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Title: The accomplishment ratio
A treatment of the inherited determinants of disparity in
school product

Author: Raymond Franzen

Release date: September 16, 2025 [eBook #76891]

Language: English

Original publication: New York: Teachers College, Columbia Univ.,
1922

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*** START OF THE PROJECT GUTENBERG EBOOK THE
ACCOMPLISHMENT RATIO ***

THE ACCOMPLISHMENT
RATIO

A Treatment of the Inherited Determinants
of Disparity in School Product

By
RAYMOND FRANZEN
A.B. (Harvard), M.A. (Columbia)
Ph.D. (Columbia)

Teachers College, Columbia University
Contributions to Education, No. 125

Published by
Teachers College, Columbia University
New York City
1922

Copyright, 1922, by Raymond Franzen

PREFACE
The results of the experiment reported here have become so much a
portion of my process of reasoning that duplication of material presented
elsewhere is unavoidable. I wish in particular to recognize my indebtedness
to the Teachers College Record for permission to reprint here revised
portions of an article which appeared in the November, 1920, number of
that journal. I will warn here any reader to whom the intricacies of a full
statistical account are irksome that the logic and conclusions presented in
this study are incorporated in a more palatable and abbreviated form in
Chapter IV of Intelligence Tests and School Reorganization (World Book
Company).
The work presented here has been made possible by the cooperation and
interest of the two principals of the Garden City public school during the
period of my work there, Miss Gladys Locke and Mrs. Edna Maule. I also
owe any success that this experiment may have had to the teachers who did
the real work of “pushing” abilities to their limit. My indebtedness to
Gladys Locke Franzen for help in expression and correction is surpassed
only by what I credit to her encouragement and cooperation at its inception.
During the period in which this experiment was planned and executed it
grew into a real problem through the advice of two of my teachers to whom
I owe all such inspiration and knowledge as I possess—Edward L.
Thorndike and Truman L. Kelley.
Raymond H. Franzen
Des Moines, Iowa, 1922.

CONTENTS
I. An Outline of the Experiment 1
The Use of Quotients and Ratios
The Derivation of Age Norms
A Method of Survey of Reading, Language and
Arithmetic
II. Statistical Treatment of the Experiment 17
The Quotients
The Ratios
Summary
III. The Psychological Conclusions of the Experiment 43
The Neglect of Genius
Is Genius Specialized?
Current Psychological Opinion
Conclusions

PART I⁠[1]
AN OUTLINE OF THE EXPERIMENT
THE USE OF QUOTIENTS AND RATIOS

Standardized measurement of educational product has won its way to a
recognized place in the school life of this country. Many of our larger cities
have research bureaus of tests and measurements, and advanced private
schools have departments of measurement. The logic of the use of
statistically derived evaluations versus the use of opinion, swayed as it is by
the haphazard captions of emotion and condition, has become widely
recognized. The case of scientific measurement in education has been
argued and won. The objections to older forms of measurement have
become the criteria of the value of the new.
Still administrators, although they have been convinced theoretically of
its importance, find it hard to see just what measurement does for their
schools. They often object that measurements are made, the tests are carried
away by the examiner, and some time later they are presented with a neat
series of distributions and are told where their school stands in relation to
certain other schools or to schools in general. This is undoubtedly a very
important piece of information; since a determination of the extent to which
a goal has been attained forms the basis of the commendation or
condemnation of the methods, curricula, and text-books employed in the
process. But administrators want to know which of the various elements of
school procedure are to be praised and which are to be blamed.
We cannot condemn or support a whole school system on the basis of
composite results (unless all possible educational objectives have been
measured, and show one common drift; or unless it is necessary that the
system fall or stand as a whole) since then we should be throwing good and
bad into a common discard. We must measure each thing separately. We
must build our ideal system of education synthetically, taking the best
methods from each of the prevalent groups of theories. There has been too
much absolutism in education, too little of a realism that sees the good and

bad in all and diminishes the bad and augments the good. If we adopt this
point of view we become really empirical in our method, living through
each educational experiment to incorporate it into a growing treasury of
tested theory, not deducing success or failure from metaphysical or
doctrinaire prejudice. In this administrators have been more scientific than
those who measure. They have always objected that they wanted
differential diagnoses. Here the answer to their needs must come through
experimentation and it is only through nation-wide study and careful
comparison and integration of results that methods of teaching can be
scientifically established.
Three uses of measurement commonly stressed are: (1) Diagnosis of
degree of attainment of goal; (2) selection of method of attainment of goal;
(3) definitive outline of goals. We have seen that the first two are of little
immediate value to the administrator. The first only gives him an accurate
notion of where he stands in any one subject without pretending to tell him
why; the second is a promissory note. Some day we shall be able to tell him
the best methods for the attainment of his goal. The third has slightly more
immediate value. Measurement splits up the goals of education, gives them
concrete formulation, allows teachers to see an advance in the class in one
function as separate from the rest; allows them, for instance, to distinguish
more clearly than they otherwise would between oral reading and silent
reading, or between addition and division. But this, too, is rather too general
to appeal to administrative economy. One would find it very difficult to sell
one’s services as a measurer to a school board or a superintendent on the
basis of these three values. They answer that universities and scientific
research give them as much as they want of these values. What an expert on
measurement could add in interpretation of results would seem of small
additional value to them.
Still there is a very marked function that such an expert can perform; but
he must serve a fourth and fifth use of measurement while he serves a
particular school. When he serves the first three he is serving the science of
education and, unfortunately, no one school will pay him to do that. The
uses of measurement that directly benefit any one school are: (4)
Classification by information and intelligence and (5) diagnosis of
individual disability. For the proper prosecution of these aims individual
measurements and age norms are essential. Only with such equipment can

we make the prognoses of future school behavior which the administrator
so urgently needs.
Grade norms cannot be used to make individual diagnoses. Though we
can see by them which children are below and which above the level that in
their grade they should attain, we cannot see just what administrators most
need to know; namely, whether the retardation and acceleration are justified
or not—how many children are working at maximum. More than that,
computations based on grade norms are very inaccurate in individual cases
because the variability within any grade is so great. As it becomes necessary
to use new norms for such purposes it is important to have them in terms
that are directly comparable to intelligence mensuration.⁠[2]
First in importance is an interpretation of the meaning of an Intelligence
Quotient. Too often it is stated as a number and left as a number with the
belief that somehow or other that is a tag which carries its own divine
implication. Its importance lies in its diagnosis of power of adaptation, and
it has a high correlation with the maximum possible rate of school progress.
Just as a pure information test diagnoses the neural bonds that have been
formed in any one field, so an intelligence test diagnoses the ability to form
bonds, to meet a new situation and form satisfactory habits—power to
learn. It may be thought of as a diagnosis of the neural chemistry of the
individual. As such it is not concerned with the connections or quantity, but
rather with the quality of the neural tissue.
As an intelligence quotient is actual mental age divided by chronological
age—which is the normal mental level of the child’s age-group—so it is the
rate at which the child has progressed to mental maturity. It is his potential
rate of progress. It is a division of what is by what normally would be.
Then, when we use IQ we express the various degrees of power of
adaptation due to various degrees of fitness of neural equipment to form
bonds, by means of a diagnosis of the rate of formation of bonds which
everyone forms sooner or later in an environment such as ours. It is
conceivable that we might test this same power without testing the presence
of such bonds at all. Such a test would detect directly the quality of the
neural equipment irrespective of quantity or conformation.
A ten-year-old child whose mental age is ten has progressed at the rate
which is normal, and his IQ is 1.00. A very exceptional ten-year-old child

whose mental age is fifteen has progressed just one and one half times as
fast as the former, and his IQ is 1.50. Another exceptional ten-year-old child
whose mental age is five has progressed at just one-half the rate of the first,
and his IQ is .50. What we mean, then, by an Intelligence Quotient is the
rate at which a child grows to the mental maturity of human beings in the
world as it is.
For purposes of presentation of a problem one can here assume (an
hypothesis the value of which will here be determined) that each child can
attain this rate of progress in each of the elementary school subjects. The
degree to which this is true is the degree to which the IQ is a valid index of
power to deal with school subjects. This assumes that inherited special
disabilities in the school subjects are uncommon, that school progress is
determined by the interplay of intelligence and environment, and that so-
called interest characteristics which aid in development are the result of an
earlier interplay of intelligence and environment. The degree to which
educational product of children can be made to approach this intelligence
will allow us to judge how far these factors are inherited, since differences
that are removable must be learned, not innate.
We can the more readily see the significance of viewing a child’s
equipment in terms of educational and mental age, when we conceive of a
Subject Quotient. This is a quotient resulting from the division of the age
level reached in the test in question by the chronological age of the pupil. It
is a measure of the rate of progress of the child in the school subject under
consideration. Thus a ten-year-old child with ten-year-old ability in
Thorndike Reading Scale Alpha 2 would have as his reading age divided by
chronological age, 1.00. This may be called his Subject Quotient in Reading
or his Reading Quotient. The division of what is by what would be if the
child were normal gives the percentage of normality, the actual rate of
progress. Since the IQ is the potential rate of progress and the SQ the actual
rate of progress, the ratio of SQ to IQ gives the percentage of what that
child could do, that he has actually done. Thus a child with an IQ of 1.32
whose reading quotient (his RQ) is 1.10, though he is doing work which is
above normal, is not doing work which is above normal for him. His RQ/IQ
is 1.10/1.32, whereas if he were progressing at his optimum rate it would
equal 1.32/1.32. This RQ/IQ is the same quantity as RA/MA. We may call
this a Subject Ratio and the average of Subject Ratios an Accomplishment

Ratio. We could, if the absolute association between reading age and mental
age were perfect, measure the approximation to ideal educational
performance of any one child in any one elementary school subject through
the approximation of this Subject Ratio to 1.00. As we will see later,
Subject Quotients approach the Intelligence Quotients when special
treatment is given; that is, the correlation of SQ and IQ becomes nearer 1.00
and the difference between the average IQ and the average SQ approaches
zero. It is safe then to expect these Subject Ratios to be at least 1.00 before
we pronounce satisfaction with the school product.
There is certainly a significant relation between IQ and SQ, and the more
perfect the educational procedure has been, the more it has called forth all
that the child is capable of, the higher it will be. To determine whether the
quotient in any school subject can be greater than the Intelligence Quotient
in any significant amount, it will only be necessary after we have perfect
age norms by months to get that quotient amongst enough pupils whom we
know to be working at maximum. What is significant here is that the more
nearly any such quotient reaches or exceeds the Intelligence Quotient the
more nearly has the child been brought up to what he is able to do under the
best conditions. The Accomplishment Ratio is the degree to which his
actual progress has attained to his potential progress by the best possible
measures of both.
This would be a mark of the child’s effort, a mark of the concentration
and interest that the child has in the school work, and as far as no inherited
traits or capacities other than intelligence affect school work it is a measure
of the efficiency of a child’s education thus far. If there are such other
innate bases, it is also a measure of those inherited traits and capacities or
their predisposition, such as concentration, effort, written expression, etc. At
any rate it is a measure of the child’s accomplishment, and so of the effort
and concentration as they really are at present working under those school
conditions. It is an index of achievement irrespective of intelligence.
A very convenient graph representing the same facts and easily
interpreted by the teacher may be constructed thus:

Here it can be easily shown that Spelling Age, Reading Age, Arithmetic
Age, etc., are in some definite relation to both Chronological Age and
Mental Age. Using the Mental Age line as a goal, these records may be kept
constantly up to date. Another use of the Accomplishment Ratio is as the
medium in which the children may keep records of their own work. As it is
a mark in terms of intelligence, dull and brilliant children may compete on a
parity to bring their Accomplishment Ratios as high as possible.
Mainly we have advanced formal education. We have in many ways
promoted the abilities to read, write, spell and figure. But our philosophy of
education has advanced far beyond that. We have other aims in education,
and consequently other methods and modes, which also must be measured
and judged. We wish to promote such qualities as stability, self-reliance,
concentration, and ambition. It does not necessarily follow that we must
measure these things directly, although every one vitally interested in
measurement cherishes the hope that we may some day measure their
behavioristic correlates,—“For the quality of anything exists in some
quantity, and that quantity can be measured.”
“Some of us might be entirely willing to rest the case after asking
whether in practical school life anyone ever saw a teacher thoroughly
confident of teaching ideals but neglectful of reading and arithmetic. The
fact is that the conscientious teacher always gives attention to both and the
successful teacher is able, without omitting one, to cultivate the other. The
theoretical possibility of thinking of the two results separately has little
significance in dealing with real teachers and real schools. Good reading is
a school virtue; and when one has measured good reading he has measured
more than the trivial or formal side of education.”⁠[3]

This I believe to be true, but I also believe that through measurement we
can actually promote those other more ethical ideals in education. Through
classification by information and by intelligence we gain a marked increase
of attention, concentration, ambition, and other objectives, measured in part
by Accomplishment Ratios. More discussion due to a greater homogeneity
promotes powers of inference and insight; being only with equals promotes
self-confidence and honor, and in many cases prevents a regrettable conceit
among supernormals; having work to do which is hard enough prevents
habits of indolence and carelessness so commonly found among intelligent
children.⁠[4]
It is a well-known fact that much work must be done in classification to
get homogeneity or real conditions of teaching. As it is, most teachers are
talking to the middle of their classes. When they do they mystify the lower
quarter and bore the upper quarter; they talk to the upper quarter and
mystify the lower three quarters; or they talk to the lower quarter and bore
the upper three quarters. When a child is bored or mystified his Subject
Quotients become less while his Intelligence Quotient remains constant.
Then his Accomplishment Ratios become less as long as he remains in a
position where he is being mistreated educationally. This, then, is the proper
measure to see whether a child is classified properly or not. At the Garden
City public school I changed as far as I was able the conditions of education
of each child in that subject wherein his Accomplishment Ratio was
markedly below 1.00. The concentration and effort of the child were
obviously low and my attempt was to change conditions and to promote
habits of consistent work. When the Accomplishment Ratio increased I
knew that the child was profiting, that he was working. Our objective was
to increase Ratios of all children, not to attain any set standard.
This Accomplishment Ratio would, to my mind, be an ideal school mark.
Besides the inaccuracy of marks to-day, which are accurate marks only of
the teacher’s opinion, biased as it is by the personal equation of her
character with that of the pupil, there is another fault of prevalent school
marking. It is based on average work. The mark is the link between
education in the school and education in the home. It gives the parents an
index of the child’s work and allows them to encourage or discourage the
child’s attitudes. Such indices have no real significance when they are based

upon average development, as the parent is generally mistaken about the
ability of the child.
Marks given by a teacher are satisfactory only for a normal child with
normal age for the grade. Brilliant children are over-praised for work
which, though over the ability for the group, is under their own ability.
Marks given to stupid children are misinterpreted by parents so as greatly to
prejudice the effort of the child. Though his work may be such as to merit
encouragement his mark may be very low. Teachers’ marks are, aside from
their inaccuracy, just, only in a group that is perfectly classified; just, only
when the children are all of the same ability and all possess the same initial
information. So far as they are unjust they are subversive of our aims, as
they then transmit a faulty message to the home and disrupt the continuity
of school and home education.⁠[5]
Such marks as are here advocated would correct this feature of our
present system, as well as the inaccuracy of our present marks. It is a mark
which evaluates the accomplishment of the child in terms of his own ability.
A brilliant child would no longer be praised for work which in terms of his
own effort is 70 per cent perfect, in terms of the maximum of the group 90
per cent. The teacher gives him a mark of 90 while we mark him 70. A
stupid child who does work which is marked 70 in terms of the maximum
of the class but 90 in terms of his own, a limited ability, is no longer
discouraged. His effort is evaluated, and the praise which he receives from
home is merited and consequently economical, since the resultant
satisfaction cements the bonds of concentration and attention. Such a mark
is an actual index of the effort that child is making and consequently forms
the proper link between the school and the home.
Parents would need no great instruction in the interpretation of these
marks, since they have always acted as though the other marks were these,
and since these also are in percentage form. The only kind of mark they can
understand is an Accomplishment Ratio. I found that the parents of the
children at Garden City were more attentive to such marks than to others,
and acted upon them more readily. Of course the parents of the very
intelligent children, who are used to marks above 90, are surprised at first
when you tell them that your mark of the child is 80; but upon explanation,
which should in all cases precede the first report to the parents, they
immediately see the value of such grading. It is fortunate in this connection

that the greatest amount of explanation is necessary about intelligent
children, as one usually deals then with intelligent parents.

THE DERIVATION OF AGE NORMS

In this study age norms were derived empirically, both regression lines
being taken into consideration. From the point of view of statistics it
becomes imperative, in order to use the technique here advised, to have the
average age of a score—since we are going to predict age from score—to
translate crude scores into indices of maturity in each subject under
consideration. We are in error in the use of grade norms, if we find the
average score of a grade and then, when we obtain that score in practice,
say that the work is of that grade. To be able to say this we must know the
average grade of a score. This takes in an entirely different cross-section of
data. If we get the average score of all children in grade 6, then we can
predict what a 6th grade child is likely to get, but we can say nothing about
a child who is not in grade 6. In order to decide that a 4th grade child has
6th grade ability, we must know that he has such ability that all children
who share this score make an average grade of 6.⁠[6] It would be wise then to
get the regression of score on age as well as the regression of age on score,
since they are not identical, the correlation between score and age being less
than unity.
We will note in passing that the data to establish these norms, except
those of reading, are not as complete as may be desired, inasmuch as it was
difficult to get test scores where the age in months also was available.
However, the general data behind the grade norms could be used to keep the
results from any crude error; and the averages were obtained for every
month from 8 years to 14 years, with a corresponding refinement in
intervals of score, which made still more improbable an error in the general
tendency of the regression lines. Then all the distributions, when grouped
by years, were corrected for truncation; that is, the tendency for the brighter
children of the older group to be in high school (the data were from
elementary schools only) and the duller children of the younger group to be
in the lower grades where they could not be reached was recognized and
corrected by finding the average, standard deviation, and number of cases
which would have existed if these forces of truncation were not operating.

This was done by the use of the other one half of the figures comprising
Table XI of Pearson’s Tables for Statisticians and Biometricians. Dr.
Truman L. Kelley pointed the way to its derivation.
These norms differ somewhat from those derived from the grade norms
by translation of grade into average age for the grade. This is because the
norm for a grade is the average score for a grade. Hence the norm of age 10
obtained in this way is the average score obtained by a grade whose average
age is 10. Then the data used to obtain this average are made up of diverse
ages, all of one grade, instead of all of one age and diverse grades. Even
then, we would have only an average score of an age which approximates
what we want, but is not as reliable to use as average age for a score.

A METHOD OF SURVEY OF READING, LANGUAGE, AND
ARITHMETIC

The following procedure was employed in the experiment. The
experiment was carried out in the public school at Garden City. Two
hundred children were given the tests. The instructions, shown below, were
followed in November, 1919, and in November, 1918; in June, 1919, and in
June, 1920, with the exception that no arithmetic test was used in
November, 1918, and June, 1919. The Binet tests were given by the author;
all of the others were given either by the author or the principal who was
careful not to deviate from the directions in any way. In June of both years
the author gave instructions for a test in one room, and then left the teacher
in charge and went on to the next. This could be done in June of each year
as the teachers were then fully acquainted with the experiment and their
coöperation was assured.

Directions
I. Administer and score the following tests according to standard
instructions. Give all tests to grades 3 and above.

Woody-McCall Mixed Fundamentals in Arithmetic
Thorndike Reading Scale Alpha 2
Thorndike Visual Vocabulary Scale, A2

Kelley-Trabue Completion Exercises in Language
Stanford-Binet Tests (given by the author)

II. Translate the scores into year-month indices of maturity by
means of the following table. (Use Mental Age for the Binet.)
Assume rectilinear development, that is, that the amount of
score which equals the development of one month is the same
as the amount of score which equals the development of any
other month. Then interpolation and extension are allowable.
Use the table in this way: Find in the table the score made by a
child (for instance in the Woody-McCall); find the age to
which it corresponds, then call this age the Arithmetic Age of
the child. For instance, if the score in Woody-McCall is 20, his
Arithmetic Age is about halfway between 10 and 11 or 10
years 6 months.

Age Woody-McCall Alpha 2 Visual Vocab. Kelley-Trabue
8—0 12.00 4.50 3.60 4.30
9—0 15.16⅔ 4.98 4.32 5.00
10—0 18.33⅓ 5.46 5.04 5.65
11—0 21.50 5.94 5.76 6.35
12—0 24.66⅔ 6.42 6.48 7.05
13—0 27.83⅓ 6.90 7.20 7.70

III. Arrange these Arithmetic Ages of all the children of your school
in order from high to low with the names opposite the scores in
the extreme left-hand column of the paper. At the right have
parallel columns of the grades. Check the grade of each child
in these columns. You will then have a sheet like this:

Grade
Name Arith. Age 4 5 6 7 8
B A B A B A B A B A
Gertrude Smith 180 #
Saul Sampson 176 #
Ed Jones 176 #

George Calut 172 #
Ida Henry 172 #
Raymond Teller 172 #
Ed Hoard 172 #
Etc.

Do the same with each of the tests. It is clear that,
independent of the unreliability of the test, if your school were
perfectly classified all the 8th grade children would come first
on each relation sheet and then the 7th grade children, etc. You
have now a picture of the overlapping of your grades. Regrade
in reading and arithmetic. Draw horizontal lines across these
relation sheets at the points of delineation. Divide your total
number of children by the number of teachers available and
then make a class division by the number of pupils, that is, call
the upper one-sixth of the total number of pupils grade 8 in this
subject, the next one-sixth, grade 7, etc. Teach all grades of
arithmetic at the same time and all grades of reading at the
same time. You can now send each pupil to the grade in which
he belongs in each subject.
IV. Call each derived age a Subject Age (SA). Divide each subject
age by the chronological age of the child. This will yield what
may be called a Subject Quotient (SQ), previously called an
Educational Quotient (EQ).⁠[7] Dividing the Reading Age by the
Chronological Age, you arrive at a Reading Quotient. This RQ
is the rate at which the child has progressed in reading. We
have the same kind of quotient for intelligence (Stanford-Binet
IQ). This IQ is the potential rate of progress of the child.
V. The ratio of any Subject Age to Mental Age⁠[8] may be called a
Subject Ratio (SR), previously called an Accomplishment
Quotient (AccQ).⁠[7] This Subject Ratio gives the proportion
that the child has done in that subject of what he actually could
have done, and is a mark of the efficiency of the education of
the child in that subject to date. The goal is to bring up these
Subject Ratios as high as possible. When they are above .90,

the child may be considered as receiving satisfactory treatment,
providing norms for subject ages are reasonably accurate. (This
figure, .90, applies to a Subject Ratio obtained by using a
Stanford-Binet Mental Age.) An Arithmetic Ratio based on one
arithmetic test and one intelligence test only is not as good as
one based on three arithmetic tests and three intelligence tests.
If Subject Ratios go far over 1.00 the chances are that the
Mental Age diagnosis is too low. The average of the Subject
Ratios of a child may be called his Accomplishment Ratio.
In the application of the above instructions, whenever opportunity
offers for classification of both subject matter and intelligence
(which means many teachers or a large school), use a Relation Sheet
(for instance for Arithmetic) and then have additional columns at the
extreme right for intelligence headed A, B, C, and D. If a child’s IQ
is in the upper quarter of the IQ’s of your school, check in the
column A opposite his name; if it is in the upper half but not in the
upper quarter check in B, and so on with C and D. Then you will be
able to split each group; for instance, the one which is defined as 8th
grade in arithmetic ability, into four sections, each of which
progresses at a rate differing from the others. The A section will
progress most rapidly, B next, C more slowly, and D most slowly.

As Garden City was a small school, adjustment of procedure to
individual differences in intelligence, besides the grouping for subject
matter, was done mostly by pushing children. Children were advanced
whole years (the grade they “belonged to” was the one in which geography
and history were taught; this was their home grade) besides the
readjustment made by the special regrading in reading and arithmetic. A
special treatment class was formed where pronounced negative deviates
were given special attention. Regrading was also instituted for spelling.
Children were promoted whenever it was considered advisable; teachers
were switched from subject to subject whenever that was considered
advisable by the principal and the author. The Thorndike Arithmetics and
other new texts were introduced to some extent. Any change possible was
made in order to bring EQ/IQ as high as possible. That was the goal. The
purpose was not to prove that any certain educational procedure would tend

to promote abilities more rapidly than others, but that abilities could be
promoted to the level of intelligence—that intelligence is substantially the
exclusive inherited determinant of variety of product among school
children. (It is to be understood that intelligence may be, and probably is,
the summation of thousands of inherited factors,—neutral elements, here
merged in the broader behavioristic concept of intelligence.)

SCIENTIFIC QUESTIONS INVOLVED IN
CLASSIFICATION

If we were able to negate other influences upon disparity of product, we
could conclude that these were not inherited. Hence it would be our burden
as educators so to manipulate education as to prevent their operation. We
will attempt to analyze the determinants of individual differences in product
in these children, to see which influences besides intelligence are part of the
inborn equipment which is not the province of education, but of eugenics,
to correct. No absolute validity is held for any of the conclusions stated
here. The subject is, at best, vague and complicated; but our conclusions
can be used as the basis for a good guess in school procedure. We can judge
general tendencies from the educational experiences of the two hundred
children whose abilities for two years are here charted.
The importance to educators of the subject in hand is excuse enough for
its treatment. All educational procedure points a prophetic finger toward the
classification of pupils and a reduction of the individual differences of
product to the inherited bases of these differences.
Classification, however, needs some more accurate psychological
foundation than the mere awareness of individual variance. We must know:
1. What tests to use.
2. How to use them.
3. Whether abilities in reading, spelling, and arithmetic or their
predispositions exist as special abilities, or whether children differ in these
simply because of their innate differences of intelligence.
4. Whether individual differences in ambition, interest, and industry, in so
far as they influence accomplishment, are due to special tendencies, or

whether they are learned manifestations of a more general heritage.
5. How these proclivities, specific or general, are related to intelligence.
Points 1 and 2 are problems of procedure which must be evolved from
our existent knowledge of measurements and statistics. Points 3, 4, and 5
are problems which must be solved from the evidence resulting from an
experiment in classification using these methods. Points 4 and 5 introduce
the vexed question of whether there is a “general factor” or some general
inherited cause of disparity in school product other than intelligence.
Should reading ability prove to be the result of certain inherited abilities, or
predisposition to abilities, we could not use a measure of mental ability
alone as the guide to what a child could attain in reading. If intelligence,
however, were the only inherited prognostic factor of school achievement,
we could mark the education which had functioned in the child’s life by the
percentage which the actual accomplishment of the child was of the
maximum accomplishment of which he was capable at that stage of his
mental development. So, too, if interest in particular subjects and ambition
are not mainly the result of rewards and punishments of early life, but are
themselves significantly rooted in the nature of the child, we could not
condemn or commend curricula and methods upon a basis of the ratio of
resultant accomplishment to mental ability, but must include a measure of
this potentiality. The practical queries whether or not a child can do reading
as well as he does arithmetic, whether his ambition and his honesty have
their origin in the same strength or weakness, can be answered only when
these problems are fully solved. The immediate consequences of knowing
that a child can usually be taught to read if he does other tasks well is of
obvious import. It would be of great service, too, to know whether lack of
application can be corrected so as to bring concentration to the level of the
other traits. If a child is normal in other ways and not in his tendency to
respond to the approval of others by satisfaction, can this “drive” be
increased or reduced to the average, or are individual differences in specific
original tendencies basic to development of character, and if they are, how
much influence do these differences exert upon school accomplishment? In
order to classify children and comprehendingly watch and control their
progress we must know the relation of achievement to the inherited bases
upon which it depends. We must be able to state a child’s progress in any

one school subject in terms of the potential capacity of the child to progress.
We must know the inherited determinants of disparity in school product.

PART II
STATISTICAL TREATMENT OF THE
EXPERIMENT
In the discussion and tables which follow:
Q stands for Quotient, which will mean a Subject Age divided by a
Chronological Age. R stands for Ratio, which will mean a Subject Age
divided by a Mental Age.
AQ means Woody-McCall Arithmetic Age divided by Chronological
Age, and AR means this AA divided by Mental Age.
VQ means Thorndike Vocabulary Age divided by Chronological Age,
and VR means this VA divided by Mental Age.
RQ means Alpha 2 Reading Age divided by Chronological Age, and RR
means this RA divided by Mental Age.
CQ means Kelley-Trabue Completion Age divided by Chronological
Age, and CR means this CA divided by Mental Age.
SQ means any Subject Quotient, that is, any Subject Age divided by
Chronological Age, and SR means any Subject Ratio, that is, any SA
divided by Mental Age.
EQ means the average of all Subject Quotients and AccR, the
Accomplishment Ratio, means the average of all Subject Ratios.
All r’s are product-moment correlation coefficients, uncorrected. As the
reliabilities (Table 4) are almost what the other coefficients are in June,
1920 (Table 5), it is apparent that the corrected coefficients, when Grade III
is excluded, would all be very near unity at that time.

THE QUOTIENTS

In Table 1 are presented all the quotients for all periods of testing,
grouped by children. The table, a sample of which is included here,⁠[9]

shows clearly how all SQ’s approach IQ as special treatment continues. The
grades indicated in this grouping are as of June, 1920. Inasmuch as many
double and triple promotions were made in an effort to get maximum
product for intelligence invested, no conclusion can here be formed of the
grade to which these children belonged at any time except June, 1920. The
correspondence between IQ and the SQ’s in June, 1920 is further shown in
Table 2. In this table the 48 children who took all tests at all periods are
ranked from high to low IQ and their SQ’s are listed opposite. The high
correspondence is readily apparent.

TABLE 1⁠[10]
Intelligence Quotients for All Periods Grouped by Children

The children are arranged by grade as they were in June, 1920, and
alphabetically within the grade. The periods of testing are lettered in their
chronological sequence; a is November, 1918, b is June, 1919, c is
November, 1919 and d is June, 1920. * = Zero Score
Grade 3

Intelligence Test Arithmetic Vocabulary Reading Completion
Quotient Period Quotient Quotient Quotient Quotient

a
b
101
c 64 58 43
d 106 88 93

a
b
128
c 80 102 81
d 152 124 153

a
b
116
c 56 90 * 49
d 94 95 77 89

a
b
87
c 90 40 35 54
d 72 74 61 52

a
b
112
c 90 137 133 112
d 112 113 121 131

TABLE 2⁠[11]
Group Taking All Tests at All Periods Arranged in Order of
Magnitude of Intelligence Quotients

Intelligence Arithmetic Vocabulary Reading Completion
Quotients Quotients Quotients Quotients Quotients
146 111 154 164 150
142 129 135 137 136
141 109 118 107 121
139 124 141 124 134
138 101 112 105 106

138 121 130 110 109
130 107 139 135 136
122 127 130 124 121
122 113 121 117 124
122 112 102 114 129

121 128 125 128 128
120 100 116 102 119
118 117 123 114 125
117 131 111 118 124
117 106 122 112 111

114 105 126 110 114
109 83 113 117 103
107 103 112 95 103
107 94 126 94 123
104 99 117 96 104

104 103 110 94 116
103 108 113 112 106
101 100 114 109 106
100 90 103 92 92
100 109 118 108 113

99 114 104 106 110
99 114 119 117 115
98 102 101 108 104
98 99 106 107 106
97 95 109 107 105

97 108 101 102 105
97 95 104 89 110
96 90 104 91 91
95 84 99 93 100
95 90 107 99 105

95 85 117 114 103
94 106 57 89 108
94 103 103 106 104
92 96 86 94 85
87 83 88 92 87

87 95 96 94 102
84 85 87 93 87
83 106 91 87 104
80 77 91 80 84
80 84 75 79 84

80 89 107 88 86
78 87 90 93 85
60 69 56 71 77

The intercorrelations of the quotients of these 48 cases for all periods
may be seen in Table 3 (page 21). The correlations with IQ and the
intercorrelations of the SQ’s have increased toward positive unity or rather
toward the limits of a correlation with tools of measurement such as we
have used. This limit is a function of the reliability of the tests employed. It
is customary to use a formula to correct for attenuation in order to find the
percentage which the correlation is of the geometric mean of the two
reliability coefficients. This is tantamount to saying that any correlation can
go no higher than the geometric mean of the reliability coefficients of the
tests used. It is better to assume that an r can go as high as the ∜(r₁₁⋅r₂₂)
since an r can go as high as the square root of its reliability coefficient. Dr.
Truman L. Kelley has shown that the correlation of a test with an infinite
number of forms of the same test would be as the square root of its
correlation with any one other form.
The reliabilities and limits defining a limit as the fourth root of the
multiplied reliability coefficients are in Table 4.
Correction for attenuation is often ridiculously high because the
reliability coefficient of one of the measures used is so low. If an element is
included in the two tests which are correlated, but not in the other forms of
each test used to get reliability, the “corrected coefficient” is corrected for
an element which is not chance. Whenever the geometric mean of the
reliabilities is less than the obtained r, the corrected r is over 1.00 and hence
absurd.⁠[12]
Therefore we use here instead, a comparison to the maximum possibility
in a true sense. Since a test correlates with the “true ability” √(r₁₁),
∜(r₁₁⋅r₂₂) is the limit of an r, its optimum with those tools. Although these
limits apply, strictly speaking, only to the total correlations, since the
reliability correlations are with all the data; we may assume that the same
facts hold with regard to the correlations of each of the grades, that is, the
reliability is a function of the test not of the data selected.

TABLE 3
Intercorrelation of All Quotients for All Periods of the 48
Children Who Took All Tests

November, 1918
IQ VQ RQ S.D. M
IQ 19.12 105.15
±1.32 ±1.86
VQ .72 20.54 102.52
±.05 ±1.41 ±2.00
RQ .64 .64 19.09 95.90
±.06 ±.06 ±1.31 ±1.86
CQ .63 .71 .77 19.34 99.44
±.06 ±.05 ±.04 ±1.33 ±1.88
June, 1919
IQ VQ RQ S.D. M
IQ 19.12 105.15
±1.32 ±1.86
VQ .73 20.80 113.54
±.05 ±1.43 ±2.02
RQ .65 .58 14.73 101.31
±.06 ±.06 ±1.01 ±1.43
CQ .62 .68 .77 19.76 101.04
±.06 ±.05 +.04 ±1.36 ±1.92
November, 1919
IQ AQ VQ RQ S.D. M
IQ 19.12 105.15
±1.32 ±1.86
AQ .46 14.08 102.90
±.08 ±0.97 ±1.37
VQ .86 .23 17.07 109.17
±.03 ±.09 ±1.18 ±1.66
RQ .65 .56 .71 13.91 101.42
±.06 ±.07 ±.05 ±0.96 ±1.35

CQ .79 .47 .83 .82 17.53 105.21
±.04 ±.08 ±.03 ±.03 ±1.21 ±1.71
June, 1920
IQ AQ VQ RQ S.D. M
IQ 19.12 105.15
±1.32 ±1.86
AQ .73 14.10 101.79
±.05 ±0.97 ±1.37
VQ .81 .60 18.89 108.94
±.03 ±.06 ±1.30 ±1.84
RQ .79 .68 .87 16.43 104.94
±.04 ±.05 ±.02 ±1.13 ±1.60
CQ .84 .77 .78 .84 15.87 108.08
±.03 ±.04 ±.04 ±.03 ±1.09 ±1.54

TABLE 4
Reliability Coefficients

One Form Two Forms of One Form with Two Forms with
of Each Each Test (by an Infinite an Infinite
Test Brown’s Formula) Number of Forms Number of Forms
r₁₁ r₁₁ √r₁₁ √r₁₁
Intelligence Quotient .888 .942
(by Brown’s Formula)⁠[13]
Arithmetic Quotient .824 .904 .908 .951
Vocabulary Quotient .820 .901 .906 .949
Reading Quotient .866 .928 .931 .963
Completion Quotient .883 .938 .940 .968

Limits of the r’s = ∜(r₁₁ × r₂₂)

Nov. 1918,
June and June 1920
Nov. 1919
IQ and AQ .925 .946
IQ and VQ .924 .946

IQ and RQ .936 .953
IQ and CQ .941 .955
The limits of the June, 1920 r’s are naturally somewhat larger than the others since two forms of
tests (except the Binet) were used; the unreliability of the quantitative indices is therefore lower and
hence the correlation with IQ may be larger.

The correlations in 1920 of another group—the whole school except
Grade III—are reproduced in Table 5. Grade III was excluded since here
there had as yet been little chance to push the r’s. Partials were obtained
with these data (Table 6). Little faith may be placed in the relative sizes of
these partials, much because the rVQ.RQ is here only .73 and, in the data
presented in Table 3, it is .87. This is due to the fact that the data in Table 3
cover all periods (2 years) while those in Table 5 cover only one. This
difference has comparatively slight influence on our general conclusions;
but it makes a huge difference in the correlation of RQ and VQ when IQ is
rendered constant, whether the one or the other set of data is used.
Moreover, the whole logic of arguing for general factors by reduction of
partial correlations from the original r has been called gravely into question
in Godfrey H. Thomson’s recent work on this subject: “The Proof or
Disproof of the Existence of General Ability.” Thomson shows that partial
correlation gives one possible interpretation of the facts, but not an
inevitable one. Thus we cannot say that because RQ and IQ and RQ and AQ
are highly correlated, correlation of IQ and AQ is dependent upon RQ. We
can say, however, that it is likely to be. IQ and AQ may be correlated by
reason of inclusion of some element not included at all in RQ. The higher
the correlations which we deal with the less we need worry about this, and
of course correlations of unity exclude any such consideration.

TABLE 5
Intercorrelation of All Quotients in June, 1920. All Children
Exclusive of Grade 3 are Here Represented

The P.E.’s are all less than .05
N = 81

Arithmetic Vocabulary Reading
IQ
Quotient Quotient Quotient

Arithmetic Quotient .733
Vocabulary Quotient .837 .628
Reading Quotient .758 .694 .734
Completion Quotient .821 .770 .825 .801

I therefore draw no conclusions from the comparative size of these
partials, nor do I get partials with any of the other data, and rest the case
mainly on the high r’s between IQ and SQ’s in 1920; increase in
correspondence of the central tendencies and range of the SQ’s by grade
with the central tendency and range of the IQ’s of the same data; small
intercorrelation of SR’s and negative correlation of AccR with IQ.
The general lowness of the partials (Table 6) does, however, indicate the
great causative relation between IQ and disparity of product. The elements
still in here are common elements in the tests and the mistreatment of
intelligence.

TABLE 6
Partial Correlations of Quotients Irrespective of Intelligence
Quotients

N = 81

Arithmetic Vocabulary Reading
Quotient Quotient Quotient
.04
Vocabulary Quotient
±.07
.31 .28
Reading Quotient
±.07 ±.07
.43 .44 .47
Completion Quotient
±.08 ±.06 ±.06

What happened by grade in 1918-1919 is summarized in Table 7. What
happened by grade in 1919-1920 is summarized in Table 8. Since there
were many changes in personnel from 1918-1919 to 1919-1920, we need
expect no continuity from Table 7 to Table 8. For the continuous influence

of the two years, see Table 3, which includes 48 children taking all tests at
all periods.

TABLE 7
All Correlations, Means, and Standard Deviations by Grade,
Showing Progress from November, 1918 to June, 1919

I stands for Intelligence Quotient
V stands for Vocabulary Quotient
R stands for Reading Quotient
C stands for Completion Quotient

r M S.D.
GRADE
Nov. June Nov. June Nov. June
III I V .467 .633 I 109.89 113.20 I 12.83 15.49
±.12 ±.07 ±1.98 ±1.91 ±1.40 ±1.35
I R .541 .492 V 96.11 109.90 V 21.21 18.69
±.11 ±.09 ±3.28 ±2.30 ±2.32 ±1.63
I C .641 .386 R 82.26 101.40 R 22.58 15.85
±.09 ±.11 ±3.49 ±1.95 ±2.47 ±1.38
C 86.89 108.40 C 22.76 15.79
±3.52 ±1.94 ±2.49 ±1.37
N= 19 30
IV I V .724 .819 I 105.90 104.82 I 18.08 18.21
±.07 ±.05 ±2.73 ±2.98 ±1.93 ±2.11
I R .665 .845 V 97.20 108.53 V 17.26 24.92
±.08 ±.05 ±2.60 ±4.08 ±1.84 ±2.88
I C .596 .717 R 91.06 107.82 R 27.85 10.35
±.10 ±.08 ±4.20 ±1.69 ±2.97 ±1.20
C 101.45 108.12 C 21.53 17.75
±3.25 ±2.90 ±2.30 ±2.05
N= 20 17
V I V .887 .822 I 101.64 99.42 I 24.76 17.63
±.04 ±.05 ±3.56 ±2.73 ±2.52 ±1.93

I R .799 .832 V 100.59 111.58 V 26.71 19.78
±.05 ±.05 ±3.84 ±3.06 ±2.72 ±2.16
I C .818 .890 R 94.59 101.42 R 22.10 12.56
±.05 ±.03 ±3.18 ±1.94 ±2.25 ±1.37
C 97.00 102.68 C 22.52 17.71
±3.24 ±2.74 ±2.29 ±1.94
N= 22 19
VI I V .793 .772 I 109.90 115.90 I 23.45 24.38
±.08 ±.09 ±5.00 ±5.20 ±3.54 ±3.68
I R .497 .726 V 108.00 126.80 V 30.20 25.25
±.16 ±.10 ±6.44 ±5.39 ±4.55 ±3.81
I C .798 .891 R 103.10 107.20 R 13.77 20.62
±.08 ±.04 ±2.94 ±4.40 ±2.08 ±3.11
C 108.90 117.10 C 15.23 18.81
±3.25 ±4.01 ±2.30 ±2.84
N= 10 10
VII and VIII I V .625 .504 I 99.29 98.92 I 11.11 11.45
±.11 ±.14 ±2.00 ±2.14 ±1.42 ±1.51
I R .622 .709 V 109.43 115.23 V 14.07 17.43
±.11 ±.09 ±2.54 ±2.95 ±1.79 ±2.31
I C .782 .730 R 97.00 98.85 R 12.59 15.77
±.07 ±.09 ±2.27 ±3.26 ±1.61 ±2.09
C 102.43 95.85 C 13.49 17.72
±2.43 ±3.31 ±1.72 ±2.34
N= 14 13
Total I V .685 .680 I 105.07 106.88 I 19.34 18.45
±.04 ±.04 ±1.41 ±1.32 ±1.00 ±0.93
I R .568 .626 V 101.12 112.67 V 22.83 21.58
±.05 ±.04 ±1.67 ±1.54 ±1.18 ±1.09
I C .639 .702 R 92.40 102.91 R 22.65 15.27
±.04 ±.04 ±1.66 ±1.09 ±1.17 ±0.77
C 98.08 106.27 C 21.48 18.19
±1.57 ±1.30 ±1.11 ±0.92
N= 85 89

TABLE 8
All Correlations, Means, and Standard Deviations of Quotients by
Grade, Showing Progress from November, 1919 to June, 1920

I stands for Intelligence Quotient
V stands for Vocabulary Quotient
R stands for Reading Quotient
C stands for Completion Quotient
A stands for Arithmetic Quotient

r M S.D.
Nov. June Nov. June Nov. June
III IA
.413 .709 I 102.00 105.53 I 9.60 10.89
±.16 ±.08 ±1.87 ±1.68 ±1.32 ±1.19
I V .649 .667 A 82.75 97.84 A 15.88 18.62
±.11 ±.09 ±3.09 ±2.88 ±2.19 ±2.04
I R .651 .609 V 94.00 103.47 V 33.44 27.66
±.11 ±.10 ±6.51 ±4.28 ±4.60 ±3.03
I C .612 .719 R 87.59 93.88 R 32.06 19.02
±.12 ±.07 ±6.24 ±3.21 ±4.41 ±2.27
C 90.17 96.84 C 28.82 25.59
±5.58 ±3.96 ±3.95 ±2.80
N= 12 19
IV I A .426 .725 I 111.48 113.00 I 14.73 15.04
±.10 ±.06 ±1.85 ±1.93 ±1.30 ±1.36
I V .635 .772 A 94.07 111.08 A 12.34 15.02
±.075 ±.05 ±1.55 ±1.99 ±1.09 ±1.40
I R .316 .569 V 109.79 115.61 V 16.97 18.39
±.11 ±.09 ±2.13 ±2.34 ±1.50 ±1.66
I C .594 .837 R 99.31 110.11 R 17.89 14.67
±.08 ±.04 ±3.24 ±1.67 ±1.58 ±1.32
C 108.14 118.14 C 15.51 12.70
±1.94 ±1.62 ±1.37 ±1.15

N= 29 28
V IA .698 .713 I 103.72 98.83 I 19.57 18.84
±.07 ±.07 ±2.69 ±2.65 ±1.91 ±1.87
IV .881 .908 A 87.58 99.71 A 12.43 16.47
±.03 ±.02 ±1.71 ±2.27 ±1.21 ±1.60
IR .773 .891 V 109.00 105.17 V 15.58 19.97
±.06 ±.03 ±2.14 ±2.81 ±1.52 ±1.99
IC .786 .923 R 104.46 103.00 R 16.99 17.07
±.05 ±.02 ±2.34 ±2.40 ±1.65 ±1.70
C 107.00 103.48 C 16.12 14.51
±2.22 ±2.04 ±1.57 ±1.44
N= 24 23
VI IA .533 .805 I 102.43 105.39 I 11.61 13.56
±.13 ±.06 ±2.09 ±2.16 ±1.48 ±1.52
IV .774 .858 A 91.43 104.53 A 11.43 11.31
±.07 ±.04 ±2.06 ±1.75 ±1.46 ±1.24
IR .420 .661 V 106.07 112.94 V 11.93 10.94
±.15 ±.09 ±2.15 ±1.74 ±1.52 ±1.23
IC .739 .620 R 96.64 106.20 R 12.38 11.88
±.08 ±.10 ±2.23 ±1.79 ±1.58 ±1.27
C 100.36 107.61 C 13.95 10.55
±2.51 ±1.68 ±1.78 ±1.19
N= 14 18
VII IA .740 .795 I 107.27 100.58 I 23.29 19.78
±.09 ±.07 ±4.74 ±2.85 ±3.35 ±2.72
IV .867 .718 A 100.00 99.31 A 9.26 11.00
±.05 ±.09 ±1.86 ±2.06 ±1.33 ±1.45
IR .862 .799 V 114.36 108.75 V 19.15 14.42
±.05 ±.07 ±3.89 ±2.81 ±2.75 ±1.98
IC .833 .677 R 101.73 98.58 R 12.28 11.56
±.06 ±.11 ±2.50 ±2.25 ±1.77 ±1.59
C 105.82 101.42 C 17.41 16.02
±3.54 ±3.12 ±2.50 ±2.21
N= 11 12

VIII IA .663 .796 I 104.83 108.79 I 15.46 18.25
±.11 ±.07 ±3.01 ±3.29 ±2.13 ±2.33
IV .828 .750 A 92.92 93.86 A 10.20 9.74
±.06 ±.08 ±1.99 ±1.76 ±1.40 ±1.24
IR .775 .722 V 111.67 117.21 V 16.44 14.02
±.08 ±.08 ±3.20 ±2.53 ±2.26 ±1.79
IC .838 .868 R 100.83 104.38 R 11.52 20.62
±.06 ±.04 ±2.24 ±3.72 ±1.59 ±2.63
C 104.92 109.64 C 18.11 17.41
±3.53 ±3.14 ±2.49 ±2.22
N= 12 14
Total I A .576 .686 I 106.02 105.87 I 16.73 16.87
±.05 ±.03 ±1.12 ±1.07 ±0.79 ±0.75
IV .679 .727 A 91.35 102.01 A 13.22 15.61
±.04 ±.03 ±0.88 ±0.98 ±0.62 ±0.69
IR .529 .609 V 107.95 110.54 V 19.76 19.57
±.05 ±.04 ±1.32 ±1.24 ±0.93 ±0.87
IC .678 .731 R 99.22 103.65 R 18.85 17.12
±.04 ±.03 ±1.26 ±1.08 ±0.89 ±0.76
C 104.06 108.00 C 18.87 18.11
±1.26 ±1.14 ±0.89 ±0.81
N= 102 114
Note—Totals without Grade III are much higher than these (Table 5). Grade III has many children
in it who have not been long enough in an academic situation to allow their SQ’s to go as high as
they may.

It is proper to note here that not much can be expected from Grades III
and VIII and from totals including Grade III, since children in Grade III
have not been there long enough to be pushed, and children in Grade VIII
have been pushed beyond the limits which the tests used will register. Our
logic is one of pushed correlations. If the association of IQ and the SQ’s is
what we are attempting to establish, it is necessary to show:
1. That the r comes near unity;
2. That the central tendencies come near coincidence;

3. That the S.D.’s come near coincidence.
The value of the r is obvious; the value of coincidence of means becomes
clearer if we think of Σ(IQ-EQ)/n, the average difference of potential rate of
progress and actual rate of progress. This average of differences is the same
as the difference of the averages, which is more readily calculated.
Obviously, if we wish to use an AccR, it is necessary to show more than
correspondence when differences in average and spread are equated as they
are by the correlation coefficient. Besides, coincidence of M’s,
correspondence of S.D.’s is also necessary since a correlation might be
positive unity, the M’s might be equal, and still the spread of one measure
might be more than the spread of the other. If the spreads are the same and
the M’s are the same, and the correlation is positive unity, each x must equal
its corresponding y. Then b₁₂ = b₂₁ = 1.00; and the M’s being equal, the
deviations are from the same point. Therefore, we will attempt to measure
similarity of M’s and S.D.’s as well as r.
It will be observed that both Tables 7 and 8 give evidence of each of
these tendencies in all grades. In Table 8 marked progress in arithmetic is
apparent. This is due to re-classification in terms of the Woody-McCall test,
which was not done in 1918-1919. In 1918-1919 no arithmetic test was
given and all re-classification was in terms of reading, being done on the
basis of both reading tests. Spelling re-classification was done each year,
but the data were not treated in this manner. It can be said that wherever re-
classification in terms of intelligence and pedagogical need was undertaken
the desired result of pushing the SQ’s up to IQ was hastened. Of all the
remedial procedure, such as changing teachers and time allotment and
books and method, all of which were employed to some extent, it is my
opinion that the re-classification was more important than everything else
combined.
It is noticeable that when r’s approach the limit which the unreliability of
the test allows them, they drop down again. This is probably due to
continued increase of SQ’s over IQ. Of course, for some SQ’s to be greater
than IQ out of proportion to the general amount lowers the correlation as
much as for some to lag behind. When the SQ’s of the children of lower
intelligence reach their IQ they continue above. This, of course, is due to
errors in establishment of the age norms. The norms are not limits of
pushing, though an attempt was made by correction for truncation to get

them as nearly so as possible. It is to be noted, however, that these norms
are up the growth curve, that is, reading age of 10 means a score such that
the average age of those getting it is 10, not the average score of children
whose mental age is 10. The average reading achievement of children all
ten years old chronologically is higher than that of a group all mentally ten,
since many of the mentally advanced have not been pushed in product. The
group used here to establish norms gives more nearly pushed norms than
the others would.
The tendency of the low IQ’s to go over unity in their SR’s is apparent in
Table 1 and in Table 12 and also in the negative correlation between AccR
and IQ.
In both years some second grade children were advanced to Grade III
during the year. This accounts for the low r’s in June, 1919, but in 1919-
1920 the Grade III correlations are raised and the means raised toward the
MIQ, even though some second grade children were put in this group during
the year.

TABLE 9
Summary of Progress in Arithmetic by Increase in r, Decrease in MIQ-
MAQ and Decrease in Difference of Standard Deviations Irrespective
of Direction

Average Intelligence Difference of
Quotient Minus Standard Deviations
GRADE r
Average Arithmetic Irrespective of
Quotient Sign (of IQ and Arith. Q)
Nov. June Nov. June Nov. June
III .413 .709 19.25 8.16 6.27 6.63
±.16 ±.08 ±2.87 ±2.05 ±2.04 ±1.45
IV .426 .725 7.41 0.46 2.39 0.47
±.10 ±.06 ±1.84 ±1.50 ±1.29 ±1.02
V .698 .713 16.14 0.54 7.14 2.06
±.07 ±.07 ±1.93 ±1.84 ±1.37 ±1.30
VI 5.33 .805 11.00 3.00 0.19 1.63
±.13 ±.06 ±2.01 ±1.19 ±1.42 ±0.85

VII .740 .795 7.27 0.62 14.03 8.15
±.09 ±.07 ±3.58 ±2.33 ±2.53 ±1.63
VIII .663 .796 11.92 [14] 5.26 [14]
⁠14.93 ⁠8.53
±.11 ±.07 ±2.25 ±2.69 ±1.59 ±1.54
Total .576 .686 14.67 3.72 3.51 1.16
±.05 ±.03 ±0.94 ±0.81 ±0.67 ±0.57

TABLE 10
Summary of Progress in Reading, November, 1918 to June, 1919, by
Increase in r, Decrease in MIQ-MRQ, and Decrease in Difference of
Standard Deviations Irrespective of Sign

Average Intelligence Difference of
Quotient Minus Standard Deviations
GRADE r
Average Reading Irrespective of
Quotient Sign (of IQ and RQ)
Nov. June Nov. June Nov. June
III .541 .492 27.63 11.80 9.75 0.36
±.11 ±.09
IV .665 .845 14.84 -3.00 9.77 7.86
±.08 ±.05
V .799 .832 7.05 -2.00 2.66 5.07
±.05 ±.05
VI .497 .726 6.80 8.70 9.68 3.76
±.16 ±.10
VII .622 .709 2.28 0.07 1.48 5.98
3 of VIII ±.11 ±.09
Total .568 .626 12.67 3.97 3.31 3.18
±.05 ±.04

TABLE 11
Summary of Progress in Reading, November, 1919 to June, 1920, by
Increase in r, Decrease in MIQ-MRQ, and Decrease in Difference of
Standard Deviations Irrespective of Sign

Average Intelligence Difference of
Quotient Minus Standard Deviations
GRADE r
Average Reading Irrespective of
Quotient Sign (of IQ and RQ)
Nov. June Nov. June Nov. June
III .651 .609 14.41 11.57 22.46 8.62
±.11 ±.10 ±5.22 ±2.55 ±3.69 ±1.81
IV .316 .569 12.17 2.43 3.16 0.76
±.11 ±.09 ±2.41 ±1.78 ±1.70 ±1.26
V .773 .891 -0.74 -4.17 2.58 1.77
±.06 ±.03 ±1.72 ±1.20 ±1.22 ±0.85
VI .420 .661 5.79 0.90 0.77 0.87
±.15 ±.09 ±2.33 ±1.53 ±1.65 ±1.09
VII .862 .799 5.54 0.92 11.00 8.31
±.05 ±.07 ±2.88 ±2.54 ±2.03 ±1.80
VIII .775 .722 4.00 4.43 3.94 2.41
±.08 ±.09 ±1.90 ±2.64 ±1.92 ±1.87
Total .529 .609 6.80 2.86 2.12 0.06
±.05 ±.04 ±1.16 ±0.30 ±0.82 ±0.67

The changes in rates of progress are expressed in summaries by subject
matter in Tables 9, 10, and 11. Approach of Arithmetic Quotient to
Intelligence Quotient is measured in Table 9 by:
1. Comparison of r in June with r in November.
2. Comparison of MIQ-MAQ in June and MIQ-MAQ in November.
3. Comparison of S.D.’s of Arithmetic and Intelligence Quotients in June
and November.
The P.E.’s of each of these differences were obtained by
P.E.diff² = P.E.₁² + P.E.₂² - 2 r₁₂ P.E.₁ P.E.₂

The only MIQ-MSQ in Table 9 which does not show a decrease at least
two times as large as the P.E. of either of the elements involved, is the 8th
grade; and this is due to the limits of the test used. As mentioned before, the
8th grade did not register its true abilities in June since a perfect, or nearly
perfect, score in the test was too easy to obtain. The small arithmetic S.D.’s
in Grade 8 and consequent great S.D.IQ-S.D.SQ is due to the same cause.
Tables 10 and 11 present the summary of facts with regard to Thorndike
Reading Quotients, the first and second years respectively.

THE RATIOS

The discussion which follows concerns Ratios, not Quotients.

TABLE 12
Intelligence Quotients and Subject Ratios for All Periods Grouped
by Child. The Order of Entries is Just as in Table 1

Grade III

Intelligence Quotient Arithmetic Ratio Vocabulary Ratio Reading Ratio Completion Ratio
a
b
101
c 63 57 43
d 105 87 92

a
b
128
c 62 80 63
d 119 97 120

a
b
116
c 48 78 * 42
d 81 82 66 77

a
b
87
c 103 46 40 62
d 83 85 70 60

a
b
112
c 80 122 119 100
d 100 101 108 117

a
b
101
c 84 93 37 55
d 90 110 98 92

a
b
90
c 76 58 72 89
d 68 121 77 102

a
b
105
c 60 43 * 57
d 104 95 83 66
The remainder of this table is filed in Teachers College Library, Columbia University.

TABLE 13

Nov., 1918 June, 1919 Nov., 1919 June, 1920
Means
Arithmetic Ratio 89.02 97.16
±1.05 ±1.07
Vocabulary Ratio 98.96 111.44 106.20 107.61
±1.48 ±1.61 ±0.90 ±0.93

Reading Ratio 96.47 101.96 98.98 100.60
±1.19 ±1.18 ±1.03 ±0.97
Completion Ratio 99.76 101.83 101.67 103.10
±1.11 ±1.23 ±0.93 ±0.85
Standard Deviations
Arithmetic Ratio 12.03 12.53
±0.74 ±0.76
Vocabulary Ratio 15.71 16.58 10.34 10.84
±1.05 ±1.14 ±0.64 ±0.66
Reading Ratio 12.63 12.14 11.82 11.36
±0.84 ±0.84 ±0.73 ±0.69
Completion Ratio 12.34 12.63 10.85 9.90
±0.82 ±0.87 ±0.67 ±0.60
Correlations of Ratios
Arithmetic and Vocabulary .60 .30
±.06 ±.08
Arithmetic and Reading .70 .64
±.04 ±.05
Arithmetic and Completion .48 .61
±.07 ±.05
Vocabulary and Reading .34 .32 .57 .47
±.08 ±.09 ±.06 ±.07
Vocabulary and Completion .45 .36 .53 .54
±.07 ±.08 ±.06 ±.06
Reading and Completion .61 .65 .67 .67
±.06 ±.06 ±.05 ±.05

In Table 12 are presented the Subject Ratios in the same order as the
Quotients appear in Table 1.⁠[15] There plainly is a rapid rise of SQ/IQ from
period to period, excluding all pupils who did not take all tests and
excluding Grade III; which includes all children taking all tests who were in
school in June, 1920, and were Grade IV and above in November, 1918.
The average AccR is 98.24 in November, 1918, and 102.78 in June, 1920.
The average IQ for these children is 105.22. The S.DAccR₁₉₁₈ is 11.17; the
S.D.AccR₁₉₂₀ is 9.09; the S.D.IQ is 19.24. It is obvious that the average

amount of product per intelligence has increased, that the range of AccR’s
has decreased (which means that factors causing disparities, other than
intelligence, have been removed), and that the S.D. of the AccR’s is about
one half the S.D. of the IQ’s. M’s are about equal so it is not necessary to
use coefficients of variability. The variability of children, intelligence aside,
is only one half what the variability is otherwise. The correlations when IQ
= X, AccR₁₉₁₈ = Y and AccR₁₉₂₀ = S and when AccR = average of
Vocabulary, Reading and Completion Ratios, are:⁠[16]

rX.Y. = -.602
rX.S. = -.493
rY.S. = +.549

The remaining disparity is then due to something which is in negative
correlation with intelligence.
The number of cases here is only 48.
The P.E.’s are then as follows:

P.E.M P.E.S.D.
X 1.91 1.35
Y 1.11 0.79
S 0.90 0.64
P.E.rX.Y. = .06
P.E.rX.S. = .08
P.E.rY.S. = .07

The differences between the M’s and between the S.D.’s of our 1918 and
our 1920 AccQ’s; namely, 102.78 - 98.24 = 4.54 and 11.17 - 9.09 = 2.08,
have formed a step in the argument. We must have the P.E.’s of these
amounts in order to establish the reliability of the quantitative indices we
employ:
P.E.diff = √P.E.X² + P.E.Y² - 2 rXY P.E.X P.E.Y
P.E.M₂₀-M₁₈ = 0.94

P.E.S.D.₁₈-S.D.₂₀ = 0.47

These differences are then reliable. If the same data were accumulated
again in the same way with only 48 cases, the chances are even that the 4.54
would be between 3.50 and 5.48 and the 2.08 between 1.61 and 2.55. That
there would be positive differences is practically certain, since the
difference between the means is over four times as large as its P.E., and the
difference between the S.D.’s over four times as large as its P.E.
To make still more certain this observation of positive amount in M of
second testing minus M of first testing and in S.D. of first testing minus
S.D. of second testing (AccR), which means an increase in central tendency
of AccR’s and a decrease in spread of AccR’s under special treatment, we
have listed in Table 13 the means and standard deviations of Subject Ratios
of each test for each period and the intercorrelations of these Subject Ratios.
These do not include exactly the same children in each period but are
inclusive of all grades for all periods. They are a measurement of increased
efficiency of the school as a whole, rather than of any one group of
children; though, of course, the bulk of the children have representation in
each of these indices. Too much continuity is not to be expected from June,
1919, to November, 1919, as the children are different. Comparison should
always be from November to June.
These tables bear out the fact presented by AccR. It is clear that there is a
marked development in the S.R.’s, both by increase of M. and decrease of
S.D. The decrease of correlation between S.R.’s is not so marked, but
neither is the negative correlation between AccR and IQ much less in June,
1920, than in November, 1918. The association of achievements in terms of
intelligence is very probably due to mistreatment, since it is in negative
correlation with IQ, as a general inherited ethical factor could not be.
We will note that the Arithmetic Ratios are in as high positive association
with the Reading Ratios as the Vocabulary Ratios are with the Reading

Ratios. This makes it highly improbable that the intercorrelation of these
remnants is due, to any large extent, to common elements in the test or to
specific abilities. The common interassociation of all Ratios seems to point
to the operation of some common factor other than intelligence as a
determinant of disparity in school progress. It would be easy to identify this
as the part of Burt’s “General Educational Factor” which is not intelligence
—that is, industry, general perseverance and initiative—were it not for the
fact that this same influence stands in negative association to intelligence.
It is our belief that it is the influence of a maladjusted system of curricula
and methods which accounts for these rather high interassociations of
achievements, irrespective of intelligence.

SUMMARY

The association of abilities in arithmetic, reading, and completion with
intelligence is markedly raised by special treatment. Disparities of
educational product are therefore to a great extent due to intelligence.
(Tables 2, 3, 5, 7, 8, 9, 10 and 11.)
The remnants (intelligence being rendered constant by division of each
SQ by IQ) intercorrelate about .5. If there were specialized inherited
abilities, these intercorrelations would not all be positive nor would they be
as uniform. (Tables 6 and 13.)
The averages of these remnants, for reading, vocabulary, and completion,
correlate -.61 in 1918 and -.49 in 1920 with IQ. These remnants are in
negative association to intelligence. If the intercorrelations of these
remnants were due to a “General Factor,” this correlation would not be
negative.
Therefore intelligence is far and away the most important determinant of
individual differences in product.
As part of the relation between tests, irrespective of intelligence, is due to
common elements in the tests, this reasoning becomes still more probable.
General factor in education, as distinct from intelligence, has not been
separated here from inherited bases of ambition, concentration, and
industry. It seems out of our province to conjure up some inherited complex
of abilities other than intelligence, specialized inherited abilities, or

proclivities and interests tending to thorough prosecution of school work. I
have therefore meant this last by the general factor.
McCall has correlations varying continually in size from -.63 to +.98
between various measurements of a group of 6B children.⁠[17] The abilities
involved were not pushed as are those considered here. Some of the low
correlations are no doubt indications of low association because of the way
children are, not the way they might be by heritage; still others, such as
handwriting and cancellation (unless bright children do badly in
cancellation tests because they are more bored than the others), are
correlated low or negatively with intelligence when the correlation is at its
maximum. Such results as those of McCall serve as a guide not to argue
about other tests by analogy. It is necessary to find which traits and abilities
can be pushed to unity in their relation to intelligence and which, like
handwriting, are practically unrelated to general mental power.
It is well to know about music tests and such tests as Stenquist’s
mechanical ability test when the correlation with intelligence is pushed,
before we decide whether the quality measured is a manifestation of
specific talent or general intelligence.
Cyril Burt obtained data much like that presented here except that instead
of getting rid of the influence of intelligence and finding determinants for
the remnants of disparity, he built up a hierarchy of coefficients as they
would be if they were due entirely to a common factor and compared these
with his obtained r’s. I will present his conclusions with regard to a general
factor which are in substantial though not complete agreement with those
advanced here.

“Evidence of a Single Common Factor.
“The correlations thus established between the several school
subjects may legitimately be attributed to the presence of common
factors. Thus, the fact that the test of Arithmetic (Problems)
correlates highly with the test of Arithmetic (Rules) is most
naturally explained by assuming that the same ability is common to
both subjects; similarly, the correlation of Composition with
Arithmetic (Problems) may be regarded as evidence of a common
factor underlying this second pair; and so with each of the seventy-

eight pairs. But is the common factor one and the same in each
case? Or have we to recognise a multiplicity of common factors,
each limited to small groups of school subjects?
“To answer this question a simple criterion may be devised. It is a
matter of simple arithmetic to reconstruct a table of seventy-eight
coefficients so calculated that all the correlations are due to one
factor and one only, common to all subjects, but shared by each in
different degrees. Such a theoretical construction is given in Table
XIX. In this table theoretical values have been calculated so as to
give the best possible fit to the values actually obtained in the
investigation, and printed in Table XVIII. It will be seen that the
theoretical coefficients exhibit a very characteristic arrangement.
The values diminish progressively from above downwards and from
right to left. Such an arrangement is termed a ‘hierarchy.’ Its
presence forms a rough and useful criterion of the presence of a
single general factor.
“On turning to the values originally obtained (Table XVIII.) it
will be seen that they do, to some extent, conform to this criterion.
In certain cases, however, the correlations are far too high—for
instance, those between Arithmetic (Rules) and Arithmetic
(Problems), and again Drawing and both Handwork and Writing
(Quality). Now these instances are precisely those where we might
anticipate special factors—general arithmetical ability, general
manual dexterity—operating over and above the universal factor
common to all subjects. These apparent exceptions, therefore, are
not inconsistent with the general rule. Since, then, the chief
deviations from the hierarchical arrangement occur precisely where,
on other grounds, we should expect them to occur, we may
accordingly conclude that performances in all the subjects tested
appear to be determined in varying degrees by a single common
factor.
“Nature of the Common Factor.
“What, then, is this common factor? The most obvious
suggestions are that it is either (1) General Educational Ability or
(2) General Intelligence. For both these qualities, marks have been

allotted by teachers, quite independently of the results of the tests.
The correlations of these marks with performances in the tests are
given in the last two lines of Table XVIII.
“Upon certain assumptions, the correlation of each test with the
Hypothetical Common Factor can readily be deduced from the
coefficients originally observed. These estimates are given in the
last line but two of the table. They agree more closely with the
observed correlations for General Educational Ability, especially if
the latter are first corrected for unreliability. (Correlations:
Hypothetical General Factor coefficients and General Educational
Ability coefficients .86; after correction .84. Hypothetical General
Factor coefficients and General Intelligence coefficients .84; after
correction .77.) We may, therefore, identify this hypothetical general
factor with General Educational Ability, and conclude provisionally
that this capacity more or less determines prowess in all school
subjects.
“The high agreement of the estimated coefficients with the
intelligence correlations suggest that General Intelligence is an
important, though not the only factor in General Educational Ability.
Other important factors are probably long-distance memory, interest
and industry. It is doubtless not a pure intellectual capacity; and,
though single, is not simple, but complex.”⁠[18]

PART III
THE PSYCHOLOGICAL CONCLUSIONS OF
THE EXPERIMENT
THE NEGLECT OF GENIUS

Schools of to-day are organized and administered so as to yield less
chance to a child to obtain as much information as is possible for him to
have in direct proportion to his mental ability. The correlation between
accomplishment and intelligence (using AccR, the average of Reading,
Vocabulary, and Completion Ratios with IQ) was -.61 in November, 1918,
and -.49 in June, 1920, in the Garden City public school. The regrading and
special promotion work from November, 1918, to June, 1920, reduced the
handicap of brightness, but could not obliterate the sparsity of returns per
increment of capacity in the upper reaches of the intelligence. Further, work
along this same line done by A. J. Hamilton in the Washington School,
Berkeley, California, indicates that this was not a peculiarity of the school
at Garden City.
The wide range of abilities which we know exists in pupils of any one
age makes it impossible to adjust our formal education to the extremes.
Much adjustment has been made in favor of the lower extreme, but little has
been done for our genius. Of course the work with extreme subnormals is
conceived and prosecuted more in the sense of clearing them away for the
good of those remaining than of fitting education to their own needs. We are
neglecting, however, our duty to those whom nature has endowed with the
essentials of leadership. They do not interfere quite as much with ordinary
classroom procedure, but they are greater social assets and need special
treatment to develop them rather than to let others develop better.
Neither of the extreme groups is certain of getting the normal stamina
necessary for good citizenship. Neither group forms good habits of study
nor accumulates such information as it might. Being aware of this
discrepancy between the gift and the recipient, we have made our lessons

easier and we have segregated the lower percentile. There is much more to
be done. We must adapt education to at least five varying classes in order to
reduce the spread within each to a commodious span. But the genius is the
most important and should have the greatest claim to our immediate
attention.
First, our social needs demand special attention for the genius in order
that we may better exploit our best nervous resources. Second, our
educational needs demand it since the very bright as well as the very stupid
disrupt calm and cogent classroom procedure. Third, they themselves
demand it in order that they may, even when they do function as leaders, be
happier in that function, since now they often lose much in social contact by
peculiarities which prevent an integration of their “drives” into a
harmonious economy of tendency. These peculiarities come from their
continuous maladjustment, since when they are with children of their own
mental maturity they are physically and physiologically handicapped; when
they are with children of their own size and muscular equipment they are so
far mentally superior that they are unhappily adjusted. Only classification
on a large scale will allow sufficient numbers of them to congregate to
correct this.
I am reminded of a boy ten years old whose IQ on the Terman test was
172. He defined a nerve as the “conduction center of sensation” and, when
asked to explain, did so in terms of sensation of heat and motive to
withdraw. He explained the difference between misery and poverty thus:
“Misery is a lack of the things we want; poverty is a lack of the things we
need.” How can we expect a boy like this to grow into a normal citizen if
we do not provide the companionship of peers in mentality and in
physique?
Fourth, our eugenic needs demand it, since we are not conserving this,
our chiefest asset, genius. Unless we conserve better these rare products, the
standard deviation of the intelligence of humanity will keep shrinking as we
select against imbeciles and against genius as well. The waste of a genius
who becomes an intellectual dilettante, as many now in fact do, is double.
We lose what he might do for society; he does not marry and we lose the
potentiality of his highly endowed germ-plasm.

And they do become dilettantes when special treatment is not given. I
know of a young man who was first of his high-school class, who got all A’s
his first year in College (at Wisconsin), and all A’s his second year (at
Harvard); and then he began to read all manner of literature with no schema
of expression, no vocation, because, as he said, all college courses are so
stupidly easy. He attended no lectures and read none of the books in one
course, and then two days before the examination he was taunted with not
being able to pass this course. He spent two nights and two days studying,
and he received B in the course. But now he is a failure because he has no
organized, purposive schema of expression; he was always in classes with
people less fortunately endowed than he, and so he never had a chance.
On these four counts then we must segregate our genius: (1) Social
exploitation of our resources. (2) Educational procedure for the sake of
other children as well as for them. (3) Happiness for them, organization of
their trends, and formation of social habits. (4) Biologic conservation of
great positive deviation from average human intelligence.

IS GENIUS SPECIALIZED?

This genius is of various kinds, political and business leaders, scientists
and artists. Have they then the same inherited nervous structure with regard
to abilities and capacities as distinct from interests? We know that they must
have something in common, something that we call intelligence, power of
adaptation. Calling this the nervous chemistry, the way the nervous system
acts its quality, we must still know whether we have also an inherited
nervous physics to deal with, or a further inherited nervous chemistry which
predisposes to specific ability. Are there inherited capacities or
predispositions to ability? We are in a position to answer this question with
regard to the elementary school subjects, and are tempted here into a more
general discussion of the matter in hand.
The need to clarify our view on what is inherited and what is due to
environment can be clearly envisaged in terms of our teachers. Whatever
psychologists may mean by “predisposition to ability” it is quite certain that
teachers make no distinction between this and the inheritance of a capacity.
They feel that some children figure better than they read, and others read
better than they figure, “by nature,” and there their obligation ends. If it is a

grave matter that we shoulder the burden of bringing a child to his optimum
achievement, then it is an immediate duty that we find how much of the
failure to produce product of one kind or another is due to unremovable
factors, and how much is due to our inadequacy. So, too, we have much
loose discussion about finding out what children can do and want to do in
the way of vocational diagnosis,—loose because it assumes that children
are born with definite vocational capacities. Certainly we can do much
more in the way of development and much more in the way of preparation
for social needs if we know just how much “predisposition to ability”
means. The teacher interprets it to mean about what was meant by the turtle
that held up Atlas who held up the world. She makes no real distinction
between predisposition to ability and specific ability, just as there was no
real causal distinction between the turtle and Atlas. She then gets at her
conception of intelligence additively,—a summation of school abilities.
The correlation of teachers’ judgment of “power of adaptation,” carefully
explained, and marks given six months previously by the same teachers was
.82. The correlation of this same average judgment with the average of
thirteen intelligence tests was only .58. These teachers obviously reached
their conclusions of the intelligence of a child in the same way as they
reached their conclusions of what marks he earned in their subjects.
The unit characteristics which make up what we describe in terms of
gross behavior as intelligence must of course be many. No one denies that if
we knew just what these units were we could describe two possible
manifestations of what we now call intelligence, of which one person could
do one only and another person could do the other only because of the
particular combinations of the units inherited. This would constitute
inheritance of predisposition to special capacities. But it is not the same to
assume that the vocations and aptitudes desirable in a world such as ours
have specialized inherited bases. It is far more probable that substantially
the same inherited characteristics are necessary to success in all the gross
cross-sections of behavior which we call vocations and abilities.
As the unit characteristics are certainly not so closely allied to our social
needs as “mechanical intelligence” and “social intelligence” or even “rote
memory for numbers,” we may not even distinguish presence of any five
hundred elements from presence of any other five hundred elements in
terms of what we now measure as intelligence. It is just as likely that all the

elements of intelligence are necessary for every vocation and that all
contribute to success of any one kind as it is likely that some are necessary
for one vocation and others for another.
This is a question of more or less. I believe that the amount to which a
person’s specific talents, his vocation as distinct from his general power, are
shaped by the combinations of elements which make up his inheritance, is
much less than believed by Francis Galton, who says: “There cannot then
remain a doubt but that the peculiar type of ability that is necessary to a
judge is often transmitted by descent.” And again: “In other words, the
combination of high intellectual gifts, tact in dealing with men, power of
expression in debate, and ability to endure exceedingly hard work, is
hereditary.”⁠[19]
I believe that the amount of influence which inheritance has upon the
kind of thing a man does in life has been overestimated; that the inherited
factors influence more the way in which he shall do whatever the
environment influences him to do. This leaves plenty of play for the close
correlation between parents and children in both intelligence and vocation.
The former is the result of inheritance, the latter is the result of
environment. All competent psychologists would agree to-day to less
specific inheritance than a basis, for instance, for the distinction in vocation
of minister and orator; and more specific inheritance than for such a
statement as “We inherit how well we will do, we learn what we will do.”
There would be substantial agreement to the statement that the inherited
nervous bases of a very intelligent plumber are more like those of a very
intelligent statesman than like those of a stupid plumber. This question is,
how much inheritance we can conceive of as being made up of neuro-
chemical elements determining us to do one kind of a thing rather than
another.
Interpretation statistically of one thousand possible elements, simply
viewed as present or absent, and again simply viewed only as combinations
and not permutations, would mean that the less the intelligence the more
specific the inheritance. The most intelligent man alive could, by what he is
born with, do anything since he has all of the one thousand factors, all of
which help him in the prosecution of any venture. But the fewer elements
he has the less well he does most things, and when lacking certain elements
he has lost the capacity to do some things more completely than others. (I

have neglected physiological characteristics necessary to an ability. A deaf
man certainly is handicapped in music. I speak of possible mental
capacities.) Such a view leaves scope for some degree of special abilities. It
accounts for the idiot-savants, it accounts for the cases where genius is
diverse as well as where it is not though it would demand that specialized
genius be very rare and that inherited specialization be much rarer in the
upper than in the lower reaches of intelligence. It allows for such cases as
Galileo, whose father was a composer, as well as the cases cited by Galton.
Heredity need not imply the same kind of genius though it does suggest it,
whereas the environment backs up this inherited implication. We further can
here absolutely resent an inheritance of such things as ability in the
common school subjects without being involved in a view to deny the
inheritance of a predisposition to mechanical rather than musical successes.
Observation of brilliant children would corroborate this view. They can
do anything. Observation of the mentally deficient is equally encouraging to
this view. It has always been puzzling that they seem to do a few things
much better than others. According to this conception there would be a
negative correlation between intelligence and specialized inheritance.
We will then consider each inherited element, not as music or as science,
but rather as an element of intelligence which will help in all lines of work,
but which may be a little more necessary for some than others. This is a
predisposition in a true sense. If a man had only one element out of one
thousand, he could do only a few things. If he had all thousand he could do
everything. Inheritance of ability is not in terms of units valuable to us
socially, but only in terms of undefined nervous elements; and we may
conceive of specialization, and still hold that there be less, the more
intelligent a man is.
To make the matter still more concrete, imagine two men each of whom
have 900 of the hypothetical 1000 elements, this being a value of +3 S.D.
from the mean intelligence of the human race. One is a composer, the other
financier. According to this view the greatest number of their inherited
bases on which they could differ would be 100 of the 900 elements. The
other 800 must be alike. Assuming that all of the elements contribute to all
of the activities, but that some of them are more essential to some activities
than to others, we could in this case say that the 100 which are different
decided in some measure the vocation of each man. But it is much more

probable that they overlap in 850 and that each has only 50 distinct
elements, and further that the 50 which are distinct in each would not all be
such as to influence one kind of ability rather than another. Then these two
men, had they interchanged environments, would probably have
interchanged vocations in that transaction. For the purposes of this
discussion we treat physiological inherited features (such as hearing), as
environment, as we are considering the mental capacity of composer as
distinct from the necessary conditions to its development. According to this
view, then, we account easily for the versatility of genius, which is so
apparent in such accounts as Terman’s The Intelligence of School
Children.⁠[20] Also, though very infrequent, we account for the genius who
could not have done other things as well as those he did.
Let us consider the case of negative deviates, say 3 S.D. from the mean
intelligence of the human race. Two men each have 100 of the 1000
hypothetical elements. It is much more probable here than not, that an
appreciable amount of the 100 elements would be distinct in each person,
though it is improbable that they would often be such as to form the basis of
an “ability.” This then would account for specific abilities amongst morons
and also for the presence but rarety of idiot-savants. Also since there are a
limited number of such combinations possible and since many overlap for
all practical purposes, we would account for the common likenesses as well
as the relatively more uncommon extreme differences. This view is
consistent with an examination of the data of this thesis which are contrary
to the common belief in special abilities or to a view of inheritance of units
which are actually the goals of education and the uses of a civilization too
recent to leave its imprint on inheritance. We found no unremovable
predispositions to one school subject more than to the others in any of the
children. We would thus argue that such predispositions as to mathematics
or to oratory are extremely rare and cannot be used as rules by which to
interpret human nature.
Woodworth says in a criticism of McDougall’s view of instincts: “What
he here overlooks is the fact of native capacities or rather, the fact that each
native capacity is at the same time a drive towards the sort of activity in
question. The native capacity for mathematics is, at the same time, an
interest in things mathematical and in dealing with such things. This is
clearly true in individuals gifted with a great capacity for mathematics.”⁠[21]

I do not wish to become involved here in a discussion of the original
nature of man on the instinctive side. I wish merely to rebel at the
assumption of specific inheritance of abilities that are really sociological
units. Mathematics is an ability which is useful to us, which we have come
to encourage in education. But it is a man-made unit. There is no reason to
believe that the inherited components of mentality are in any direct way
related to such talents as mathematics or music. The units may vaguely
predispose, but the units are not mathematics and music. We may say that
the inherited physical and chemical units of the nervous system may be so
distributed as to predispose one man to mathematics, and another to music,
but we must not argue for inherited interests as correlates. The evidence is
all that the inherited nervous chemistry of the individual is what on the side
of behavior, we define as intelligence—power of adaptation. We may
logically fall back on the inheritance of predisposition to ability, meaning
thereby the inheritance of such nervous qualities as will better fit the
individual to cope with mathematical than with musical situations; but if we
adopt this cautious ground in disputation we cannot argue in another matter
for an inherited interest in mathematics, innate because of the inborn
mathematical talent. If the inherited qualities merely predispose they merely
delimit; just as a man born without arms would probably not become a great
baseball player, nor a deaf man a great musician, nor a man with poor motor
control a skilled mechanic—so we are predisposed nervously for capacities.
Hence can we argue that the inborn root of the interest is the capacity? Is it
not safer to assume that interests in success, approval of fellowmen and
general mental activity led to the development of the capacity by virtue of a
favorable environment, and led by the same environment to interests
centered about its activity?
It is far from my intention to say that inheritance is not as specific
nervously as it is in matters of blood pressure and texture of skin. As we, in
our limited knowledge, still define abilities in terms of behaviour and not by
nervous elements, my contention is that intelligence should be regarded as
the sum total of this inheritance, much as general strength is, in terms of the
body. We have still to find the component units of this intelligence. We can
then define predisposition to ability. To split intelligence into inherited units
of mathematics, reading, composition, mechanics, etc., is as unjustifiable as
to split inherited vigor of body into baseball capacity, running capacity,
climbing capacity, etc. Mathematics and music are what we do with

intelligence, not what intelligence is made of. Of course everyone agrees to
this. The lack of emphasis upon the chance that the inherited units are
general in their application, that the same inherited elements are involved in
many of the behavior complexes which we call traits and abilities, is what
confuses the situation.

CURRENT PSYCHOLOGICAL OPINION

We must know what these elements are, and how many contribute to
which capacities. Then we can decide the question of specialized
inheritance. In all crude behavior data it is impossible to separate the
influence of nature and nurture. A theory of specialized inheritance will
inevitably infringe upon common sense in its claims. Of the following
statements, it would be easier for most of us to endorse 1 and 2 than 3 and
4, whereas few would agree with 5 and 6.
1. “Unless one is a blind devotee to the irrepressibility and
unmodifiability of original nature, one cannot be contented with the
hypothesis that a boy’s conscientiousness or self-consciousness is
absolutely uninfluenced by the family training given to him. Of intelligence
in the sense of ability to get knowledge rather than amount of knowledge
got, this might be maintained. But to prove that conscientiousness is
irrespective of training is to prove too much.” (Thorndike, Educational
Psychology, III, pp. 242.)
2. “Some attempts have been made to apply these laws to behavior
complexes, but as yet psychology has provided little foundation for such
studies. The most thorough-going attempts have been made with human
mental traits and some evidence has been collected here in favor of the view
that differences in the instinctive behavior of individuals are inherited
according to Mendelian ratios. But in the field of human psychology too
little is known of the genesis of character, of the distinction between nature
and acquired behaviour to provide a very firm foundation for the work of
the geneticist.” (Watson, Behaviour, p. 156. Italics are mine.)
3. “Even, however, when we omit the trades as well as the cases in which
the fathers were artists, we find a very notable predominance of craftsmen
in the parentage of painters, to such an extent indeed that while craftsmen
only constitute 9.2 per cent among the fathers of our eminent persons

generally, they constitute nearly 35 per cent among the fathers of the
painters and sculptors. It is difficult to avoid the conclusion that there is a
real connection between the father’s aptitude for craftsmanship and the
son’s aptitude for art.
“To suppose that environment adequately accounts for this relationship is
an inadmissible theory. The association between the craft of builder,
carpenter, tanner, jeweller, watchmaker, wood-carver, rope-maker, etc., and
the painter’s art is small at the best and in the most cases non-existent.”
(Ellis, quoted in Thorndike, Educational Psychology, III, p. 257.)
4. “—the statesman’s type of ability is largely transmitted or inherited. It
would be tedious to count the instances in favor. Those to the contrary are
Disraeli, Sir P. Francis (who was hardly a statesman, but rather bitter a
controversialist) and Horner. In all the other 35 or 36 cases in my Appendix,
one or more statesmen will be found among their eminent relations. In other
words, the combination of high intellectual gifts, tact in dealing with men,
power of expression in debate and ability to endure exceedingly hard work,
is hereditary.” (Galton, Hereditary Genius, pp. 103, 104.)
Thorndike comments on this last quotation: “Of course there is, in the
case of all of Galton’s facts the possibility that home surroundings decided
the special direction which genius took, that really original nature is
organized only along broad lines. Moreover, it is difficult to see just what in
the nervous system could correspond to a specialized original capacity, say,
to be a judge. Still the latter matter is a question of fact, and of the former
issue Galton’s studies make him the best judge. We should note also that it
is precisely in the traits the least amenable to environmental influence such
as musical ability, that the specialization of family resemblance is most
marked.”
This cautious and sagacious commentary is in marked contrast to the
following:
5. “But no training and no external influence can entirely supersede the
inborn tendencies. They are the product of inheritance. Not only unusual
talents like musical or mathematical or linguistic powers can be traced
through family histories, but the subtlest shades of temperament, character
and intelligence can often be recognized as an ancestral gift.” (Munsterberg:
Psychology, General and Applied, p. 230.)

6. “Statistical studies which covered many characteristic opposites like
industrious and lazy, emotional and cool, resolute and undecided, gay and
depressed, fickle and constant, cautious and reckless, brilliant and stupid,
independent and imitative, loquacious and silent, greedy and lavish, egoistic
and altruistic and so on, have indicated clearly the influence of inheritance
on every such mental trait.” (Munsterberg, Psychology, General and
Applied, p. 237.)
Undoubtedly Munsterberg here refers to the data accumulated by
Heymans and Wiersma since they used such opposites as these, and also
used what might be called statistical methods. Speaking of the same data
Thorndike says:
“In view of the insecurity of their original data it seems best not to enter
upon an explanation of their somewhat awkward method of measuring the
force of heredity, and not to repeat the figures which are got by this method.
Also they do not attempt to estimate an allowance for the influence of
similarity in home training, though they state that some such allowance
must be made.” (Educational Psychology, III, p. 262.)
Hollingworth and Poffenberger, commenting on the data of Galton and
Ellis mentioned in the quotation above, say:
“Francis Galton has made a statistical study of the inheritance of
specified mental abilities and found that the abilities required for success as
a judge, statesman, minister, commander, poet, artist, and scientific man,
are inherited. But the nature of his data makes him unable to make exact
allowances for influences of training and environmental influences.
Consequently, his figures might really show general intelligence to be
inherited and the form of its expression to be dependent upon environment.
“Other investigators, among them F. A. Woods and Havelock Ellis, have
made similar statistical studies and conclude that there is inheritance of
even such qualities as temper, common sense, and the like, but these reports
are also subject to the same complicating influence of environment.”
(Applied Psychology, p. 43.)
It can readily be seen, from these quotations, that there is fundamental
disagreement among psychologists with regard to the inheritance of specific
ability,—fundamental disagreement in three ways: (1) Interpretation of

Galton’s and Ellis’s data. (2) Opinion on the matter. (3) Degree of precision
possible in giving judgment.
We have noted that it is very difficult to understand what the neural bases
for such special abilities as Galton speaks of could be; that they are social,
not neural or psychological units. A view of a large number of inherited
elements all of which contribute to what we call general intelligence and
each of which is slightly more necessary to some vocation than others,
would account for all the observed facts, is neurally imaginable, and does
not need to view ability to be a “judge” or “artistic talents” as biological
entities. It further explains the differences in their limited abilities of
mentally deficient children.
Burt says in this connection: “Among children of special (M.D.) schools,
the evidence for a general factor underlying educational abilities and
disabilities of every kind is not so clear. In administrative practice, ‘mental
deficiency’ implies among different children deficiencies in very different
capacities, both general and specific.” (Cyril Burt: The Distribution and
Relation of Educational Abilities, p. 83.)
For these reasons it is justifiable to attempt to present evidence of the
inheritance of school abilities with a view to showing that school abilities
are not dependent upon special inherited aptitudes, as teachers so often
assume, but that general intelligence is the only inherited cause of disparity
in product. Investigations where the correlation between educational
product and intelligence, irrespective of chronological age, was less than
around .75, used data where many removable causes were not removed, and
consequently measured results of the environment as well as heredity. A
case such as this follows:
“The influence of inheritance upon a very specific mental quality, namely,
spelling ability, has been tested experimentally, although here there is some
difficulty in separating the influence of heredity from that of environment.
Earle studied the spelling ability of 180 pairs of brothers and sisters who
had uniform school training and found a correlation of .50. This means that
if one child deviated by a certain amount from the average child in spelling
ability, his brother or sister would deviate from the average child just half as
much; that is, he would resemble his brother or sister to that extent.”
(Hollingworth and Poffenberger: Applied Psychology, p. 44.)

The data presented in this thesis indicate that that correlation could have
been pushed as high as the r between the intelligence of the pairs of
brothers. In other words, a child could be made to resemble his brother as
nearly in spelling ability as he did in intelligence. All disparity could be
reduced to that of general intelligence. Then intelligence alone is inherited
as far as the data here presented have any bearing on the matter in hand.
The influence of environment is in this case a matter of no consequence,
since the subjects all had the same schooling, and home influence does not
as a rule teach children to spell; but the data are not irrespective of the
influence of intelligence.

INDICATIONS OF THE GARDEN CITY DATA

Table 3 presents intercorrelations between IQ and quotients in the various
subjects. The correlations are in each instance irrespective of chronological
age since all quantitative indices are expressed as quotients. We have seen
that they go up from September, 1918, to June, 1920. Every possible means
was used to push these correlations to their limit, to remove all removable
factors. We have seen that the data show here, as in Tables 7 and 8, that
there is little association between traits which is not a result of differences
in intelligence. Table 3 shows the same 48 children throughout. The r’s are
not corrected for attenuation. Though the r’s are high throughout and go
higher under special treatment, the association can still be more accurately
registered by some attention to relation of the means and the S.D.’s. Two
traits to be identical must have r = 1.00 S.D.x = S.D.y and Mx = My. We
have seen that the r increases, M-M decreases and S.D.-S.D. regardless of
sign decreases. (Tables 9, 10 and 11.)
But as the S.D.’s of the Subject Quotients (though they do approach S.D.
of IQ) sometimes go below the S.D. of IQ, we must know why. It is because
the low IQ’s do better per their intelligence than the high IQ’s. We have
seen above that the correlation between IQ and average of the Vocabulary,
Reading, and Completion Subject Ratios is -.61 in November, 1918, and
-.49 in June, 1920.
Then the ratio of achievement to intelligence is in definite relation to
intelligence—a negative relation. It is this same tendency to adapt our
education to a low level which has prevented a perfect association between

intelligence and the various subjects. The relation of one subject to another,
irrespective of intelligence, would be zero if there were no other factors
except intelligence responsible for the product. After two years of such
attempts as an ordinary public school will allow, we have removed many of
the causes of disparity and increased the association between potential
progress and progress in arithmetic, reading and language. The correlations,
correspondence of S.D.’s, and Σ(IQ-EQ)/n registered in Tables 9, 10, and 11
give evidence of this as does also the increase in the AccR, an average of
the Arithmetic, Reading, Vocabulary and Completion Ratios. (Table 13.)
Are the unremoved causes other than intelligence unremovable? These
causes might be, besides the unreliability of tests and the common elements
in the tests, the specialized inheritance we have considered, ethical qualities
of endurance, ambition, initiative and industry or a general factor. The
correlations between Arithmetic Ratios and Reading Ratios and the other
intercorrelations of Subject Ratios will yield us an index of how much of
this remaining disparity is due to specialized inheritance. These
intercorrelations for all years are embodied in Table 13. The partial
correlations of quotients when intelligence is rendered constant will be
found in Table 6. These intercorrelations, and the partials as well, give an
indication of some general factor other than intelligence since the r’s
irrespective of intelligence are uniform and all are positive. Only the
correlation of arithmetic with vocabulary, intelligence being rendered
constant, goes to zero. Though this might be due in part to common
elements in the tests, it is more likely that there is another factor in
operation. Inheritance of specific abilities could not have this uniform effect
on the correlations.
These correlations all being positive and the r’s being very uniform, both
correlation of ratios and the partials, makes the interpretation of specialized
inheritance of ability extremely unlikely. The correlation of Arithmetic
Ratios with Reading Ratios is higher in 1920 than that of Vocabulary Ratios
with Reading Ratios. It leaves the possibility that the unremoved factors are
inherited ethical differences or that they are a “general educational factor.”
The negative correlation of AccR with intelligence, however, being as high
as these positive remnants of interrelation, would tend to make more
probable an interpretation of this as a remnant of disparity, intelligence
accounted for, which is entirely due to the organization of our schools.

All disparity not due to intelligence was worked on as far as it was
possible. Thereupon the association of intelligence and educational product
increased markedly and the negative association of intelligence with
achievement in terms of intelligence decreased somewhat. However, some
association of abilities not due to intelligence remains. Exactly as much
negative association of achievement in terms of intelligence, with
intelligence, remains. So, when some of the disparities due to the
environment have been removed and therefore the correlation of Arithmetic
Ratio with Vocabulary Ratio and Reading Ratio has been decreased, the
causes which contributed to a correlation such as lack of interest having
been removed, there still remains some relation of school qualities. But
there also still remains a negative association between this accomplishment
and intelligence which means that we still have a remnant of such
removable influence as is due to badly adjusted curricula.
This enables us to interpret our partials. The partials are not nearer zero
because although we have partialed out the effect of intelligence, we have
not partialed out the factor which controls the negative relation to
intelligence of these very partial resultants, since that is the effect of the
methods and curricula. Though we did advance bright pupils and give them
more chance, we have not given them a chance proportionate to the stupid
children. And that is true since we often wanted to advance pupils and were
not allowed to; whereas we were never allowed to demote pupils except in
particular subject matter. The stupid children were always at the frontier of
their intelligence at the educational cost of the others.
It is this remnant which has usually been interpreted as “general factor”
or as inherited factors basic to initiative, ambition, and industry. The fact of
importance is that these remnants, these marks of children independent of
their intelligence, are associated negatively with intelligence to the same
degree that they are associated positively to each other. Unless we wish to
assume that the “general factor” or the inherited bases of initiative and
industry are associated negatively with intelligence we must account for the
remnant in some other way. It seems far more reasonable to attribute this
remaining association to the educational handicaps of intelligence which we
were unable to remove.
The original tendencies of man, as distinct from his original equipment,
have not been considered in this study. If the quantitative differences in

endowment of this kind were added to the denominator of our
accomplishment ratio formula, we would have a better measure and better
results. We share in this investigation a general limitation of educational
psychology—the requisite technique to measure individual differences of
instincts and the ethical traits of which they are the predisposition. Industry,
ambition, and initiative are not inherited units. They are, however, the rules
of an economy of expression and as such are dependent upon individual
differences in strength of instinct.

CONCLUSIONS

1. IQ can be used as a limit of school achievement expressed as SQ.

a Progress in Σ(IQ-SQ)/n may be used as a measure of school
efficiency.
b SQ/IQ may be used as a measure of individual efficiency.

2. Correlations between intelligence and achievement are very different
before and after the abilities are pushed.

a Many r’s are reported where conclusions are drawn as though they
had been pushed. These conclusions should be restated.
b Intelligence and achievement are far more closely associated than
has been assumed to date.

3. Disparity of school product can be reduced to individual differences in
intelligence.

a Little specific inheritance of school abilities.
b Little unremovable difference in industry, conscientiousness and
concentration.
c Intelligence is the only inherited general factor.

4. Negative association between AccR and IQ.

a To-day’s educational procedure involves a handicap to
intelligence.
b The genius has been neglected.

FOOTNOTES
[1] Part of this section is reprinted with revisions from Teachers College
Record, Vol. XXI, No. 5 (November, 1920).
[2] For scientific purposes we want year-month means and standard
deviations, that we may say that Charlie Jones is 2.1 S.D. above the mean for his
age level, while Harold Smith is .1 S.D. below that mean. It is in terms such as
these that we may be able to compare accomplishment in one function with
accomplishment in another, progress in one with progress in another. For many
of our problems we need a common denominator of measurement so that we
may compare progress between tests and age-groups. The best common
denominator is, I believe, S.D. in an age-group. Thus we may locate a child in
any age-group in any test and compare that location with the position of any
other child in any other test in his age-group.
For practical purposes, however, it is for many reasons more convenient to use
quotients in elementary schools. Principals would rather deal with quotients
since it is easier to explain them in terms of attainment and capacity. It is the use
of such quotients that this thesis discusses.
[3] Judd, C. H., “A Look Forward,” in Seventeenth Yearbook, Pt. II, of the
N.S.S.E., 1918.
[4] When the disadvantages of “pushing” children are discussed, the
disadvantages of keeping children at their chronological age levels should be
considered as well. Although it is true that a supernormal child placed in that
grade for which he is mentally equipped loses much in social contact, it is also
true that he loses a great deal by remaining in the grade where he physiologically
belongs. There he develops habits of conceit, indolence, and carelessness. It is in
all cases much better to group intelligent children and enrich the curriculum than
to “push” them; but pushing may be better than leaving them where they belong
by age. It is a possibility worth considering that the explanation of the
“peculiarities” of genius lies in the fact that he has never associated with equals.
When his fellows are mentally his equals they are physically far older and when
they are physically his equals they are mentally inferior.
[5] Whether only the Accomplishment Ratio as a percentage should be given
the parents, or whether they should know both the IQ and all the SQ’s, is a
question on which I am not prepared to give an opinion. I incline to believe that
the parents should know only the final marks and am sure that I advise telling
the children these only.
[6] There will be reported elsewhere a fuller consideration of this aspect of the
technique of derivation of norms, together with a complete presentation of the
data used to obtain the age norms herein used.
[7] “The Accomplishment Quotient,” Teachers College Record, November,
1920.

[8] Or the ratio of the Subject Quotient to the Intelligence Quotient, which is
the same as the ratio of the Subject Age to the Mental Age.
[9] This table is too bulky for complete publication but may be found on file
in Teachers College Library, Columbia University.
[10] The remainder of this table is filed in Teachers College Library,
Columbia University. Decimals are dropped in this table.
[11] Decimals are dropped in this table.
[12] Truman L. Kelley: Statistics, The Macmillan Co.
[13] This correlation was obtained by correlating one half of the Binet against
the other one half and then using Brown’s Formula to determine the correlation
of a whole Binet against another whole Binet.
[14] These quantities do not decrease because a perfect score on the arithmetic
test was too easy to obtain at this time. The children had reached the limits of
this test.
[15] Table 12 is too bulky for complete publication. The first page is
reproduced here and the complete table is filed at the library, Teachers College,
Columbia University.
[16] No arithmetic was given in 1918, therefore arithmetic was not used in
these averages.
[17] William Anderson McCall: Correlations of Some Psychological and
Educational Measurements, Teachers College Contributions to Education, No.
79.
[18] Cyril Burt: The Distribution and Relations of Educational Abilities, pp.
53-56.
[19] Quotations from Galton: Hereditary Genius, ’92, pp. 61-62 and pp. 103-
104.
[20] Terman, Lewis: The Intelligence of School Children. Boston: Houghton
Mifflin, 1919.
[21] Woodworth, R. S.: Dynamic Psychology, p. 200. New York: Columbia
University Press, 1918.

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