes, and Almena Dawley: “A 
Study of Women Delinquents in New York State” (New York, Century 
Co., 1920, 542 pp.). 
3 Report of the Prison Survey Committee. (Albany, N. Y.: J. B. 
Lyon Co., 1920, 412 pp.) 
4J. B. Miner: “Deficiency and Delinquency.” (Baltimore, Warwick 
and York, 1918, 355 pp.) 
6 J. H. Williams: “The Intelligence of the Delinquent Boy,” Jour, of 
Delinquency. Monograph 1, Jan. 1919, 198 pp. 
6William Healy: “The Individual Delinquent” (Boston, Little, 
Brown & Co., 1915; 830 pp.). 252 
INTELLIGENCE MEASUREMENT 
The following from Goring: 
“It is clear that the relationship between mental de- 
fectiveness and the committing of all types of crime, with 
the exception of some kinds of fraud, is an extremely 
intimate one. The strength of this bond transcends 
that of any we have hitherto been able to discover: and 
it is evident that defective intelligence is one of the 
primal sources of crime in this country.” (P. 181.) 
And again, 
“ Probably the chief source of the high degree of rela- 
tionship between weak-mindedness and crime resides in 
the fact that the criminal thing which we call criminality, 
and which leads to the perpetration of many, if not of 
most, anti-social offenses to-day, is not inherent wicked- 
ness, but natural stupidity. At any rate, we need only 
study the penal records of habitual criminals to realize 
fully that the one characteristic of the offenses of 90 per 
cent of the 150,000 persons convicted to prison every 
year — the one characteristic, apart from their intoler- 
ableness in a well-ordered society, is the incredible stu- 
pidity of these offenses.” (Pp. 182-183.) 
And finally, 
“ Our final conclusion is that English criminals are 
selected by a physical condition, and a mental constitu- 
tion which are independent of each other — that the one 
significant physical association with criminality is a 
generally defective physique; and that the one vital 
mental constitutional factor in the etiology of crime is 
defective intelligence.” (P. 184.) 
Next, Fernald, Hayes, and Dawley: (The comparison 
here was made direct with Group X.) 
“It is evident from consideration both of the distribu- 
tion and of the means that the delinquent group is in- 
ferior mentally to the army group.” (P. 419.) SUPPLEMENTAL OBSERVATIONS 
253 
“The difference in mental age of 1.6 years (Group X 
— 13.4 years, New York delinquent women—11.8 
years) may be accepted as valid, beyond any reasonable 
question, since it amounts to more than ten times the 
standard deviation of the difference.” (P. 420.) 
And in summary, remembering that these statements 
refer only to white English-speaking groups, “ the average 
mental capacity of the delinquent women whom we have 
examined is lower than that of any groups of non- 
delinquent adults with regard to whom we have data,” 
and “ the above statement does not imply a selection of 
individuals entirely from the lower end of the scale of 
intelligence for the delinquent group. There is, in fact, 
an extensive amount of overlapping of the delinquent 
with the non-delinquent groups.” (P. 433.) 
And in conclusion, “It is evident from the foregoing 
statement that our findings are in accord with Goring’s 
as regards the fact of a difference and its direction. They 
indicate, however, a slighter degree of difference than 
he implies.” (P. 434.) 
Of course, this smaller difference is inevitable in view 
of the reduction of the standard. 
These quotations are from the Prison Survey Com- 
mittee of New York: 
“A large section of the prison population consists of 
custodial rather than punitive cases. The prisoner who 
is mentally or physically unable to cope with the condi- 
tions of a free society should not be allowed to complete 
the cycle of commitment, release, and recommitment, 
and indulge between times in a criminal career as the 
only means within his knowledge of obtaining a liveli- 
hood. Dr. Glueck, after a study of 602 cases at Sing 
Sing Prison, found that 28.1 per cent showed intelligence 
equivalent to that of the average American child of 254 
INTELLIGENCE MEASUREMENT 
twelve years or under.1 Examinations made in various 
prisons and reformatories, as shown by the State Prison 
Commission for 1918, estimated from 15 per cent to 25 per 
cent of the prison population as segregable on account 
of mental deficiency. These figures, taken in connection 
with the fact that the same report states that 87 per cent 
of the felons admitted to the prisons in 1917 had served 
previous terms, make obvious the fact that a large per- 
centage of those who are released are incapable, either 
from certain mental defects or from lack of training in 
the institutions, of maintaining themselves in society. 
It is believed that before any great advance can be made 
in the training of prisoners the mental deficients must be 
sorted out, segregated, and dealt with as a separate unit. 
Elementary, advanced, and industrial education, wage 
incentives, self-government, and parole measures will 
be of little avail with this class of prisoners, whose 
mental limitations prevent them from taking advantage 
of any privilege or opportunity.” (P. 104.) 
One is interested to inquire to what extent this general- 
ization applies to approximately half the American popu- 
lation, for the data of Group X, if regarded as represen- 
tative of the country at large, indicates that only 52.7 
per cent of American citizens are 13 years mentally or 
over! And again on p. 114 we find the remark, “From 
the figures obtained from various penal and correctional 
institutions, and from the examinations made by the 
Prison Survey Committee, it is believed that from 8 to 
14 per cent of the prisoners, other than those in insane 
hospitals, are mental defectives requiring institutional 
care.” 
And now these remarks of Miner, whose regard for 
careful statistical analyses is a high guarantee of the 
soundness of his generalizations: “In the face of the fact 
1 Those of Group X under 13 years mentally amounted to 47.2%. 
Almost twice as many! SUPPLEMENTAL OBSERVATIONS 
255 
that mental deficiency is undoubtedly the most impor- 
tant single factor to be considered today in the institu- 
tional care of delinquents, one hesitates to correct even 
the most exaggerated impressions as to its importance.” 
(P. 167.) 
“ On the basis of our summary of tested delinquents in 
the last chapter it seems extremely conservative to sup- 
pose that 10 per cent of the manifest and potential 
criminals are as deficient mentally as the lowest 1.5 per 
cent of the general population. Even with this assump- 
tion, we find that the chances would be 48 out of a hun- 
dred that a person of this degree of deficiency would be 
convicted of crime.” (P. 216.) 
“The most significant fact demonstrated by the corre- 
lations between juvenile delinquency and deficiency is 
that there is a positive relationship which is significant 
in amount. With the maximum estimate the correlation 
is nearly six times its error. This is the first time that 
the relationship has actually been calculated in connec- 
tion with any group of juveniles.” (P. 223.) 
And in his conclusions, “We have summarized some 
of the best and most recent investigations in which 
a notable advance toward solving this problem has been 
made by means of the correlation method. This has 
proved to be a new and vigorous force for directing social 
progress. By no other method have we approached so 
near the solution of the cause of delinquency. It enables 
us to restate the problem of criminality as mainly a 
problem in the treatment of a hereditary criminal dia- 
thesis, in which mental deficiency is the largest factor.” 
And then by way of a final word, “Unless the present 
evidence, however, is outweighed by improved data 
obtained in the future, the most strategic point for 
attacking persistent delinquency is through the relation 
to deficiency, with heredity holding the heights.” 
(Pp. 244-245.) 256 
INTELLIGENCE MEASUREMENT 
The following are four of the conclusions of Williams: 
“(2) That the general level of intelligence among 
delinquent, dependent, and potentially delinquent boys 
is decidedly lower than that of ordinary children and 
adults of the same ages. 
“(3) That feeble-mindedness is much more common 
among delinquent, dependent, and potentially delinquent 
boys than in the population as a whole; and that approxi- 
mately 30 per cent of the delinquent and dependent boys 
included in this investigation are definitely feeble- 
minded. 
“ (4) That low intelligence among delinquent boys is 
the chief contributing factor in their delinquent conduct. 
“(5) That any level of intelligence lower than that 
of the average-normal accounts in part for delinquency, 
the extent to which it is responsible depending upon the 
degree of intelligence, which may be best expressed by 
the intelligence quotient.” (P. 181.) 
For 1000 young repeated offenders Healy reports “as 
beyond peradventure feeble-minded, we found about 10 
per cent, but the figure will be increased as some of the 
younger in the lower groups fail to advance with age.” 
(P. 140.) 
And again, “The subject of mental defect is of great 
import in the study of delinquency and its causation. 
Just what percentage of delinquents are feeble-minded 
appears to be a matter of perennial interest, but well- 
founded statistics, even if obtained in particular places, 
may not be applicable to different situations. There can 
be no doubt that separate reformatory or prison popula- 
tions if tested would show from 10 to 30 per cent, or even 
more, to be feeble-minded.” (P. 447.) 
“But the gist of the situation is that mental defect 
forms the largest single cause of delinquency to be found 
by correlating tendency to offend with characteristics 
of the offender.” (P. 447.) SUPPLEMENTAL OBSERVATIONS 
257 
To return to the report in The Survey, in which one is 
given to understand that the penitentiary prisoners of 
Illinois are equal to men generally in mental capacity, 
if not slightly superior. Analyses such as these contra- 
dict all previous experience, and their cumulative force 
will bring about a distorted perspective, which may only 
confound the layman and the prison administrator in the 
adequate handling of our anti-social and unsocial classes. 
(i 2) The outstanding advantage of an individual test 
lies in the fact that a rapport between examiner and 
examinee may be established. This is of unquestioned 
value in increasing a subject’s efficiency and in inter- 
preting the results of any given performance. In an 
individual examination failures can be explained more 
adequately, interest, application and distractions can 
be observed, malaise or other discomforts irritating the 
subject may be properly discounted. In a group test 
this is not possible. Your achievement within the forty- 
five minutes is the measure of your intelligence. No 
allowances can be made for any disturbing or distracting 
influences. To what extent the army averages have 
been reduced because of this inaccuracy cannot be even 
guessed. Combined with other reducing factors, the 
surprisingly low average mental age found is, to a certain 
extent, to be expected. 
(13) Applying the ‘‘test of common sense” to the 
i&i standard, although unscientific, it possesses, never- 
theless, a certain degree of validity. So-called “common 
sense” is generally a combination of attitudes or points 
of view based upon long experience, both of the individual 
and of the group in which an individual finds himself. 258 
INTELLIGENCE MEASUREMENT 
Common sense is opposed to the conception that mental 
power reaches its maturity at years. Even now 
when we tell the layman that intelligence maturity is 
generally reached at 16, he is shockingly surprised. In 
reality, the whole problem of determining at what age 
children reach intelligence maturity is still one awaiting 
solution. It is realized that this objection to the 
year standard is not a very weighty one, yet common 
sense should be considered as one among a number of the 
acid-tests of truth. 
(14) Numerous factors of personality and temper- 
ament probably had varying influences upon the result. 
Such elements as ambition, conscientiousness, obedience, 
application, interest, were forces of variable manifesta- 
tion in some manner leaving an impress upon per- 
formance. The assumption that there was an ultimate 
balance, excesses discounting deficiencies, is perhaps not 
warranted in view of the circumstance that one cannot 
achieve a high score on the basis of any other condition 
than actual mental ability. 
(15) Thus far statistical sanction (the normal proba- 
bility curve) has indicated no error in the 16-year cri- 
terion. If 13I is the average mental age of adults, 
shall we find the same normal distribution of mental 
ages and intelligence quotients with the year cri- 
terion? Of course, some raise the question why we 
should expect a normal distribution even with the 16- 
year criterion. 
Taking the data of Table 333 (p. 790),1 no mental age 
1R. M. Yerkes: “Psychological Examining in the United States 
Army.” SUPPLEMENTAL OBSERVATIONS 
259 
of Group X exceeds 19.9 years. That is the result of the 
Binet examination of 653 men. For the white draft, 
93,955 men, Groups I, II and III (group tests) no mental 
age exceeds 22.9 years. According to the evidence of the 
Stanford-Binet Test, intelligence of 20 or over should be 
found with the following relative frequencies: 
Mental Age 
I. Q. Interval 
Frequency in 1000 
2o|—2lf 
126-135 
l6 
2i|—23£ 
I36-X45 
2 
Unless there is a great reduction in average intelligence 
(from 16 to 13) with increase of life age, these ratios of 
mental power (I. Q.) should be found in a correct 
random sampling of people at large. 
Actually, the highest I. Q. using as a base does 
not exceed about 147 for Group X, and for the white 
draft, Groups I, II and III, it does not exceed about 174. 
(From data of p. 790.) 
(16) In order to determine the range of mental ages 
characteristic of adults we may be compelled to fall 
back upon some other measuring device than the Binet 
scale thus far standardized. It is inevitable, for example, 
that no member of Group X will test above 19.9, for the 
reason that a perfect performance of all the Stanford- 
Binet items can yield only a mental age of 19 years. A 
peculiar idiosyncrasy which the writer has not seen 
mentioned in the literature is the possibility of a slightly 
inferior performer obtaining some mental rating out of 
a possible maximum of 19I/2 years, whereas one who 
passes all the tests in the whole series successfully 260 
INTELLIGENCE MEASUREMENT 
achieves a maximum of only 19. Thus with a basal age 
of 14, a subject is confronted with 6 tests in age 16, 
each having a value of 5 months, total 30 months; and 
6 tests in age 18, each having a value of 6 months, total 
36 months. The grand total is 66 months,, or 5 years 
and 6 months above the basal age 14. This would yield 
a maximum of ig}/2 years. On the other hand, with a 
basal age of 16, a subject is confronted with only 6 tests, 
each having a value of 6 months, total 36 months, and 
the maximum is only 19 years. Until the Binet scale is 
more effectively extended into the upper ages, our 
knowledge of the nature and range of mental ability of 
adults will be dependent upon a certain amount of 
speculation. 
(17) On the basis of the army statistics less than 
15 per cent of the draftees examined measured over 
16 years in intelligence. It is difficult to conceive in the 
light of the writer’s ten years’ testing experience that 
85 per cent of adults examined have been below average 
and that only 15 per cent have been above average. If 
memory is not a deceptive servant, experience seems to 
point toward an average closer to 16 than to i$}4- 
Whether the experience of other examiners corroborates 
this impression cannot be determined without a proper 
questionnaire. 
(18) The argument may be made that the army 
averages for intelligence are valid because the exemption 
of the feeble-minded counterbalances the elimination of 
the superior men. This is questionable for the reason 
that only the extremest variety of inferior ability was 
eliminated, whereas only a fair degree; of superiority SUPPLEMENTAL OBSERVATIONS 
261 
was both recognizable as a possibility and a stimulus 
for officership, and in civil life for exemption because 
of indispensable social service. The chances are that the 
processes of selection which yielded Groups I, II, III 
and X favored the selection of those who, on the whole, 
were somewhat below the average of the population at 
large. 
(19) A satisfactory standard of the’ average mental 
age of adults should include as well statistics gathered 
from the mental examination of women. These ad- 
ditional figures would serve both as a balance and as a 
check upon the averages obtained from the examination 
of men. 
(20) Finally, the danger of accepting the army figures 
on their face value is expressed on p. 7901 as follows: 
“The former group is large (Groups I, II and III) and 
representative, but involves an error dependent on the 
fact that these men were examined by alpha and beta 
and not by a mental age scale. The second group (Group 
X) suffers from the fact that it is small and cannot be 
demonstrated to be representative.” 
In conclusion, the writer wishes to express again his 
keen appreciation of the splendid contributions made by 
the psychologists during the war, regretting that condi- 
tions made it impossible for him to share in that epoch- 
making work. The above discussion has been motivated 
only by a desire to reduce the inevitable difficulties of 
clinical psychologists, should we hastily accept the 13)4 
age standard. Caution is advised until this question 
1 R. M. Yerkes: “ Psychological Examining in the United States 
Army.” 262 
INTELLIGENCE MEASUREMENT 
of the average mental age of adults, now that it has been 
so forcibly raised, is more satisfactorily settled. In the 
meantime, the ends of clinical and applied psychology 
may be more adequately served, and those engaged in 
the handling of our unsocial and anti-social classes 
may find themselves functioning more efficiently, by 
adhering to the 16-year standard, and by making 
their psychological and clinical deductions on that 
basis. 
2. INCREASING DIVERGENCE VS. PARALLEL PROGRESS OF 
MENTAL DEVELOPMENT 
A great deal of effort is being spent at the present time 
to determine the constancy of the rate of intelligence 
development (constancy of I. Q.). No new material 
will be here presented to enlighten this controversy, 
except to advise the utilization of a more efficient method 
for studying rate changes. In all of the discussions thus 
far, use has been made of equally-spaced cross-section 
paper in order to graph growth and I. Q. changes. This 
has resulted in greatly hindering clear analysis and, to 
an extent, has tended toward the development of mis- 
leading conclusions. A new method for graphing these 
ratios is recommended. 
Psychological and educational studies seem to indicate 
that age and variability are positively correlated. With 
a given increase in age we observe a corresponding in- 
crease in variability. But when the nature of this 
variability has been graphed a number of inaccuracies 
have inevitably developed. 263 
SUPPLEMENTAL OBSERVATIONS 
To illustrate with concrete examples: In his analysis 
of the arithmetic abilities of children, Woody1 states, 
“In the construction of these scales, it has been assumed 
that achievement in the solution of problems in the 
fundamental processes is distributed according to the 
normal surface of frequency. Furthermore, it has been 
assumed that the variability of any grade from the 
second to the eighth is equal to that of any other.” (P. 
30.) Graph 45 illustrates this hypothesis. 
5CH00L 
GRADE 
P.E. SCALE 
GRAPH 45 
Relations of Grade Distributions to Each Other in Addition 
Plotted in somewhat different fashion, Graph 46 is 
obtained. It will be observed that progress follows 
parallel lines. Variability does not increase, and pre- 
sumably, children of low ability in all the grades will 
manifest the same difference in comparison with those 
of high ability, throughout. This is one point of view: 
1 C. Woody: “Measurements of Some Achievements in Arithmetic.” 
Teachers College, Columbia University Contributions to Education, No. 
80, 1916, 63 pp. 264 
INTELLIGENCE MEASUREMENT 
that there are mental traits which manifest parallel 
progress with increasing age. 
On the other hand, we have the view that there is an 
GRAPH 46 
Parallel Progress of Mental Traits 
Grade 
increasing divergence of mental traits with increasing 
age. This is graphically represented by Miner in his 
discussion of intelligence development.1 (P. 253.) It 
will be evident from these curves that the bright and 
dull children deviate more and more from the average 
with increase of age. 
To which mode of development does intelligence 
compare? Are there different endowments at birth pre- 
senting a normal curve of distribution, this curve being 
merely reduplicated at higher ages, as in Graph 46; or 
are there different endowments at birth presenting a 
1J. B. Miner: “Deficiency and Delinquency.” SUPPLEMENTAL OBSERVATIONS 
265 
Permission Warwick & York. 
Mature 
Hypothetical Development Curves {Normal Distribution) 
Increasing Divergence op Mental Traits 
GRAPH 47 
Ages 2-3 
Increases 
Objective Units 266 
INTELLIGENCE MEASUREMENT 
normal curve of distribution, which upon increase of 
life age becomes more and more flat as in Graph 47? If 
the I. Q. is constant, then Graph 46 should adequately 
picture I. Q. distributions at various ages. But if for 
the brighter children the I. Q. increases, and for the 
feeble-minded it decreases, Graph 47 would more ade- 
quately represent the true state of affairs. 
Studies of rate of development will not proceed toward 
a clear analysis of the situation until the method of 
graphic presentation changes from the use of equally- 
spaced cross-section paper to that of logarithmically- 
spaced cross-section paper. 
Graph 49 has been derived from Fig. 10 (p. 75) of 
Doll’s monograph,1 only the curves for ages 3, 5, 8 
and 10 being transcribed. The curves as originally 
presented are indicated in Graph 48. The outstanding 
features of difference between the two methods of presen- 
tation are so obvious that they do not require descrip- 
tion. It will be apparent in Graph 49 that (1) I. Q. 
constancy at all intelligence levels, at all life ages, and 
at all mental ages produces a line possessing a 45 degree 
angle. (2) If the I. Q. increases, the angle inevitably 
increases. (3) If the I. Q. decreases, the angle inevitably 
decreases. (4) These increases and decreases appear in 
the graph in correct, not distorted ratios. (5) The angle 
at which growth proceeds is both an index of I. Q. con- 
stancy as well as a direct expression of rate of growth. 
By comparing Graph 49 with Graph 48 it will be ob- 
served that on evenly-spaced cross-section paper various 
growth curves must be interpreted in terms of the re- 
1 E. A. Doll: “The Growth of Intelligence.” 267 
SUPPLEMENTAL OBSERVATIONS 
spective slopes of specific I. Q.’s, each I. Q. rate having 
a different slope. In Graph 49, however, all slopes, no 
matter what the I. Q., if indicative of constancy of 
development, are at a 45-degree angle. On equally- 
spaced charts uniformity in rate-growth would have to 
GRAPH 48 
Average Growth Curves 
of Each Mental Age (After Doll) 
(F. M. Subjects) 
Mental Age 
Life Age 
be represented by different algebraic formulae. This has 
an important bearing upon the interpretation of com- 
parative curves. It appears, upon a superficial examina- 
tion of the four curves of Graph 48, that there is 
practically little variation between them, the curves for 
VIII and X being almost exact duplications of the 
curves for III and V. Yet when VIII and X are com- 
pared with III and V in Graph 49, no such striking 268 
INTELLIGENCE MEASUREMENT 
GRAPH 49 
Mental Age Growth Curves 
Mental Age(mos.) 
Life Age (mos.) SUPPLEMENTAL OBSERVATIONS 
269 
similarity is evident. In Graph 48, curves III and VIII, 
especially between the ages of 8 to 14 are almost parallel. 
The actual differences are brought out more definitely 
in Graph 49, especially for ages 14, 15 and 16. Taking 
the individual curves, it is more evident in Graph 49 that 
age X manifests a regular reduction of I. Q. from age 11 
to 16; that age VIII also manifests a constant regular 
reduction of I. Q. somewhat greater than age X; that 
age V shows a slight increase in rate of growth up to 
132 months (age n), then there is a rapid regression, 
the ratio of which remains the same up to age 16; and 
that age III manifests only a slight decrease in rate of 
growth up to 108 months (age 9), then follows a sudden 
constant rate of regression up to 168 months (age 14), 
then the reduction takes a rapid increase up to age 16. 
Reference to Fig. 12 (p. 107) of Doll’s monograph 
will emphasize again the need for this suggested method 
for graphing growth curves. In this figure are presented 
the individual growth curves showing early arrest with 
consequent I. Q. decreases. All these curves (Cases 9, 
17, 16, 48, 64, 98, 134, 164) are practically parallel, and 
it was necessary to indicate under each curve the different 
I. Q. values at each life age. The differences of I. Q. 
at the two ends of each curve are here presented: 
Case No. 
I. Q. Range 
'' Difference 
9 
25-17 
12 
17 • • • 
38-25 
13 
16 
51-38 
13 
48 
47-37 
IO 
64 
62-46 
l6 
98 
70-46 
24 
134 
91-55 
36 
164 
93-75 
18 270 
INTELLIGENCE MEASUREMENT 
On logarithmic cross-section paper these differences 
would have been more apparent. 
Graph 50 illustrates, in another fashion, the advan- 
tages of the ratio graph over the customary method of 
plotting rate progress. Two curves are here presented, 
labeled I and II. The two curves run exactly parallel 
GRAPH 50 
I. Q. Fluctuations 
Intelligence Quotient 
Sg8ggS8S^§SS 
1501 
130 - 
110 - 
100- 
90- 
80 
70 
60 
50 
45-*- 
I 
1_ 
A 
B 
II 
ii 
M 1 1 1 1 1 1 1 U 
7 8 9 10 11 12 13 14 15 16 
9i si n sx zi it on m o 
Life Age 
0 
Life Age 
in (A), yet in (B), where rate is more adequately repre- 
sented, no such parallel progress is observed. It is a 
matter of common knowledge that at lower ages, because 
of the exaggerated significance of small deviations, there 
is bound to be greater inconstancy. A deviation of 6 
months at age 6 will produce a marked change of I. Q. 
At age 16, however, a fluctuation of that size is 
relatively insignificant. To what extent this condition 
accounts for some of the spurious inconstancies at lower SUPPLEMENTAL OBSERVATIONS 
271 
ages is yet to be determined. It is probable that cross- 
section paper reversing the divisions, so that at higher 
ages fluctuations of a given magnitude are granted greater 
weight, and at lower ages, less weight, may equalize the 
inevitable discrepancies. 
One of the important tasks confronting experimental 
psychologists who are investigating the problem of in- 
telligence development is to determine the nature of its 
progress. Do endowments unfold or develop at a uniform 
rate, or are there increments or decrements, regular or 
irregular? To answer this question, perhaps a variety 
of intelligence tests, other than the Binet, may have to 
be utilized. And the statistical interpretation of the 
problem will be greatly facilitated by the use of the 
ratio chart.1 
3. A PERFORMANCE INTELLIGENCE SCALE 
The work of the last few years has contributed con- 
siderable material on performance intelligence tests. 
The block designs, it is hoped, will be found to be a 
practicable addition thereto. Although this test may be 
utilized as a measure of intelligence by itself, its greatest 
value, however, may be realized in combination with 
other performance tests which are capable of incorpora- 
tion in such a scale. 
The time is ripe for the development of a performance 
intelligence scale comparable in construction to the 
Binet. An especially rich field for data is the monograph 
1 Irving Fisher: “The ‘Ratio’ Chart.” Quarterly Publications 
American Statistical Association, 1917, pp. 577-601. 272 
INTELLIGENCE MEASUREMENT 
dealing with the results of intelligence tests in the 
army.1 
It was not regarded within the province of this 
piece of research to develop such a scale, the purpose 
being rather to standardize a new set of tests, discussing 
therewith numerous allied questions and problems. 
1R. M. Yerkes: “Psychological Examining in the Army.” APPENDIX I 
Grouped Distributions of Ability 
OUTLINE 
A. Three Groups 
a. 6 a 
b. 5 a 
c. 12 Q 
B. Five Groups 
a. 6 a 
b. so- 
C. 12 Q 
C. Seven Groups 
a. 6 <r 
b. $ <r 
c. 12 Q 
D. Nine Groups 
a. 6 (t 
b. 5 <r 
c. 12 Q 
E. Practical Applications 
a. School Marks 
b. Economic Demand 
c. Testing Psychological Tests 
273 274 
INTELLIGENCE MEASUREMENT 
GROUPED DISTRIBUTIONS OF ABILITY 
It is the purpose of this section to assist those attempt- 
ing to determine how accurately a test or scheme of tests 
approximates normal probability in its distribution of 
results, when the effort is made to classify the individuals 
measured into three, five, seven, or nine groups. The 
discussion of groupings to determine which leads to most 
satisfactory results will be deferred for later treatment. 
A. Three Groups 
Let us assume that we wish to classify individual dif- 
ferences in mental ability or in any trait or characteristic 
into three groups. What proportion of ioo per cent 
would we expect to find in each group?1 
Let us consider three possibilities, where the limits of 
the distribution-range are 
0) ± 3 o' 
(b) ± 2.5 cr 
(c) ± 6 Q. 
(a) ± 3 cr. Range is 6 cr. 
Since we are dealing with three groups, each will have 
an extent of 6/3 cr, or 2 cr. Consequently the limits 
for the three groups will be 
First Group, .00 to 2.00 
Second Group, 2.01 to 4.00 
Third Group, 4.01 to 6.00 
1 The final figures in this article are obtained from the formula of the 
normal probability curve, 
« 1 
y=~Tr=' 
erV 2 7r e~■ 
2 ff5 APPENDIX I 
275 
From a table1 giving the values of x/cr we find that the 
first group includes 15.73% °f cases, 
first and second groups include 84.27% of cases. 
Therefore: 
1st Group includes 15.73% °f cases 
2nd Group includes 68.54% °f cases 
3rd Group includes 15.73% of cases 
(b) ± 2.5 <7 Range is 5 o' 
Since we are dealing with three groups, each will 
have an extent of 5/3 a, or 1.667 (T- Consequently the 
limits for the three groups will be 
First Group, .000 to 1.667 
Second Group, 1.668 to 3.333 
Third Group, 3.334 to 5.000 
From the x/cr table2 we find that the 
first group includes 19.63% of cases, 
first and second groups include 80.37% of cases. 
Therefore: 
1st Group includes 19.63% of cases 
2nd Group includes 60.74% °f cases 
3rd Group includes 19.63% of cases 
jj& i H. O. Rugg, “Statistical Methods Applied to Education,” 1917, 
Table VI, pp. 396-400. 
2Table V, pp. 392-395, in Rugg- 276 
INTELLIGENCE MEASUREMENT 
(c) zt 6 Q. Range is 12 Q. 
Since we are dealing with three groups, each will have 
an extent ofi2/3Q, or4Q. Consequently the limits for 
the three groups will be 
First Group, 6 Q — 2 Q 
Second Group, 2 (2 Q) 
Third Group, 6 Q — 2 Q 
From the x/P. E. table (Table IV, p. 391 in Rugg, 
interpolated) the percentage included within each group 
will be 
First Group, 50.00 — 41.13% 
Second Group, 2 (41.13)% 
Third Group, 50.00 — 41.13% 
Therefore: 
1st Group includes 8.87% °f cases 
2nd Group includes 82.26% of cases 
3rd Group includes 8.87% of cases 
B. Five Groups 
Let us assume that we wish to classify individual 
differences in a given trait into five groups. What pro- 
portion of 100 per cent would we expect to find in each 
group? Let us again consider three possibilities where 
the limits of the score-range are 
(a) ±3<r 
(bj ± 2.5 or 
(c) ±6Q APPENDIX 1 
277 
(a) ±3 <r Range is 6 cr 
Since we are dealing with five groups, each will have 
an extent of 6/5 <r, or 1.2 cr. The limits for the five 
groups will be 
First Group, .00 to 1.20 
Second Group, 1.21 to 2.40 
Third Group, 2.41 to 3.60 
Fourth Group, 3.61 to 4.80 
Fifth Group, 4.81 to 6.00 
From our tables we find that the 
1st group includes 3.45% of cases 
1st and 2nd groups include 27.29% of cases 
1st, 2nd, and 3rd groups include 72.71% of cases 
1st, 2nd, 3rd, and 4th groups include 96.55% of 
cases 
Therefore: 
1st Group includes 3.45% of cases 
2nd Group includes 23.84% of cases 
3rd Group includes 43.42% of cases 
4th Group includes 23.84% of cases 
3th Group includes 3.45% of cases 
(ib) ± 2.5 a Range is 5 cr 
Extent of each group is 5/5 cr, or 1 cr. The limits for 
the five groups will be 
First Group, .00 to 1.00 
Second Group, 1.01 to 2.00 
Third Group, 2.01 to 3.00 
Fourth Group, 3.01 to 4.00 
Fifth Group 4.01 to 5.00 278 
INTELLIGENCE MEASUREMENT 
From our tables we find that the 
ist group includes 6.06% of cases 
1st and 2nd groups include 30.23% of cases 
ist, 2nd, and 3rd groups include 69.77% °f cases 
ist, 2nd, 3rd, and 4th groups include 93.94% of 
cases 
Therefore: 
ist Group includes 6.96% of cases 
2nd Group includes 24.17% of cases 
3rd Group includes 39.54% of cases 
4th Group includes 24.17% of cases 
5th Group includes 6.06% of cases 
(1c) ± 6 Q Range is 12 Q 
Extent of each group is 12/5 Q, or 2.40 Q. The limits 
for the five groups will be 
First Group, 6.00 Q to 3.60 Q 
Second Group, 3.60 Q to 1.20 Q 
Third Group, 2.00 to 1.20 Q 
Fourth Group, 3.60 Q to 1.20 Q 
Fifth Group, 6.00 Q to 3.60 Q 
From the tables we find that the percentage included 
within each group will be 
First Group, 50.00 to 49.24% 
Second Group 49.24 to 29.08% 
Third Group, 2.00 to 29.08% 
Fourth Group, 49.24 to 29.08% 
Fifth Group, 50.001049.24% APPENDIX I 
279 
Therefore: 
ist Group includes 0.76% of cases 
2nd Group includes 20.16% of cases 
3rd Group includes 38.16% of cases 
4th Group includes 20.16% of cases 
3th Group includes 0.76% of cases 
C. Seven Groups 
(a) ± 3 <t Range is 6 cr 
Extent of each group is 6/7 a, or .857 cr. The limits 
for the seven groups are: 
First Group, .000 to .857 
Second Group, .858 to 1.714 
Third Group, 1.715 to 2.571 
Fourth Group, 2.572 to 3.429 
Fifth Group, 3430 to 4.286 
Sixth Group, 4.287 to 5.143 
Seventh Group, 5.144 to 6.000 
From the x/cr table we find that the 
ist group includes 1.47% of cases 
ist and 2nd groups include 9.78% of cases 
ist, 2nd, and 3rd groups include 33.26% of cases 
ist, 2nd, 3rd, and 4th groups include 66.74% of 
cases 
Therefore: 
ist Group includes 1.47% of cases 
2nd Group includes 8.31% of cases 
3rd Group includes 23.48% of cases 
4th Group includes 33.48% of cases 280 
INTELLIGENCE MEASUREMENT 
5th Group includes 25.48% of cases 
6th Group includes 8.51% of cases 
7th Group includes 147% of cases 
(h) ± 2.5 (7 Range is 5 a 
The extent of each group is 5/7 a, or .714 a. The 
limits for the seven groups are 
First Group, .000 to .714 
Second Group, .715 to 1.429 
Third Group, 1.430 to 2.143 
Fourth Group, 2.144 to 2-857 
Fifth Group, 2.858 to 3.572 
Sixth Group, 3-573 to 4.286 
Seventh Group, 4.287 to 5.000 
From the x/V table we find that the 
1st group includes 3.08% of cases 
1st and 2nd groups include 13.59% of cases 
1st, 2nd, and 3rd groups include 3543% of cases 
1st, 2nd, 3rd, and 4th groups include 64.57% of 
cases 
Therefore: 
1st Group includes 3.08% of cases 
2nd Group includes 10.51% °f cases 
3rd Group includes 21.84% °f cases 
4th Group includes 2Q.i4% of cases 
5th Group includes 21.84% °f cases 
6th Group includes 10.51% of cases 
7th Group includes 3.08% of cases APPENDIX I 
281 
(c) ± 6 Q Range is 12 Q 
The extent of each group is 12/7 Q, or 1.71 Q. The 
limits for the seven groups will be 
First Group, 6.00 Q — 4.285 Q 
Second Group, 4.285 Q — 2.571 Q 
Third Group 2.571 Q — .857 Q 
Fourth Group, 2 (.857 Q) 
Fifth Group, 2.571 Q — .857 Q 
Sixth Group, 4.285 Q — 2.571 Q 
Seventh Group, 6.00 Q — 4.285 Q 
From the tables we find that the percentage included 
within each group will be 
First Group, 50.00 to 49.81% 
Second Group, 49.81 to 45.85% 
Third Group, 45.85 to 21.84% 
Fourth Group, 2 (21.84%) 
Therefore: 
1st Group includes .19% °f cases 
2nd Group includes 3.96% of cases 
3rd Group includes 24.01% of cases 
4th Group includes 43.68% of cases 
5th Group includes 24.01% of cases 
6th Group includes 3.96% of cases 
yth Group includes .19% of cases 
It is recommended that wherever possible larger group 
differentations be utilized in educational and psycholog- 
ical investigations. This practice not alone yields more 
intelligible material but is of superior service in correla- 
tional analyses. 282 
INTELLIGENCE MEASUREMENT 
D. Nine Groups 
(a) ± 3 a Range is 6 a 
Extent of each group is 6/9 a, or .667 <7. The limits 
for the nine groups are 
First Group, .000 to .667 
Second Group, .668 to 1.333 
Third Group, 1.334 to 2.000 
Fourth Group, 2.001 to 2.667 
Fifth Group, 2.668 to 3.333 
Sixth Group, 3.334 to 4.000 
Seventh Group, 4.001 to 4.667 
Eighth Group, 4.668 to 5.333 
Ninth Group, 5.334 to 6.000 
From the x/V table we find that the 
1st group includes .84% of cases 
1st and 2nd groups include 4.64% of cases 
1st, 2nd, and 3rd groups include 15.73% °f cases 
1st, 2nd, 3rd, and 4th groups include 36.82% 
1st, 2nd, 3rd, 4th, and 5th groups include 63.18% 
Therefore: 
1st Group includes .84% of cases 
2nd Group includes 3.80% of cases 
3rd Group includes 11.09% °f cases 
4th Group includes 21.09% °f cases 
3th Group includes 26.36% of cases 
6th Group includes 21.09% °f cases 
yth Group includes 11.09% of cases 
8th Group includes 3.80% of cases 
9th Group includes .84% of cases APPENDIX I 
283 
(b) ± 2.5 a Range is 5 <7 
The extent of each group is 5/90-, or .556 a. The 
limits for the nine groups are 
First Group, .000 to .556 
Second Group, .557 to i.m 
Third Group, 1.112 to 1.667 
Fourth Group, 1.668 to 2.222 
Fifth Group, 2.223 to 2.778 
Sixth Group, 2.779 to 3.333 
Seventh Group, 3.334 to 3.889 
Eighth Group, 3.890 to 4.444 
Ninth Group, 4.445 to 5.000 
From the x/ a table we find that the 
1st group includes 1.98% of cases 
1st and 2nd groups include 7.63% of cases 
1st, 2nd, and 3rd groups include 19.63% of cases 
1st, 2nd, 3rd, and 4th groups include 38.43% of cases 
1st, 2nd, 3rd, 4th, and 5th groups include 61.57% of 
cases 
Therefore: 
1st Group includes 1.98% of cases 
2nd Group includes 5.65% of cases 
3rd Group includes 12.00% of cases 
4th Group includes 18.80% of cases 
3th Group includes 23.14% of cases 
6th Group includes 18.80% of cases 
7 th Group includes 12.00% of cases 
8th Group includes 3.65% of cases 
pth Group includes i.98% oj cases 284 
INTELLIGENCE MEASUREMENT 
(c) ± 6 Q Range is 12 Q 
The extent of each group is 12/9 Q, or 1.33 Q. The 
limits for the nine groups will be 
First Group, 6.00 Q — 4.667 Q 
Second Group, 4.667 Q - 3.333 Q 
Third Group, 3.333 Q — 2.000 Q 
Fourth Group, 2.000 Q — .667 Q 
Fifth Group, 2 (.667 Q) 
Sixth Group, 2.000 Q — .667 Q 
Seventh Group, 3.333 Q — 2.000 Q 
Eighth Group, 4.667 Q - 3.333 Q 
Ninth Group, 6.00 Q — 4.667 Q 
From the tables we find that the percentage included 
within each group will be 
First Group, 50.00 to 49.91% 
Second Group, 49.91 to 48.78% 
Third Group, 48.78 to 41.13% 
Fourth Group, 41.13 to 17.36% 
Fifth Group, 2 (17.36%) 
Therefore: 
1st Group includes .09% of cases 
2nd Group includes 1.13% of cases 
3rd Group includes 7.63% of cases 
4th Group includes 23.77% °f ca$es 
3th Group includes 34.72% of cases 
6th Group includes 23.77% °f cases 
7th Group includes 7.63% of cases 
8th Group includes 1.13% of cases 
gth Group includes .09% of cases APPENDIX I 
285 
In the following tables are given the various per- 
centages for three, five, seven, and nine groups, where 
the ranges are 6, 5, and 12 Q respectively. 
TABLE LXXXV 
Group 
Below 
Middle 
Above 
Total 
4 
3 
2 
I 
O 
I 
2 
3 
4 
3 
15-73 
68.54 
15-73 
100% 
5 
345 
23.84 
4542 
23.84 
345 
100% 
7 
I.47 
8.31 
2348 
33-48 
23.48 
8.31 
1.47 
100% 
9 
.84 
3.80 
11.09 
21.09 
26.36 
21.09 
11.09 
3.80 
.84 
100% 
Range 6 a 
TABLE LXXXVI 
Range 5 a 
Group 
Below 
Middle 
Above 
Total 
4 
3 
2 
I 
O 
I 
2 
3 
4 
3 
19.63 
60.74 
19.63 
100% 
S 
6.06 
24.17 
39-54 
24.17 
6.06 
100% 
7 
3.08 
10.51 
21.84 
29.14 
21.84 
10.51 
3.08 
100% 
9 
1.98 
5-65 
12.00 
18.80 
23.14 
18.80 
12.00 
5-65 
1.98 
100% 
TABLE LXXXVII 
Grow 
Below 
Middle 
Above 
Total 
4 
3 
2 
I 
O 
I 
2 
3 
4 
3 
8.87 
82.26 
8.87 
100% 
5 
0.76 
20.16 
58.16 
20.16 
0.76 
100% 
7 
O.19 
3-9<5 
24.01 
43.68 
24.01 
3-96 
0.19 
100% 
9 
0.09 
I-I3 
7-65 
23-77 
34-72 
23-77 
7-65 
I-I3 
.09 
100% 
Range 12 Q 
The values in the body of the tables are percentages. 286 
INTELLIGENCE MEASUREMENT 
E. Practical Applications 
1. School Marks: In assigning grades to pupils 
teachers often utilize a five-group classification, the 
range being assumed 5 <r. Thus Starch in his “Educa- 
tional Measurements” states: “On the basis of all these 
experimental results it would seem that the most satis- 
factory marking system would be a scale of five steps: 
A, or Excellent which should be assigned to approxi- 
mately 7% of the pupils. 
B, or Superior, which should be assigned to approxi- 
mately 24% of the pupils. 
C, or Average, which should be assigned to approxi- 
mately 38% of the pupils. 
D, or Inferior, which should be assigned to approxi- 
mately 24% of the pupils. 
E, or Unsatisfactory, which should be assigned to ap- 
proximately 7% of the pupils.” (P. 15.) 
And Rugg in his “Statistical Methods Applied to Educa- 
tion” (p. 219) gives the same figures. 
The chief advantages of this system of marking are, 
first, that the theoretical values for each group are 
based upon correct statistical theory; second, the groups 
— superior, average, inferior, etc. — cover equal ranges 
of ability; and third, the personal equation of the ex- 
aminer is greatly reduced, if not entirely eliminated. 
When the score-range or mark-range is 6 <r, or 12 Q, 
and should more than a five-group classification be de- 
sired, the tables in this article may be found of value. 
2. Satisfying Economic Demand: In view of the fact 
that physical and mental traits yield distributions APPENDIX I 
287 
closely resembling the normal probability curve, it is 
logical to assume that the satisfaction of needs to which 
these traits are allied would be compelled to conform 
more or less closely to this probability. For example, 
head circumference, length of foot, length of torso, 
length of hand, etc., are traits which yield Gaussian or 
bell-shaped distributions. Therefore, the hatter, the 
shoe manufacturer, the shirt manufacturer, the glover, 
and so on, must take account of grouped variability. 
If the hatter is going to manufacture nine sizes of hats 
and if head circumference is found distributed over a 
range of 6 <r, then having chosen equal units of differ- 
ence between hat sizes, the per cent of each size must be 
as follows: (from smallest to largest size), 1,4, n, 21, 26, 
21, 11, 4, 1. 
3. Testing Tests: In standardizing tests or scales, it 
is desirable to determine how closely one’s results con- 
form to the normal frequency. Where one’s score-range 
is 6 cr, or 5 <r, or 12 Q, the tables in this article readily 
lend themselves for such comparisons. Should the 
score-range be different, then a new table of values has 
to be derived, utilizing the same method as we have 
followed above. Thus, in Terman’s “The Stanford Re- 
vision and Extension of the Binet-Simon Scale for Meas- 
uring Intelligence ” we note a comparison of nine groups of 
obtained intelligence quotients with the percentage one 
would theoretically expect to find. The range of in- 
telligence quotients is from 56 to 145, or about 8 Q. 
The obtained percentages for the nine groups are: .33, 
2.3, 8.6, 20.1, 33.9, 23.1, 9., 2.3, .55 (p. 42). The theoreti- 
cal values are: .16, 1.6, 8.5, 23.42, 32.64, 23.42, 8.5, 1.6, 288 
INTELLIGENCE MEASUREMENT 
.i6. The correspondence is remarkably close and is a 
strong argument in favor of the validity of the intelli- 
gence quotient, as well as of the Stanford Revision of the 
Binet scale. 
With the application of statistical methods to psycho- 
logical, educational, and industrial problems becoming 
more common, we may expect a wider and wider use of 
grouped variability. APPENDIX II 
New Correlation Method 
In his “Mental and Social Measurements” (2nd 
edition) (pp. 172-177) Thorndike points out that the 
formula for r stated as follows, 
S(*-y) , v 
r y/Zx2- V2y2’ 
is a simpler form of the Pearson coefficient of correlation 
known as 
r — (,) 
naA<TB 
In Table 42, facing p. 176, Thorndike presents the 
method for determining r by formula (1). 
The writer has had frequent occasion to observe that 
because of the elimination of the frequency interval 
which contains the median, together with the number 
of cases therein found, the normal balance of the cor- 
relation is seriously disturbed. Thus, correlation tables 
are met with in which the frequency is skewed and the 
median barely falls into the interval containing it. In 
spite of this condition, the entire interval is disregarded 
in the calculations for r. Some very weird coefficients 
inevitably result, differing considerably from r as would 
have been determined bv means of formula (2). 
289 290 
INTELLIGENCE MEASUREMENT 
It was to correct this occasional inaccuracy that the 
following method has been used throughout this mono- 
graph. 
Table LXXXVIII presents the procedure commonly 
practiced. Table LXXXIX illustrates the suggested 
method of determining the value of r. Scientific accu- 
racy is increased without increase of labor. 
It will be observed that the number of cases is 57, the 
median case being the 29th. For ability in A, the median 
just barely falls into the fourth frequency interval. For 
ability in B, the median falls well into the fourth fre- 
quency interval. Table LXXXIX takes this difference 
into account in the following manner: For the x variable 
the median falls upon the first case in 17. If this group 
is divided into four sections each section will contain 
cases. The general rule is, when the median case fall 
in the first fourth section divide your table into two 
segments, the dividing line being drawn to the left of 
the frequency interval; when the median case falls 
within the second or third fourths (the middle half), 
then only, should the whole frequency be eliminated. 
In that event lines are drawn both to the right and left 
of the interval. If, however, the median falls in the last 
fourth, the table is again divided into only two segments, 
the dividing line being drawn to the right of the fre- 
quency interval. This procedure is illustrated in Table 
LXXXIX, the median for ability in A falling in the first 
quarter of 17, and the median for ability in B falling in 
the middle half of the frequency 12. 
The mathematical proof has been supplied by Dr. J. 
E. Coover and follows the tables. APPENDIX II 
291 
Correlation Method Commonly Used 
TABLE LXXXVIII 
z 
2 
3 
4 
5 
6 
7 
Total 
. 6 . 
i 
2 
2 
I 
6 3 
« 7 • • • 
5 
i 
I 
I 
8 2 
.5 8 . . . 
3 
s 
2 
IO I 
.$ 9 • • • 
2 
6 
2 
2 
| 12 o 
=§«>••• 
i 
i 
5 
2 
9 i 
XI 
4 
3 
I 
8 2 
12 . 
i 
2 
I 
4 3 
Total 
5 
8 
IS 
17 
8 
3 
I 
57 | 
x—► 
3 
2 
I 
o 
I 
2 
3 
y 
Ability in A 
Z*2 Zy2 + Zsy - Zsy 
23-i2= 23 ig-i2= 19 30 2 2 3 
11 • 22 — 44 i6-22= 64 6 6 1 
6-32 = 54 io~32 = 90 4 4 Total = 6 
Total = 121 Total = 173 6 12 
6 9 2 xy = 86 
2 
5 
Total = 92 
86 86 
\/i2i-\/i73 11 X 13.2 
86 
= ijrr+-59 292 
INTELLIGENCE MEASUREMENT 
Correlation Method Used in This Monograph 
TABLE LXXXIX 
I 
2 
3 
4 
5 
6 
7 
Total 
6 . . . 
i 
2 
2 
I 
6 
3 
M 
7 • • • 
5 
i 
I 
I 
8 
2 
g 
8 . . . 
3 
5 
2 
IO 
I 
a 
o . . . 
2 
6 
2 
2 
1 
12 
O 
IO . 
i 
i 
5 
2 
9 
I 
•3 
ii 
4 
3 
I 
8 
2 
12 . 
I 
2 
I 
4 
3 
Total 
S 
8 
IS 
17 
8 
3 
I 
57 
T 
x—> 
s 
3 
I 
I 
3 
S 
7 
y 
Ability in A 
Zx2 Zy2 + Zxy — Z xy 
32-12= 32 I9-i2= I9 50 5 36 
16-32 = 144 i6-22= 64 98 12 
8-s2 = 200 10-32 — 9p 63 2 
1 • 72 = 49 Total = 173 9 6 g 
Total = 425 6 18 Total = 23 
2 10 
5 3° 
21 
Total = 188 Zxy = 165 
165 165 i65_ 
r ~ V425V173 _ 20-6-13-2 ~ 271.9 
= + .61 
Using Pearson’s longer formula (Formula 2) 
_ 82.45 _ 82,45 
r 57 X 1.36 X 1.74 134-88 
= + .61 
Note: Utilizing the method suggested by Thorndike (Table 42, in 
reference above-mentioned), r for Table LVI, p. 145, is + .73; by this 
method r is reduced to + .71 APPENDIX II 
293 
The Pearson-Bravais formula for the coefficient of 
correlation 
2 xy 
r — — 
n (TxP-y 
may be converted into the formula 
2 xy 
r = J ===r 
V2 x2 X 2 y2 
in both of which, 
x — the deviations from the mean of the x's, 
and y = the deviations from the mean of the y's. 
When the deviations are calculated from an arbitrary 
origin in order to keep them integral and facilitate cal- 
culation, it is customary to make corrections as shown in 
the formula 
2 x'y' 
n Vl xVl y 
r = 
<yx <sy 
in which x' and y' are deviations from an arbitrary origin 
and cr' is the Standard Deviation in terms of the class 
2 x' 
units; vlx = = the correction for the mean. 
n 
When the number of cases is small, and the correction 
is deemed negligible, the following formula has frequently 
been used: 
2*V 
" V2 z'2 X 2 y'2 294 
INTELLIGENCE MEASUREMENT 
and the cases falling in the classes from which x’ and y' 
have their origin are disregarded and have no influence on 
the calculation of the coefficient. If the means of x and y 
chance to fall midway in the classes chosen for the origin 
of their deviations, no correction would be necessary, 
and the coefficient would be the same as when calculated 
by the longer complete formula. For this reason the 
median class is usually chosen for the origin of deviations. 
If, however, either or both means chance to fall near the 
class-limit, the error may be appreciable. 
Hence, the same formula has been used in such a way 
as to place the origin of deviations at either the mid-point 
of the median class or one of its class-limits, according 
to which lies nearest to the median value in the distribu- 
tion. This modification decreases the possible difference 
between the mean and the origin of deviations from 
]/2 to °f a class-unit, and when the origin of deviations 
falls nearest a class-limit increases the proportion of the 
cases in the table that are utilized in the calculation of 
the coefficient. 
When the origin of the deviations is placed at a class- 
limit, the class deviations run as follows: .5,1.5, 2.5, etc.; 
decimals are eliminated by multiplying by 2; as, 1, 3, 5, 
7, etc. Correction for this change in the class-deviations 
is automatic in the formula: 
(1) Suppose origins for xr and y' both fall at class- 
limits, and a double-prime designates the class-deviations 
that are multiplied by 2. 
Then 
v r'V' ■£ r"2 E v"2 
2*y =%JL2_, 2*'2 ==4r, 2/* = 
* 2X2 (2)• (2)* APPENDIX II 
295 
S x"y" 
j 4 S x'y' 
./S x"2 Sy"2 VS V2 X S 7* 
y 4 4 
(2) Suppose only the origin of V falls on a class-limit: 
rp u v ,, svy S*"2 
Then 2 * ? = > 2* = 
2 »"/ 
, 2 S x'y' 
“ 1/izw=^fp?^=r' 
The amount of error involved in the use of the formula 
may be tested without recalculating by the following 
correction: 
(a) For the numerator: 
S x' X S / 
n 
(b) For the denominator: 
WWW*®} APPENDIX III 
Elaboration of Sheppard's Table 
In order to add to the convenience of those utilizing 
tables of values of the normal probability integral, 
Sheppard’s Table for Q (or P. E.), presented as Table 
45 (p. 200) in Thorndike’s “Mental and Social Measure- 
ments” (2d edition), and as Table XLVII (p. 116) in 
Buckingham’s “Spelling Ability,” has been elaborated, 
giving the straight-line interpolations to one-hundredths 
P. E. in Table XC following: 
296 APPENDIX III 
297 
X 
pTe. 
Per Cent of Cases 
.OO 
.01 
.02 
■03 
.04 
■OS 
.06 
■07 
.08 
.09 
.00 
00.00 
0.27 
0.54 
0.81 
1.08 
i-35 
1.62 
1.89 
2.15 
2.42 
.10 
2.69 
2.96 
3-23 
3-49 
3-76 
4-03 
4.30 
4-57 
4-83 
5-09 
.20 
5-36 
5.63 
5-9° 
6.16 
6-43 
6.70 
6.96 
7-23 
7-49 
7.76 
•30 
8.02 
8.28 
8.54 
8.81 
9.07 
9-33 
9-59 
9-85 
IO.XI 
10.37 
40 
10.63 
10.89 
11.15 
11.41 
11.67 
n-93 
12.19 
12.44 
12.70 
12.95 
•5<> 
13.21 
13.46 
13-71 
13-97 
14.22 
14.47 
14.72 
14.97 
15.21 
15.46 
.60 
IS-7I 
15.96 
16.21 
16.45 
16.70 
16.95 
17.19 
17-43 
17.68 
17.92 
.70 
18.16 
18.40 
18.64 
18.87 
19.11 
19-35 
19-59 
19.82 
20.06 
20.29 
.80 
20.53 
20.76 
20.99 
21.22 
21.45 
21.68 
21.91 
22.13 
22.36 
22.58 
.QO 
22.81 
23.03 
23-25 
23.48 
23.70 
23.92 
24.14 
24.35 
24-57 
24.78 
I .OO 
25.00 
25.21 
25.42 
25.64 
25-85 
26.06 
26.27 
26.47 
26.68 
26.88 
I.IO 
27.09 
27.29 
27.49 
27.70 
27.90 
28.10 
28.30 
28.49 
28.69 
28.88 
1.20 
29.08 
29.27 
29.46 
29.66 
29.85 
30.04 
30-23 
30.41 
30.60 
30.78 
1.30 
30.97 
31.15 
31-33 
31-52 
31.70 
31-88 
32.05 
32.23 
32.40 
32.58 
140 
32-75 
32.92 
3309 
33-26 
33-43 
33.6o 
33-76 
33-92 
34-09 
34-25 
1.50 
3441 
34.57 
34-73 
34.89 
35-05 
35-21 
35.36 
35-51 
35-67 
35-82 
1.60 
35-97 
36.12 
36.27 
36.41 
36.56 
36.71 
36.85 
36.99 
37.14 
37.28 
1.70 
3742 
37.56 
37-70 
37.83 
37-97 
38.11 
38.24 
38.37 
38.50 
38.63 
1.80 
38.76 
38.89 
39-01 
39-14 
39.26 
39-39 
39-51 
39.63 
39-76 
39.88 
I.90 
40.00 
40.1 X 
40.23 
40.34 
40.46 
40.57 
40.68 
40.79 
40.91 
41.02 
2.00 
4I.I3 
41.24 
41-34 
41-45 
41.55 
41.66 
41.76 
41.86 
41.97 
42.07 
Per Cents of the Normal Frequency Surface Corresponding to Given Values of P. E. 
(The Median is the Point of Origin of P. E. Values) 
TABLE XC 298 
INTELLIGENCE MEASUREMENT 
X 
Per Cent of Cases 
P. E. 
.00 
.01 
.02 
.03 
.04 
•05 
,06 
.07 
.08 
.09 
2.10 
42.17 
42.27 
42.36 
42.46 
42-55 
42.65 
42.74 
42.83 
42.93 
43.02 
2.20 
43-n 
43.20 
43.28 
43-37 
43-45 
43-54 
43-62 
43-71 
43-79 
43.88 
2.30 
43-96 
44.04 
44.12 
44.19 
44.27 
44-35 
44.42 
44-50 
44-57 
44.65 
2.40 
44.72 
44-79 
44.86 
44-94 
45.01 
45.08 
45-15 
45-21 
45.28 
45-34 
2.50 
45-41 
45-47 
45-54 
45.60 
45-67 
45-73 
45-79 
45-85 
45-9° 
45-96 
2.60 
46.02 
46.08 
46.14 
46.19 
46.25 
46.31 
46.36 
46.41 
46.47 
46.52 
2.70 
46.57 
46.62 
46.67 
46.72 
46.77 
46.82 
46.87 
46.91 
46.96 
47.00 
2.80 
47-°5 
47-09 
47.14 
47.18 
47-23 
47.27 
47-31 
47-35 
47.40 
47-44 
2.QO 
47.48 
47-52 
47-56 
47-59 
47-63 
47.67 
47-71 
47-74 
47.78 
47-8i 
3 00 
47-85 
47-88 
47.92 
47-95 
47-99 
48.02 
48.05 
48.08 
48.11 
48.14 
310 
48.17 
48.20 
48.23 
48.25 
48.28 
48.31 
48.34 
48.37 
48.39 
48.42 
3.20 
48.45 
48.48 
48.50 
48.53 
48.55 
48.58 
48.60 
48.63 
48.65 
48.68 
3 30 
48.70 
48.72 
48.74 
48.77 
48.79 
48.81 
48.83 
48.85 
48.87 
48.89 
3 40 
48.91 
48.93 
48.95 
48.96 
48.98 
49.00 
49.02 
49.04 
49-05 
49.07 
3-50 
49.09 
49.11 
49.12 
49.14 
49-15 
49.17 
49.18 
49.20 
49.21 
49-23 
3.60 
49.24 
49-25 
49.27 
49.28 
49-3° 
49-31 
49-32 
49-33 
49-35 
49-36 
3 70 
49-37 
49-38 
49-39 
49.41 
49.42 
49-43 
49.44 
49-45 
49.46 
49-47 
3.80 
49.48 
49.49 
49-5° 
49-51 
49-52 
49-53 
49-54 
49-55 
49-55 
49-56 
3 90 
49-57 
49-58 
49-59 
49-59 
49.60 
49.61 
49.62 
49-63 
49-63 
49.64 
4.00 
49-65 
49.66 
49.66 
49.67 
49.67 
49.68 
49.69 
49.69 
49.70 
49.70 
4.10 
49-71 
49.72 
49.72 
49-73 
49-73 
49-74 
49-75 
49-75 
49.76 
49.76 
4.20 
49-77 
49-77 
49.78 
49.78 
49-79 
49-79 
49-79 
49.80 
49.80 
49.81 
4-30 
49.81 
49.81 
49-82 
49.82 
49-83 
49-83 
49-83 
49.84 
49.84 
49-85 
4.40 
49-85 
49-85 
49.86 
49.86 
49.87 
49.87 
49.87 
49.87 
49.88 
49.88 
TABLE XC — Continued APPENDIX III 
299 
X 
p7¥. 
Per Cent of Cases 
.00 
.01 
.02 
■03 
.04 
.05 
.06 
■07 
.08 
.09 
4-50 
49.88 
49.88 
49.88 
49.89 
49.89 
49.89 
49.89 
49.89 
49.90 
49.90 
4.60 
49.90 
49.90 
49.90 
49.91 
49.91 
49.91 
49.91 
49.91 
49.92 
49.92 
4.70 
49.92 
49.92 
49.92 
49-93 
49-93 
49-93 
49-93 
49-93 
49.94 
49.94 
4.80 
49.94 
49.941 
49.942 
49.944 
49-945 
49.946 
49.947 
49.948 
49.950 
49-951 
490 
49-952 
49-953 
49-954 
49-955 
49.956 
49-957 
49.958 
49-959 
49.960 
49.961 
5.00 
49.962 
49.963 
49.964 
49.965 
49.966 
49.967 
49.968 
49.969 
49.969 
49.970 
510 
49.971 
49.972 
49.972 
49-973 
49-973 
49.974 
49-975 
49-975 
49.976 
49.976 
520 
49-977 
49.978 
49.978 
49.979 
49.979 
49.980 
49.980 
49-98x 
49-981 
49.982 
5-30 
49.982 
49.982 
49.983 
49-983 
49.984 
49.984 
49.984 
49.985 
49.985 
40.086 
540 
49.986 
49.986 
49.987 
49.987 
49.988 
49.988 
49.988 
49.989 
49.989 
49.990 
550 
49.990 
49.990 
49-99° 
49.991 
49.991 
49.991 
49.991 
49.991 
49.992 
49.992 
5-6o 
49.992 
49.992 
49.992 
49-993 
49-993 
49-993 
49-993 
49-993 
49,994 
49.994 
5-70 
49.994 
49.994 
49.994 
49-995 
49-995 
49-995 
49-9951 
49.9952 
49-9953 
49-9954 
5 80 
49-9955 
49-9956 
49-9957 
49-9958 
49-9959 
49.9960 
49.9961 
49.9962 
49.9963 
49.9964 
590 
49.9965 
49.9966 
49.9967 
49.9968 
49.9969 
49.9970 
49-9971 
49.9972 
49-9973 
49.9974 
TABLE XC — Continued APPENDIX IV 
Typical Block-Design Records 
The following records will illustrate the nature of the 
record blank used in the original standardization of the 
tests. Twenty designs were utilized, from which seven- 
teen have been selected in the final revision of the test. 
This type of record sheet lends itself to a convenient 
notation of errors in performance and to recording brief 
notes to assist in the interpretation of the results. 
300 APPENDIX IV 
301 
NO. 26 Examined-Nov. 15.1917-2:15 P. M. 
2nd Grade 
Life Age - 7y. 6m. 
Wilbur C—N 
1 Binet Age-8y. Om. 
+ 
2 Time 
Limit - 11 Seems lost- 
— still hunting 
for the right 
block 
3 Time 
Limit -16 Nothing done 
— still trying 
2 blocks - 
Placing flat - on side - ver. & hor. 
4 Limit -13 
— ISIS) ® HI 
nn b 
5 Limit - 12 
Power of 
— analysis 
seems 
lacking 
6 Limit - 9 
0 i 
BLOCK-DESIGN SCORE 
= 3 
B.D. MENTAL AGE =6 Y. 3 M. 302 
INTELLIGENCE MEASUREMENT 
NO. 263 Examined-Ap. 24,1918-10 A. M. 
3-4 Grade 
Albert R—S Life Age -10y. 4m. 
1 21*-7 11 Limit-29 
+ — I Binet Age- 
Ibb] lly'4m' 
2 1'19*-12 12 Limit-34 
(5'0*-36; not yet O.K ) 
+ — Had O. K. onee, then 
destroyed 
3 44*-9 13 Limit - 31 
+ (BLOCK-DESIGN - [R R R| 
\SCORE=46 rrH1 
] B.D.M.A. = 1 1 
4 1'5*-11 | 11Y. 10M. 14 3'54*-41 
+ + 
6 49*-ll 15 Limit - 29 
6 33*-10 16 Limit - 49 
(4'13*-52; O.K.) 
+ 
i <+> 
7 2'17*-30 17 2'48*-30 
+ + 
8 Limit-21 18 Limit - 47 
“ 2 “ Res^l 
\ this O.K. I 
9 2'8*-20 19 Limit-48 (S: “The 
|\R\W Picture is 
-f- — so small & 
pff R \| there are 
so many blocks, - It gits 
10 1'58*-18 20 Limit - 42 you stuck") 
+ 
9 2'8'-20 APPENDIX IV 
303 
NO. 176 Examined-Ap. 2,1918-9 A. M. 
4B Grade 
Life Age - 9y. 2m. 
James B—H 
1 22'-8 Binet Age-8Y. 10M. 
+ NOTE: 
Has set something 
like these at home. 
2 32*-4 Larger eize, but not 
same colors. 
+ 
3 46*-10 
+ 
BLOCK-DESIGN SCORE = 16 
+ B.D. MENTAL AGE = 8 Y. 9 M. 
5 1'34*-15 
+ 
6 Limit - 16 
7 Limit - 30 
S: “I don’t see how 
— 1/bSI J you get these yellow 
ones on the side here.” 
8 Limit - 20 
Later 
- fll (w)Rr 
Wy\ [r|w 
\ 
9 Limit - 16 
Later -v 
" FW 
\ A 
10 
Rest 
O.K. SUBJECT-INDEX 
Abbreviated Army Performance 
Test, 157 
Ability, grouped distributions of, 
273 f. 
native, 248 
“spread” of, 193 
Absolute standard, 180 
Abstraction, 13 
Acceleration, 49 f. 
Adaptation, n, 32, 168 f., 174, 
238 f. 
Adaptive difficulties, 238 
Adolescence, 13,20 
Adulthood, 13 
Adults, mental age of, 237 f. 
Age-grade distribution, 39 f. 
Age-progress analysis, 39 f. 
Age standardization, 104 f. 
Ambition, 258 
Analogies, 16 
Analysis, 6 f., 12 f., 20 f., 26 f., 
170 f. 
defined, 7 
Analyst, 20 
Analytic activity, 12 f., 18, 171, 
175 
tendency, 19 
type, 21 
Analytic-synthetic power, 28, 126 
Analyzing ability, 23 
Anatomists, 28 
Animal discrimination, 30 
learning, 23 
psychology, 21 
Animals, 22, 24 f. 
Anti-social classes, 257 
Aphasias, 26 
Application, 258 
Arithmetic, 63, 89 f., 190 f. 
Army Alpha (see Military Test), 
157, 246 
Army Beta, 157 
tests (see Military Tests), 138, 
238 f. 
Assimilating, 18 
Assimilation, 7, 11 f. 
Assimilative type, 21 
Associated Charities, 221 
Association, 23 f., 173 
of ideas, 4, 11 f. 
Associationist school, 3 
Attention, 22 f., 174 
Auto-criticism, 174 
Average man, 85 
Behavior habit, 23 
Behaviorist, 9 
Bias, 144 
Binet scale, 16, 41 f., 68, 78 f., 157, 
168, 205 f. 
accuracy, 118 
Birthplace, 39 f., 58 
Blending, 7, 12 
Block design records, 300 f. 
test, 39 f. 
Blocks, 64 f. 
Borderzone case, 187, 210 f., 235 
Boys’ and Girls’ Aid Society, 220 
Buckingham spelling test, 72 
Business men, 198 
Chance, 85 f. 
Childhood, 13 
Chinese, 158 
Choice, 22 
Chronological age, 25 
norms, 121 f. 
Clinical differentiation, 210 f. 
psychology, 210 f. 
Combination, 12 
Combinative ability, 7, 10, 26, 
305 306 
SUBJECT-INDEX 
Combining, 175 
“Common-sense check, 187 
test of, 257 
Comparing, 171, 175 
Comparison, 7, 12 f. 
Completing, 175 
Completion, 10, 12 
Composite norms, 112 f. 
Concepts, 4, 14 
Conceptual thinking, 15 
Conduct evaluation, 219 
Conscientiousness, 258 
Consciousness, 7 f. 
of end, 175 
Consistency, 156, 204 f. 
Construction Test A and B, 157 
Constructive activity, 12 
Convict, the English, 251 
Correlation, 10, 68, 143 f., 180 f. 
comparisons, 157 f. 
formulae, 100 
method revised, 289 f. 
Correlational analysis, 281 
Cortex integrity, 31 
Cortical ablations, 31 
Cosmic hypothesis, 171 
Crime causes, 252 f. 
Criminal diathesis, 255 
habitual, 252 
type, 250 
Critical ninths, method of, 228 f. 
Criticising, 175 
Crowd psychology, 247 
Cube Construction Test, 157 
Cube Imitation Test, 157 
Deaf, 235 
Deciding, 175 
Deduction, 12 
Defective intelligence, 252 
Defectiveness, 169 
Definitions of moral terms, 219 
Deliberating, 175 
Delinquency, 169, 198 
Delinquents, children, 251 
potential, 256 
women, 251, 253 
Department, 63 
Design eliminations, 161 f. 
Designs, 65 f. 
Desire, 22 
Diagnostic accuracy, 179 
criteria, 142, 176 f. 
efficiency, 164, 200, 233 f. 
syllabus, 211 
tools, 143 
Differential psychology, 80 
Differentiation, 7, 12 
Digit-Symbol Test, 157 
Direct comparison, method of, 
224 f. 
Disarranged sentences, 247 
Discrimination, 7, 12 f., 17, 22 f., 
171, 175 
Discriminative type, 21 
Dissociation, 25 
Drawing, 18, 26, 63, 190 f. 
Economic demand, 273 f., 286 
Education, 26, 169 
Educational statisticians, 100 
statistics, 78 
treatment, 177 
Electronic theory, 171 
Emotion, 8 
Endocrines, 236 
Endowment 158, 190, 264 f. 
Epistemology, 5 
Equal units scale, 84 f. 
Ethical Discrimination Test, 214 f. 
Etna School, 222 
Evolution, doctrine of, 171 
Experience, 169 
Experimentation, 17 
Faculties, 27 
Faculty psychology, 173 
Fatigue, 22 
Fear, 22 
Feeble-minded, 19, 28, 173, 176, 
179, 181 f., 185, 196, 199, 
208 f. 
Feeble-mindedness defined, 209, 
235 f- 
Ferguson Form Boards, 157 
Final norms, 166 f. 
test revision, 161 f. 
Foot, length of, 287 
Foreign born, 51, 158 
Form Board ability, 157 SUBJECT-INDEX 
307 
Form Board test, 157 
“Fountain of Youth,” 187 
Functional efficiency, 182 
Functionalist, 9 
Fusion, 7, nf. 
Gaussian curve, 287 
Generalizing abstraction, 2 
Genetic psychology, 21, 25 
Genius, 17 
Geography, 26, 63 
Germinal determiners, 22 
Glover, 287 
Graphic functions, 18 
Graphic presentation of norms, 
126 f. 
Grip, 92 f. 
Group differentiation, 151 
Group testing, 137 f., 195 
vs. individual testing, 247 
Grouped measures of variability, 
58, 287 f. 
Habit, 8, 22 
Haggerty Intelligence Examina- 
tion, 137 f. 
Hand length, 287 
“Hand” subjects, 191 
Hatter, 287 
Head circumference, 287 
Height, 81 f., 88, 175 
Heredity, theory of, 171 
Hierarchies of mental functioning, 
5 f., 10, 19, 29, 170 
Higher animals, 22 
Higher thought, 8 
History, 63 
Hoboes, 198 
Home conditions, 39 f., 58 f. 
Household arts, 63, 190 f. 
Human traits, 80 f. 
Ideas, 8 
Ideation, 170 
Ideational activity, 15 
Idiots, 244 f. 
Illinois Examination, 214 f., 246 
Illinois Prison Survey, 250 
Illiterates, 76 f. 
Imagery, 26 
Images, 8, 26 
Imagination, 4, 173 
Imaginative-synthetic period, 20 
Imbeciles, 244 f. 
Indiana Survey Tests, 158 
Individual differences, 16 f., 80, 84, 
169, 182 
Induction, 12 
Industrial applications, 169 
education, 254 
problems, 288 
Inferior endowment, 158 
Information, 169 
Innate ideas, 4 
Instincts, 248 
Integration, 7 f., 11, 29 f. 
Integrative function, nervous sys- 
tem, 29 
Intellectual behavior, 172 
Intelligence, 10, 16, 22, 24, 28, 32, 
168 f. 
defined, 168 f. 
distribution, 89, 193 
maturity, 258 
of women, 261 
quotient, 176 f. 
constancy, 266 f. 
reduction, 269 
ratios, 179 
Interest, 258 
Interpolation, 94 
Inter-test correlations, 158 
Introspection, 7, 8 
Introspective evidence, 166, 172 
Invention, 171 
Inventors, 16 
Italians, 158 
Japanese, 158 
Judging, 175 
Judgment, 4, 8, 170 f., 173 
Knowledge, 6 
“ Kombinationsfdhigkeit, ”170 
“ Kombinationsgabe,” 168 
“ Kombinations-methode,” 103 
Language, 63, 190 f. 
expression, 192, 201 
factor, 180, 191, 195, 202, 235 308 
SUBJECT-INDEX 
Language, handicapped, 158, 235 
symbols, 191 
vs. performance, 192 f., 234 f. 
Learning, 8, 23 
Life ages, 39 f. 
Linear projection method, 98 f. 
Linguistic facility, 179 
Logarithmic graphs, 268 f. 
Loquacious “types,” 199 
Lower organisms, 30 
Malaise, 257 
Manikin and Feature Profile Test, 
J57 
Manipulation, 175 
Manual training, 63, 190 f. 
Mare and Foal Test, 157 
Mayfield children, 39 f. 
Maze Test, 157 
Meanings, 12 f., 25 
Measuring rods, 172 
Mechanical ingenuity, 126 
Memory, 4, n, 22, 26, 173 
Menlo Park children, 39 f. 
Mental ability, 10 
age equivalents, 73 
norms, 105 f. 
of adults, 237 f. 
ages, 41 f. 
true, 179 
capacities, 78 
correlation, 22 
deficiency (see feebleminded), 209 
development, 7, 262 f. 
rate of, 266 f. 
diagnosis, 179 f. 
dynamics, 5 
endowment, 9, 25 
evolution, 22 
“functions,” 173, 204 
growth, 175 
curves, 267 f. 
rate changes, 262 f. 
hierarchies, 5 f., 10, 19, 29, 170 
initiative, n 
power, 258 
synthesis, 19 ] 
traits, 87 
increasing divergence of, 264 . 
parallel progress of, 264 f. 
Mentartraits, types, 20 
Metameric nervous system, 29 
Metazoa, 28 
Method of, ranks, 81 f. 
scoring, 69 f. 
Military Test (see Army Tests), 
173, 195 f. 
“Mind” subjects, 191 
Moral, judgment, 219 
problems, 219 
Moron, 24, 244 f. 
Morons, successful and unsuccess- 
ful, 246 
Multicellular organisms, 28 
Music, 63 
National Intelligence Tests, 241, 
246 
Nationality, 39 f., 54, 58 
Nature study, 63 
Nerve cell properties, 29 
Nervous, protoplasm, 27 
system, 10, 28 f. 
tissue, 13 
Neurologists, 28 
Neuron, 30 
New York, Prison Commission, 
254 
Prison Survey, 251 
Norm, discrepancies, 121 
setting, 137 
Normal, curve fetish, 100 
distribution curve, 209, 263 f. 
probability, 173 f., 193 f. 
probability curve, 85 f., 91 f., 99, 
258 f. 
Norms, 54, 71 f. 
Obedience, 258 
Offenders, repeated, 256 
Ogive, 81 f. 
Original tendencies, 65 
Otis Tests, 158 
Over-refining, 100, 139 
Pain, 22 
Palo Alto children, 39 f. 
Pantomime, 75 
Parole measures, 254 
Patience Test, 174 SUBJECT-INDEX 
309 
Pearson-Bravais formula, 292 
Pedagogical, implications, 25 
progress, 78 
Penitentiary prisoners, 250 
Percentile, method, 80 f. 
technique, 92 f. 
Perception, 8, n f., 22,25, 170, *73 
Performance, 191, 234 f. 
intelligence scale, 271 
test, 179 
vs. language, 192 f., 234 f. 
Periodic Law, 171 
Personal opinion, 197 
Personality, 258 
P. E., scale method, 99 f. 
standardization, 130 f. 
Physical traits, 87 
Physiological set, 25 
Picture, Arrangement Test, 157 
Completion Test, 157 
Pintner’s Non-Language Group- 
Test, 158 
Pleasure, 22 
Poets, 16 
Point scale method, 98 f. 
Porteus Maze Tests, 157 
Portuguese, 158 
Power vs. speed tests, 244 f. 
Practical geniuses, 16 
Pragmatic test, 101, 249 
Predicting school progress, 242 
Pressey Tests, 158 
Prison population, 251 
Prisoners, 198 
vs. men generally, 250 f. 
Probability, 85 f. 
Probable error, 173, 204 f. 
Problem solution, 168 
Prognostic diagnoses, 177 
Progressive score reduction, theory 
of, 239 f. 
Protoplasm, 29 
Protozoa, 22, 28 
Proverbs, 219 
Psychical centers, 27 
Psycho-clinician, 177, 211 
Psychological, profile, 80 
criterion, 246 f. 
Psychology, defined, 8 
Public Welfare Bureau, 222 
Qualitative differences, 81 
Quantitative differences, 81 
Quartile deviation, 94 
Questionnaire, 39 f., 61 f. 
Race differences, 6, 54, 235 
Rapport, 257 
Ratio chart, 271 
Reading, 63, 190 f. 
ability, 241 f. 
quotients, 193 
Reasoning, 5, 8, 170, 173 
Record sheet, 300 f. 
“Reducing” factors, 239 
Reflex, 8 
Reformatory prisoners, 251 
Reproducing Designs Test, 157 
Retardation, 49 f. 
Rising increments, 175 
Rivalry, 248 
Sampling, 121, 126, 248 f. 
Scale making, 78 f. 
Scattering, 156, 163 
School, marks, 188, 273 f. 
range of, 286 f. 
progress, 56 f. 
standing, 190 f. 
training, 189 
Schooling, 10 
Science, 63 
Scientific men, 16, 171 
Score, card, 69 f. 
values, 73 
inconsistent, 182 
variability, 198 
Scribbling, 18 
Seguin Form Board, 157 
Selecting, 18 
Self-criticism, 18 
Self-government, 254 
Senescence, 13 
Sensation, 8, 173 
Sensations, nature of, 4 f. 
Sense organs, 28 
Sensory capacities, 27 
Serviceability, 235 f. 
Sex differences, 39 f., 118 f., 125 f., 
147, 150 f., 165 f., 190 f. 
explanation, 120, 166 310 
SUBJECT-INDEX 
Sheppard’s Tables, 130 
elaboration, 296 f. 
Ship Test, 157 
Shirt manufacturer, 287 
Shoe manufacturer, 287 
Silent, areas, 31 
“type,” 199 
Similarity, 24 
Sing Sing prisoners, 253 
Social, class, 39 f., 58 f. 
relations, 219 
treatment, 177 
worker, 212 f. 
Sonoma State Home, 41 f., 181 
Specialized capacities, 195, 204 
Speed vs. power tests, 244 f. 
Spelling, 63, 99 
Standard deviation, 94 
Standardization, 54, 64, 102 f. 
bias, 1x2 
technique, 78 f., 135 
technique vs. number, 54 
Stanford-Binet Test, 157 
Statistical fallacies, 80 f., 137 f. 
Structuralist, 8 
Superior endowment, 158 
Supplementary information, 179 
Syllogistic reasoning, 169 
Symbols, 25 
Synthesis, 5 f., 9, 12 f., 18 f., 22 f., 
29, 32, 170 f. 
defined, 7 
Synthesist, 20 
Synthesizing ability, 10, 168 
Synthetic activity, 13 
incapacity, 18 
type, 21 
Synthetic-analytic incapacity, 25 
tendency, 12, 25 
Teachers’ estimates, 39 f., 58 f. 
judgments, 187 
Temperament, 258 
Terminal nuclei, 31 
Test, compensation, 179 
correspondence, 184 
criteria, 79 
material, 64 f. 
penalties, 155 
scores, range of, 286 f. 
Test, weighting, 138 f. 
Testing psychological tests, 273 f., 
287 f. 
Tests, directions, 74 f. 
Thalamus, 31 
Thinkers, 171 
Thinking, 11 
Thought, 4, 24 
Thurstone Tests, 158 
Time, 68 f. 
and move norms, 142 f. 
and moves, 99 f. 
limits, 69 
Torso, length of, 287 
Tossing pennies, 85 f. 
Trabue language tests, 41 f., 68, 
72, 99, 173, I9S f- 
Transmutation tables, 100 
Trial and error, 23 
True-false test, 247 
True mental age, 179 
Types, 13, 20 f. 
Unsocial classes, 257 
Validity, 172 f. 
Variability, 175 f-, 201, 204 f. 
263 f., 287 f. 
Verbal expression, 182 
Verbalistic tests, 234 f. 
Vineland Training School, 41 f., 181 
Vocabulary, 173, 195 f. 
Vorticella, 28 
Wage incentives, 254 
Weight, 175 
Weighting moves, 100 f. 
time, 100 f. 
Will, 8 
Woman’s Protective Division, 217 
Women, intelligence of, 261 
Woody Arithmetic Test, 73, 99 
Work capacity, 182 
Writing, 63 
Year scale, 127 f. 
method, 78 f. 
Yerkes-Bridges Point Scale, 84 
Zero points, 84 AUTHOR-INDEX 
Adler, H. A., 250 
Bacon, 3, 4 
Bain, 16 
Baldwin, B. T., 88 
Baldwin, Lola G., 218 
Bartlett, F. C., 33 
Bergson, 33 
Binet, A., 16, 168, 173 f. 
Bolton, J. S., 33 
Book, W. F., 33 
Boring, E. G., 87, 135, 209 
Bridges, J. W., 98 
Buckingham, B. R., 72, 99, 130, 
139, 208, 296 
Cabot, R. C., 209 
Claparede, Ed., 81 
Clement, J. A., 158 
Coover, J. E., 290 
Dawley, Almena, 251 
Descartes, 3, 4 
Doll, E. A., 83, 179, 227, 266, 267, 
269 
Duprat, L., 33 
Ebbinghaus, 103, 168, 170 
Ferguson, G. O. Jr., 157 
Fernald, Mabel R., 251 
Fichte, s 
Fischer, C. R., 83 
Fisher, Irving, 271 
Fisher, Sara C., 24, 33 
Franz, S. I., 31 f., 33 
Galton, F., 81 
Gauss, 85, 87 
Glueck, B., 253 
Goring, C., 250, 251 
Gregor, A., 33 
Haggerty, M. E., 137, 139 
Hardwick, Rose S., 98 
Hayes, Mary H. S., 251 
Healy, W., 103, 157, 251 
Hegel, s 
Herbart, 5 
Hobbes, 3, 4 
Hobhouse, L. T., 10, 14, 22, 24 f., 
33 
Hume, 4 
James, W., 14, 16 f., 23, 26 f. 33 
Jennings, H. S., 22, 28 f., 33 
Judd, C. H., 8, 13, 34 
Kant, 5 f. 
Kelley, T. L., 79 
Kite, E. S., 174 
Knox, H. A., 103 
Kohs, S. C., 80, 205, 213, 214, 237 
Ladd, G. T., 12, 16, 22 f., 31, 34 
Laplace, 85, 87 
Leibniz, 4 
Locke, John, 4 
Mach, E., 17, 32, 34 
Manley, Ida M., 222 
Mateer, Florence, 179 
Maudsley, 21 
McCall, W. A., 193 
Merriman, M., 210 
Meumann, E., 13, 18 f., 21, 26, 34, 
168, 170 
Meynert, 31 
Miner, J. B., 80, 213, 251, 264 
Morat, J. P., 31, 34 
Ordahl, Geo., 181 
Otis, A., S., 79, 99, 158 
311 312 
AUTHOR-INDEX 
Parker, B., 81 
Paterson, D. G., 54, 83, 98, 104 
Pearson, K., 289, 292 
Pillsbury, W. B., 34 
Pintner, R., 54, 83, 84, 98, 103, 
104, 158 
Porteus, S. D., 157 
Pressey, S. L., 158 
Quetelet, 85 
Reamer, Jeanette C., 84 
Ribot, Th., 34 
Rignano, Eug., 20 f., 34 
Ross., Eliz. L. S., 157 
Rossolimo, G., 80 
Royce, J., 8, n, 25 f., 34 
Rugg., H. O., 275, 286 
Schelling, 5 
Schopenhauer, 5 
Sheppard, 208 
Sherrington, C. S., 29 f., 31, 34 
Smedley, F. W., 81, 83, 92 f. 
Spinoza,4 
Starch, D., 89, 286 
Stern, W., 168, 233 
Stout, G. F., 15, 34 
Tashiro, 22 
Terman, L. M., 16, 51, 89, 168, 
174, 196, 197 f., 205, 226 229, 
235, 287 
Thorndike, E. L., 13, 25, 35, 99, 
208, 289, 292, 296 
Thurstone, L. L., 158 
Titchener, E. B., 12, 34 
Trabue, M. R., 72, 99, 130, 139 
Wallin, J. E. W., 237 
Watson, J. B., 35 
Whipple, G. M., 241 
Williams, J. H., 251 
Woodworth, R. S., 12, 16, 22 f., 
31* 34 
Woody, C., 73, 89, 99, 130, 139, 
263 
Woolley, H. T., 83 
Wundt, W., 27, 34 
Yerkes, R. M., 98, 157, 229, 238, 
244, 248 f., 272 
Yoakum, C. S., 157 
Yule, G. U., 87 
Ziehen, Th., 35, 168, 170