path: root/76891-0.txt

*** START OF THE PROJECT GUTENBERG EBOOK 76891 ***





                         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:

[Illustration:

  Age Scale +------------------------------------------------ Mental Age
            | _Reading Age_
            +----------------------------------------- Chronological Age
            |     _Spelling Age_
            |              _Arithmetic Age_
            +----------------------------------------------------------
]

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.| 4 | 5 | 6 | 7 | 8
                      | Age  +-+-+-+-+-+-+-+-+-+-
                      |      |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_  |          |          |        |
       101     | _b_  |          |          |        |
               | _c_  |    64    |    58    |        |    43
               | _d_  |   106    |    88    |        |    93
               |      |          |          |        |
               | _a_  |          |          |        |
       128     | _b_  |          |          |        |
               | _c_  |    80    |   102    |        |    81
               | _d_  |          |   152    |  124   |   153
               |      |          |          |        |
               | _a_  |          |          |        |
       116     | _b_  |          |          |        |
               | _c_  |    56    |    90    |   *    |    49
               | _d_  |    94    |    95    |   77   |    89
               |      |          |          |        |
               | _a_  |          |          |        |
        87     | _b_  |          |          |        |
               | _c_  |    90    |    40    |   35   |    54
               | _d_  |    72    |    74    |   61   |    52
               |      |          |          |        |
               | _a_  |          |          |        |
       112     | _b_  |          |          |        |
               | _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 ∜(_r_₁₁⋅_r_₂₂) 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” √(_r_₁₁),
∜(_r_₁₁⋅_r_₂₂) 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      One Form    Two Forms
                       of Each      of Each       with an      with an
                        Test        Test (by      Infinite     Infinite
                                    Brown’s        Number       Number
                                    Formula)      of Forms     of Forms

                         _r_₁₁        _r_₁₁       √_r_₁₁       √_r_₁₁

  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 = ∜(_r_₁₁ × _r_₂₂)

                     Nov. 1918,
                 June and Nov. 1919       June 1920
  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 _r__{VQ.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

  Vocabulary Quotient      .04
                           ±.07

  Reading Quotient         .31          .28
                          ±.07         ±.07

  Completion Quotient      .43          .44          .47
                          ±.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

  GRADE             _r_                 M                S.D.

                Nov.   June        Nov.    June       Nov.    June

         I V    .467    .633  I  109.89   113.20  I  12.83   15.49
               ±.12    ±.07       ±1.98    ±1.91     ±1.40   ±1.35

  III    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
  -----------------------------------------------------------------

         I V    .724    .819  I  105.90   104.82  I  18.08   18.21
               ±.07    ±.05       ±2.73    ±2.98     ±1.93   ±2.11

  IV     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
  -----------------------------------------------------------------

         I V    .887    .822  I  101.64    99.42  I  24.76   17.63
               ±.04    ±.05       ±3.56    ±2.73     ±2.52   ±1.93

  V      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
  -----------------------------------------------------------------
         I V    .793    .772  I  109.90   115.90  I  23.45   24.38
               ±.08    ±.09       ±5.00    ±5.20     ±3.54   ±3.68

  VI     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
  -----------------------------------------------------------------
         I V    .625    .504  I   99.29    98.92  I  11.11   11.45
               ±.11    ±.14       ±2.00    ±2.14     ±1.42   ±1.51

  VII    I R    .622    .709  V  109.43   115.23  V  14.07   17.43
  and          ±.11    ±.09       ±2.54    ±2.95     ±1.79   ±2.31
  VIII
         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
  -----------------------------------------------------------------
         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
  TOTAL        ±.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

         I A    .413    .709  I  102.00   105.53  I   9.60   10.89
               ±.16    ±.08       ±1.87    ±1.68     ±1.32   ±1.19

  III    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
  -----------------------------------------------------------------
         I A    .426    .725  I  111.48   113.00  I  14.73   15.04
               ±.10    ±.06       ±1.85    ±1.93     ±1.30   ±1.36

  IV     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
  -----------------------------------------------------------------
         I A    .698    .713  I  103.72    98.83  I  19.57   18.84
               ±.07    ±.07       ±2.69    ±2.65     ±1.91   ±1.87

  V      I V    .881    .908  A   87.58    99.71  A  12.43   16.47
               ±.03    ±.02       ±1.71    ±2.27     ±1.21   ±1.60

         I R    .773    .891  V  109.00   105.17  V  15.58   19.97
               ±.06    ±.03       ±2.14    ±2.81     ±1.52   ±1.99

         I C    .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
  -----------------------------------------------------------------
         I A    .533    .805  I  102.43   105.39  I  11.61   13.56
               ±.13    ±.06       ±2.09    ±2.16     ±1.48   ±1.52

  VI     I V    .774    .858  A   91.43   104.53  A  11.43   11.31
               ±.07    ±.04       ±2.06    ±1.75     ±1.46   ±1.24
         I R    .420    .661  V  106.07   112.94  V  11.93   10.94
               ±.15    ±.09       ±2.15    ±1.74     ±1.52   ±1.23

         I C    .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
  -----------------------------------------------------------------
         I A    .740    .795  I  107.27   100.58  I  23.29   19.78
               ±.09    ±.07       ±4.74    ±2.85     ±3.35   ±2.72

  VII    I V    .867    .718  A  100.00    99.31  A   9.26   11.00
               ±.05    ±.09       ±1.86    ±2.06     ±1.33   ±1.45

         I R    .862    .799  V  114.36   108.75  V  19.15   14.42
               ±.05    ±.07       ±3.89    ±2.81     ±2.75   ±1.98

         I C    .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
  -----------------------------------------------------------------
         I A    .663    .796  I  104.83   108.79  I  15.46   18.25
               ±.11    ±.07       ±3.01    ±3.29     ±2.13   ±2.33

  VIII   I V    .828    .750  A   92.92    93.86  A  10.20    9.74
               ±.06    ±.08       ±1.99    ±1.76     ±1.40   ±1.24

         I R    .775    .722  V  111.67   117.21  V  16.44   14.02
               ±.08    ±.08       ±3.20    ±2.53     ±2.26   ±1.79

         I C    .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
  -----------------------------------------------------------------

         I A    .576    .686  I  106.02   105.87  I  16.73   16.87
               ±.05    ±.03       ±1.12    ±1.07     ±0.79   ±0.75

  TOTAL  I V    .679    .727  A   91.35   102.01  A  13.22   15.61
               ±.04    ±.03       ±0.88    ±0.98     ±0.62   ±0.69

         I R    .529    .609  V  107.95   110.54  V  19.76   19.57
               ±.05    ±.04       ±1.32    ±1.24     ±0.93   ±0.87

         I C    .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 _b_₁₂ =
_b_₂₁ = 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 M_{IQ}, 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
M_{IQ}-M_{AQ} AND DECREASE IN DIFFERENCE OF STANDARD DEVIATIONS
IRRESPECTIVE OF DIRECTION

                              Average Intelligence      Difference of
  GRADE             _r_          Quotient Minus      Standard Deviations
                               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]14.93       5.26 [14]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 M_{IQ}-M_{RQ}, AND DECREASE IN DIFFERENCE OF STANDARD
DEVIATIONS IRRESPECTIVE OF SIGN

                              Average Intelligence      Difference of
  GRADE             _r_          Quotient Minus      Standard Deviations
                                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 M_{IQ}-M_{RQ}, AND DECREASE IN DIFFERENCE OF STANDARD
DEVIATIONS IRRESPECTIVE OF SIGN

                              Average Intelligence      Difference of
  GRADE             _r_          Quotient Minus      Standard Deviations
                                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 M_{IQ}-M_{AQ} in June and M_{IQ}-M_{AQ} 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._{diff}²  = P.E.₁² + P.E.₂² - 2 _r_₁₂ P.E.₁ P.E.₂

The only M_{IQ}-M_{SQ} 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         Arithmetic    Vocabulary    Reading    Completion
    Quotient             Ratio         Ratio        Ratio       Ratio

               _a_
  101          _b_
               _c_          63            57                       43
               _d_         105            87                       92

               _a_
  128          _b_
               _c_          62            80                       63
               _d_                       119           97         120

               _a_
  116          _b_
               _c_          48            78           *           42
               _d_          81            82           66          77

               _a_
   87          _b_
               _c_         103            46           40          62
               _d_          83            85           70          60

               _a_
  112          _b_
               _c_          80           122          119         100
               _d_         100           101          108         117

               _a_
  101          _b_
               _c_          84            93           37          55
               _d_          90           110           98          92

               _a_
   90          _b_
               _c_          76            58           72          89
               _d_          68           121           77         102

               _a_
  105          _b_
               _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.D_{AccR₁₉₁₈} 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]

  _r__{X.Y.} = -.602
  _r__{X.S.} = -.493
  _r__{Y.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._r__{X.Y.} = .06
      P.E._r__{X.S.} = .08
      P.E._r__{Y.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._{X}² + P.E._{Y}² - 2 _r__{XY} 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
M_{_x_} = M_{_y_}. 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.

[Illustration]




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.




*** END OF THE PROJECT GUTENBERG EBOOK 76891 ***