The Measurement of Intelligence

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_Year XIV._ (_6 tests, 4 months each._)
1. Vocabulary, 50 words. (Stanford addition.)
2. Induction test. (Gets rule by 6th folding.) (Stanford addition.)
3. President and king. (Power; accession; tenure. 2 to 3.)
4. Problems of fact. (2 to 3.) (Binet's two and one Stanford
addition.)
5. Arithmetical reasoning. (1 minute each. 2 to 3.) (Adapted from
Bonser.)
6. Clock. (2 to 3. Error must not exceed 3 or 4 minutes.)
6.22. 8.10. 2.46.
Al. Repeats 7 digits. (1 to 2. Order correct.)

"AVERAGE ADULT." (_6 tests, 5 months each._)
1. Vocabulary, 65 words. (Stanford addition.)
2. Interpretation of fables. (Score 8.) (Stanford addition.)
3. Difference between abstract words. (3 real contrasts out of 4.)
Laziness and idleness; evolution and revolution; poverty and
misery; character and reputation.
4. Problem of the enclosed boxes. (3 to 4.) (Stanford addition.)
5. Repeats 6 digits backwards. (1 to 3.) (Stanford addition.)
6. Code, writes "Come quickly." (2 errors. Omission of dot counts
half error. Illustrate with "war" and "spy.") (From Healy and
Fernald.)
Al. 1. Repeats 28 syllables. (1 to 2 absolutely correct.)
Al. 2. Comprehension of physical relations. (2 to 3.) (Stanford addition.)
Path of cannon ball; weight of fish in water; hitting distant
mark.

"SUPERIOR ADULT." (_6 tests, 6 months each._)
1. Vocabulary, 75 words. (Stanford addition.)
2. Binet's paper-cutting test. (Draws, folds, and locates holes.)
3. Repeats 8 digits. (1 to 3. Order correct.) (Stanford addition.)
4. Repeats thought of passage heard. (1 to 2.) (Binet's and Wissler's
selections adapted.)
5. Repeats 7 digits backwards. (1 to 3.) (Stanford addition.)
6. Ingenuity test. (2 to 3. 5 minutes each.) (Stanford addition.)

SUMMARY OF CHANGES. A comparison of the above list with either the Binet
1908 or 1911 series will reveal many changes. On the whole, it differs
somewhat more from the Binet 1911 scale than from that of 1908. Thus, of
the 49 tests below the "adult" group in the 1911 scale, 2 are eliminated
and 29 are relocated. Of these, 25 are moved downward and 4 upward. The
shifts are as follows:--

Down 1 year, 18
Down 2 years, 4
Down 3 years, 2
Down 6 years, 1
Up 1 year, 3
Up 2 years, 1

Of the adult group in Binet's 1911 series 1 is eliminated, 2 are moved
up to "superior adult," and 1 is moved up to 14. Accordingly, of Binet's
entire 54 tests, we have eliminated 3 and relocated 32, leaving only 19
in the positions assigned them by Binet. The 3 eliminated are: repeating
2 digits, resisting suggestion, and "reversed triangle."

The revision is really more extensive than the above figures would
suggest, since minor changes have been made in the scoring of a great
many tests in order to make them fit better the locations assigned them.
Throughout the scale the procedure and scoring have been worked over and
made more definite with the idea of promoting uniformity. This phase of
the revision is perhaps more important than the mere relocation of
tests. Also, the addition of numerous tests in the upper ranges of the
scale affects very considerably the mental ages above the level of
10 or 11 years.

EFFECTS OF THE REVISION ON THE MENTAL AGES SECURED. The most important
effect of the revision is to reduce the mental ages secured in the lower
ranges of the scale, and to raise considerably the mental ages above
10 or 11 years. This difference also obtains, though to a somewhat
smaller extent, between the Stanford revision and those of Goddard and
Kuhlmann.

For example, of 104 adult individuals testing by the Stanford revision
between 12 and 14 years, and who were therefore somewhat above the level
of feeble-mindedness as that term is usually defined, 50 per cent tested
below 12 years by the Goddard revision. That the dull and border-line
adults are so much more readily distinguished from the feeble-minded by
the Stanford revision than by other Binet series is due as much to the
addition of tests in the upper groups as to the relocation of existing
tests.

On the other hand, the Stanford revision causes young subjects to test
lower than any other version of the Binet scale. At 5 or 6 years the
mental ages secured by the Stanford revision average from 6 to 10 months
lower than other revisions yield.

The above differences are more significant than would at first appear.
An error of 10 months in the mental age of a 5-year-old is as serious as
an error of 20 months in the case of a 10-year-old. Stating the error in
terms of the intelligence quotient makes it more evident. Thus, an error
of 10 months in the mental age of a 5-year-old means an error of almost
15 per cent in the intelligence quotient. A scale which tests this much
too low would cause the child with a true intelligence quotient of 75
(which ordinarily means feeble-mindedness or border-line intelligence)
to test at 90, or only slightly below normal.

Three serious consequences came from the too great ease of the original
Binet scale at the lower end, and its too great difficulty at the upper
end:--

1. In young subjects the higher grades of mental deficiency were
overlooked, because the scale caused such subjects to test only a little
below normal.

2. The proportion of feeble-mindedness among adult subjects was greatly
overestimated, because subjects who were really of the 12- or 13-year
mental level could only earn a mental age of about 11 years.

3. Confusion resulted in efforts to trace the mental growth of either
feeble-minded or normal children. For example, by other versions of the
Binet scale an average 5-year-old will show an intelligence quotient
probably not far from 110 or 115; at 9, an intelligence quotient of
about 100; and at 14, an intelligence quotient of about 85 or 90.

By such a scale the true border-line case would test approximately as
follows:--

At age 5, 90 I Q (apparently not far below normal).
At age 9, 75 I Q (border-line).
At age 14, 65 I Q (moron deficiency).

On the other hand, re-tests of children by the Stanford revision have
been found to yield intelligence quotients almost identical with those
secured from two to four years earlier by the same tests. Those who
graded feeble-minded in the first test graded feeble-minded in the
second test: the dull remained dull, the average remained average, the
superior remained superior, and always in approximately the same
degree.[18]

[18] See "Some Problems relating to the Detection of Border-line Cases
of Mental Deficiency," by Lewis M. Terman and H. E. Knollin, in _Journal
of Psycho-Asthemes_, June, 1916.

It is unnecessary to emphasize further the importance of having an
intelligence scale which is equally accurate at all points. Absolute
perfection in this respect is not claimed for the Stanford revision, but
it is believed to be at least free from the more serious errors of other
Binet arrangements.

CHAPTER V

ANALYSIS OF 1000 INTELLIGENCE QUOTIENTS

An extended account of the 1000 tests on which the Stanford revision is
chiefly based has been presented in a separate monograph. This chapter
will include only the briefest summary of some of those results of the
investigation which contribute to the intelligent use of the revision.

THE DISTRIBUTION OF INTELLIGENCE. The question as to the manner in which
intelligence is distributed is one of great practical as well as
theoretical importance. One of the most vital questions which can be
asked by any nation of any age is the following: "How high is the
average level of intelligence among our people, and how frequent are the
various grades of ability above and below the average?" With the
development of standardized tests we are approaching, for the first time
in history, a possible answer to this question.

Most of the earlier Binet studies, however, have thrown little light on
the distribution of intelligence because of their failure to avoid the
influence of accidental selection in choosing subjects for testing. The
method of securing subjects for the Stanford revision makes our results
on this point especially interesting.[19] It is believed that the
subjects used for this investigation were as nearly representative of
average American-born children as it is possible to secure.

[19] See p. 52 _ff._ for method used to avoid accidental selection of
subjects for the Stanford investigation.

The intelligence quotients for these 1000 unselected children were
calculated, and their distribution was plotted for the ages separately.
The distribution was found fairly symmetrical at each age from 5 to 14.
At 15 the range is on either side of 90 as a median, and at 16 on either
side of 80 as a median. That the 15- and 16-year-olds test low is due to
the fact that these children are left-over retardates and are below
average in intelligence.

[Illustration: FIG. 2. DISTRIBUTION OF I Q'S OF 905 UNSELECTED
CHILDREN. 5-14 YEARS OF AGE]

The I Q's were then grouped in ranges of ten. In the middle group were
thrown those from 96 to 105; the ascending groups including in order the
I Q's from 106 to 115, 116 to 125, etc.; correspondingly with the
descending groups. Figure 2 shows the distribution found by this
grouping for the 905 children of ages 5 to 14 combined. The subjects
above 14 are not included in this curve because they are left-overs and
not representative of their ages.

The distribution for the ages combined is seen to be remarkably
symmetrical. The symmetry for the separate ages was hardly less marked,
considering that only 80 to 120 children were tested at each age. In
fact, the range, including the middle 50 per cent of I Q's, was found
practically constant from 5 to 14 years. The tendency is for the middle
50 per cent to fall (approximately) between 93 and 108.

Three important conclusions are justified by the above facts:--

1. Since the frequency of the various grades of intelligence decreases
_gradually_ and at no point abruptly on each side of the median, it is
evident that there is no definite dividing line between normality and
feeble-mindedness, or between normality and genius. Psychologically, the
mentally defective child does not belong to a distinct type, nor does
the genius. There is no line of demarcation between either of these
extremes and the so-called "normal" child. The number of mentally
defective individuals in a population will depend upon the standard
arbitrarily set up as to what constitutes mental deficiency. Similarly
for genius. It is exactly as we should undertake to classify all people
into the three groups: abnormally tall, normally tall, and abnormally
short.[20]

[20] See Chapter VI for discussion of the significance of various I Q's.

2. The common opinion that extreme deviations below the median are more
frequent than extreme deviations above the median seems to have no
foundation in fact. Among unselected school children, at least, for
every child of any given degree of deficiency there is another child as
far above the average I Q as the former is below. We have shown
elsewhere the serious consequences of neglect of this fact.[21]

[21] See p. 12 _ff._

3. The traditional view that variability in mental traits becomes more
marked during adolescence is here contradicted, as far as intelligence
is concerned, for the distribution of I Q's is practically the same at
each age from 5 to 14. For example, 6-year-olds differ from one another
fully as much as do 14-year-olds.

THE VALIDITY OF THE INTELLIGENCE QUOTIENT. The facts presented above
argue strongly for the validity of the I Q as an expression of a child's
intelligence status. This follows necessarily from the similar nature of
the distributions at the various ages. The inference is that a child's
I Q, as measured by this scale, remains relatively constant. Re-tests of
the same children at intervals of two to five years support the
inference. Children of superior intelligence do not seem to deteriorate
as they get older, nor dull children to develop average intelligence.
Knowing a child's I Q, we can predict with a fair degree of accuracy the
course of his later development.

The mental age of a subject is meaningless if considered apart from
chronological age. It is only the ratio of retardation or acceleration
to chronological age (that is, the I Q) which has significance.

It follows also that if the I Q is a valid expression of intelligence,
as it seems to be, then the Binet-Simon "age-grade method" becomes
transformed automatically into a "point-scale method," if one wants to
use it that way. As such it is superior to any other point scale that
has been proposed, because it includes a larger number of tests and its
points have definite meaning.[22]

[22] For discussion of the supposed advantages of the "point-scale
method," see Yerkes and Bridges: _A New Point Scale for Measuring Mental
Ability_. (Warwick and York, 1915.)

SEX DIFFERENCES. The question as to the relative intelligence of the
sexes is one of perennial interest and great social importance. The
ancient hypothesis, the one which dates from the time when only men
concerned themselves with scientific hypotheses, took for granted the
superiority of the male. With the development of individual psychology,
however, it was soon found that as far as the evidence of mental tests
can be trusted the _average_ intelligence of women and girls is as high
as that of men and boys.

If we accept this result we are then confronted with the difficult
problem of finding an explanation for the fact that so few of those who
have acquired eminence in the various intellectual fields have been
women. Two explanations have been proposed: (1) That women become
eminent less often than men simply for lack of opportunity and stimulus;
and (2) that while the average intelligence of the sexes is the same,
extreme variations may be more common in males. It is pointed out that
not only are there more eminent men than eminent women, but that
statistics also show a preponderance of males in institutions for the
mentally defective. Accordingly it is often said that women are grouped
closely about the average, while men show a wider range of distribution.

[Illustration: FIG. 3. MEDIAN I Q OF 457 BOYS (UNBROKEN LINE) AND
448 GIRLS (DOTTED LINE) FOR THE AGES 5-14 YEARS]

Many hundreds of articles and books of popular or quasi-scientific
nature have been written on one aspect or another of this question of
sex difference in intelligence; but all such theoretical discussions
taken together are worth less than the results of one good experiment.
Let us see what our 1000 I Q's have to offer toward a solution of the
problem.

1. When the I Q's of the boys and girls were treated separately there
was found a small but fairly constant superiority of the girls up to the
age of 13 years. At 14, however, the curve for the girls dropped below
that for boys. This is shown in Figure 3.

The supplementary data, including the teachers' estimates of
intelligence on a scale of five, the teachers' judgments in regard to
the quality of the school work, and records showing the age-grade
distribution of the sexes, were all sifted for evidence as to the
genuineness of the apparent superiority of the girls age for age. The
results of all these lines of inquiry support the tests in suggesting
that the superiority of the girls is probably real even up to and
including age 14, the apparent superiority of the boys at this age being
fully accounted for by the more frequent elimination of 14-year-old
girls from the grades by promotion to the high school.[23]

[23] It will be remembered that this series of tests did not follow up
and test those who had been promoted to high school.

2. However, the superiority of girls over boys is so slight (amounting
at most ages to only 2 to 3 points in terms of I Q) that for practical
purposes it would seem negligible. This offers no support to the opinion
expressed by Yerkes and Bridges that "at certain ages serious injustice
will be done individuals by evaluating their scores in the light of
norms which do not take account of sex differences."

3. Apart from the small superiority of girls, the distribution of
intelligence in the two sexes is not different. The supposed wider
variation of boys is not found. Girls do not group themselves about the
median more closely than do boys. The range of I Q including the middle
fifty per cent is approximately the same for the two sexes.[24]

[24] For an extensive summary of other data on the variability of the
sexes see the article by Leta S. Hollingworth, in _The American Journal
of Sociology_ (January, 1914), pp. 510-30. It is shown that the findings
of others support the conclusions set forth above.

4. When the results for the individual tests were examined, it was found
that not many showed very extreme differences as to the per cent of boys
and girls passing. In a few cases, however, the difference was rather
marked.

The boys were decidedly better in arithmetical reasoning, giving
differences between a president and a king, solving the form board,
making change, reversing hands of clock, finding similarities, and
solving the "induction test." The girls were superior in drawing designs
from memory, aesthetic comparison, comparing objects from memory,
answering the "comprehension questions," repeating digits and sentences,
tying a bow-knot, and finding rhymes.

Accordingly, our data, which for the most part agree with the results of
others, justify the conclusion that the intelligence of girls, at least
up to 14 years, does not differ materially from that of boys either as
regards the average level or the range of distribution. It may still be
argued that the mental development of boys beyond the age of 14 years
lasts longer and extends farther than in the case of girls, but as a
matter of fact this opinion receives little support from such tests as
have been made on men and women college students.

The fact that so few women have attained eminence may be due to wholly
extraneous factors, the most important of which are the following: (1)
The occupations in which it is possible to achieve eminence are for the
most part only now beginning to open their doors to women. Women's
career has been largely that of home-making, an occupation in which
eminence, in the strict sense of the word, is impossible. (2) Even of
the small number of women who embark upon a professional career, a
majority marry and thereafter devote a fairly large proportion of their
energy to bearing and rearing children. (3) Both the training given to
girls and the general atmosphere in which they grow up are unfavorable
to the inculcation of the professional point of view, and as a result
women are not spurred on by deep-seated motives to constant and
strenuous intellectual endeavor as men are. (4) It is also possible that
the emotional traits of women are such as to favor the development of
the sentiments at the expense of innate intellectual endowment.

INTELLIGENCE OF THE DIFFERENT SOCIAL CLASSES. Of the 1000 children, 492
were classified by their teachers according to social class into the
following five groups: _very inferior_, _inferior_, _average_,
_superior_, and _very superior_. A comparative study was then made of
the distribution of I Q's for these different groups.[25]

[25] The results of this comparison have been set forth in detail in the
monograph of source material and some of the conclusions have been set
forth on p. 115 _ff._ of the present volume.

The data may be summarized as follows:--

1. The median I Q for children of the superior social class is
about 7 points above, and that of the inferior social class
about 7 points below, the median I Q of the average social
group. This means that by the age of 14 inferior class children
are about one year below, and superior class children one year
above, the median mental age for all classes taken together.

2. That the children of the superior social classes make a
better showing in the tests is probably due, for the most part,
to a superiority in original endowment. This conclusion is
supported by five supplementary lines of evidence: (a) the
teachers' rankings of the children according to intelligence;
(b) the age-grade progress of the children; (c) the quality
of the school work; (d) the comparison of older and younger
children as regards the influence of social environment; and
(e) the study of individual cases of bright and dull children
in the same family.

3. In order to facilitate comparison, it is advisable to express
the intelligence of children of all social classes in terms of
the same objective scale of intelligence. This scale should be
based on the median for all classes taken together.

4. As regards their responses to individual tests, our children
of a given social class were not distinguishable from children
of the same intelligence in any other social class.

THE RELATION OF THE I Q TO THE QUALITY OF THE CHILD'S SCHOOL WORK. The
school work of 504 children was graded by the teachers on a scale of
five grades: _very inferior_, _inferior_, _average_, _superior_, and
_very superior_. When this grouping was compared with that made on the
basis of I Q, fairly close agreement was found. However, in about one
case out of ten there was rather serious disagreement; a child, for
example, would be rated as doing _average_ school work when his I Q
would place him in the _very inferior_ intelligence group.

When the data were searched for explanations of such disagreements it
was found that most of them were plainly due to the failure of teachers
to take into account the age of the child when grading the quality of
his school work.[26] When allowance was made for this tendency there
were no disagreements which justified any serious suspicion as to the
accuracy of the intelligence scale. Minor disagreements may, of course,
be disregarded, since the quality of school work depends in part on
other factors than intelligence, such as industry, health, regularity of
attendance, quality of instruction, etc.

[26] See p. 24 _ff._

THE RELATION BETWEEN I Q AND GRADE PROGRESS. This comparison, which was
made for the entire 1000 children, showed a fairly high correlation, but
also some astonishing disagreements. Nine-year intelligence was found
all the way from grade 1 to grade 7, inclusive; 10-year intelligence all
the way from grade 2 to grade 7; and 12-year intelligence all the way
from grade 3 to grade 8. Plainly the school's efforts at grading fail to
give homogeneous groups of children as regards mental ability. On the
whole, the grade location of the children did not fit their mental ages
much better than it did their chronological ages.

When the data were examined, it was found that practically every child
whose grade failed to correspond fairly closely with his mental age was
either exceptionally bright or exceptionally dull. Those who tested
between 96 and 105 I Q were never seriously misplaced in school. The
very dull children, however, were usually located from one to three
grades above where they belonged by mental age, and the duller the
child the more serious, as a rule, was the misplacement. On the other
hand, the very bright children were nearly always located from one to
three grades below where they belonged by mental age, and the brighter
the child the more serious the school's mistake. The child of 10-year
mental age in the second grade, for example, is almost certain to be
about 7 or 8 years old; the child of 10-year intelligence in the sixth
grade is almost certain to be 13 to 15 years of age.

All this is due to one fact, and one alone: _the school tends to promote
children by age rather than ability_. The bright children are held back,
while the dull children are promoted beyond their mental ability. The
retardation problem is exactly the reverse of what we have thought it to
be. It is the bright children who are retarded, and the dull children
who are accelerated.

The remedy is to be sought in differentiated courses (special classes)
for both kinds of mentally exceptional children. Just as many special
classes are needed for superior children as for the inferior. The social
consequences of suitable educational advantages for children of superior
ability would no doubt greatly exceed anything that could possibly
result from the special instruction of dullards and border-line
cases.[27]

[27] See Chapter VI for further discussion of the school progress
possible to children of various I Q's.

Special study of the I Q's between 70 and 79 revealed the fact that a
child of this grade of intelligence _never_ does satisfactory work in
the grade where he belongs by chronological age. By the time he has
attended school four or five years, such a child is usually found doing
"very inferior" to "average" work in a grade from two to four years
below his age.

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