An extended account of the 1000tests 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.

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 5to14. 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.

The IQ’s were then grouped in ranges of ten. In the middle group were thrown those from 96to105; the ascending groups including in order the IQ’s from 106to115, 116to125, etc.; correspondingly with the descending groups. Figure2 shows the distribution found by this grouping for the 905 children of ages 5to14 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 80to120 children were tested at each age. In fact, the range, including the middle 50percent of IQ’s, was found practically constant from 5to14years. The tendency is for the middle 50percent to fall (approximately) between 93and108.

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]

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 IQ as the former is below. We have shown elsewhere the serious consequences of neglect of this fact.[21]

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 IQ’s is practically the same at each age from 5to14. 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 IQ 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 IQ, 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 IQ, 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 IQ) which has significance.

It follows also that if the IQ 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]

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.

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 1000IQ’s have to offer toward a solution of the problem.

1. When the IQ’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 13years. At 14, however, the curve for the girls dropped below that for boys. This is shown in Figure3.

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 age14, 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]

2. However, the superiority of girls over boys is so slight (amounting at most ages to only 2to3points in terms of IQ) 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 IQ including the middle fifty percent is approximately the same for the two sexes.[24]

4. When the results for the individual tests were examined, it was found that not many showed very extreme differences as to the percent 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, Æsthetic 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 14years, 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 14years 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 1000children, 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 IQ’s for these different groups.[25]

The data may be summarized as follows:—

1. The median IQ for children of the superior social class is about 7points above, and that of the inferior social class about 7points below, the median IQ 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 IQ to the quality of the child’s school work.

The school work of 504children 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 IQ, 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 IQ 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.

The relation between IQ and grade progress.

This comparison, which was made for the entire 1000children, showed a fairly high correlation, but also some astonishing disagreements. Nine-year intelligence was found all the way from grade1 to grade7, inclusive; 10-year intelligence all the way from grade2 to grade7; and 12-year intelligence all the way from grade3 to grade8. 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 96and105IQ 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 7or8years old; the child of 10-year intelligence in the sixth grade is almost certain to be 13to15years 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]

Special study of the IQ’s between 70and79 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.

On the other hand, the child with an IQ of 120 or above is almost never found below the grade for his chronological age, and occasionally he is one or two grades above. Wherever located, his work is always “superior” or “very superior,” and the evidence suggests strongly that it would probably remain so even if extra promotions were granted.

Correlation between IQ and the teachers’ estimates of the children’s intelligence.

By the Pearson formula the correlation found between the IQ’s and the teachers’ rankings on a scale of five was .48. This is about what others have found, and is both high enough and low enough to be significant. That it is moderately high in so far corroborates the tests. That it is not higher means that either the teachers or the tests have made a good many mistakes.

When the data were searched for evidence on this point, it was found, as we have shown in ChapterII, that the fault was plainly on the part of the teachers. The serious mistakes were nearly all made with children who were either over age or under age for their grade, mostly the former. In estimating children’s intelligence, just as in grading their school success, the teachers often failed to take account of the age factor. For example, the child whose mental age was, say, two years below normal, and who was enrolled in a class with children about two years younger than himself, was often graded “average” in intelligence.

The tendency of teachers is to estimate a child’s intelligence according to the quality of his school work in the grade where he happens to be located. This results in overestimating the intelligence of older, retarded children, and underestimating the intelligence of the younger, advanced children. The disagreements between the tests and the teachers’ estimates are thus found, when analyzed, to confirm the validity of the test method rather than to bring it under suspicion.

The validity of the individual tests.

The validity of each test was checked up by measuring it against the scale as a whole in the manner described on p.55. For example, if 10-year-old children having 11-year intelligence succeed with a given test decidedly better than 10-year-old children who have 9-year intelligence, then either this test must be accepted as valid or the scale as a whole must be rejected. Since we know, however, that the scale as a whole has at least a reasonably high degree of reliability, this method becomes a sure and ready means of judging the worth of a test.

When the tests were tried out in this way it was found that some of those which have been most criticized have in reality a high correlation with intelligence. Among these are naming the days of the week, giving the value of stamps, counting thirteen pennies, giving differences between president and king, finding rhymes, giving age, distinguishing right and left, and interpretation of pictures. Others having a high reliability are the vocabulary tests, arithmetical reasoning, giving differences, copying a diamond, giving date, repeating digits in reverse order, interpretation of fables, the dissected sentence test, naming sixty words, finding omissions in pictures, and recognizing absurdities.

Among the somewhat less satisfactory tests are the following: repeating digits (direct order), naming coins, distinguishing forenoon and afternoon, defining in terms of use, drawing designs from memory, and Æsthetic comparison. Binet’s “line suggestion” test correlated so little with intelligence that it had to be thrown out. The same was also true of two of the new tests which we had added to the series for try-out.

Tests showing a medium correlation with the scale as a whole include arranging weights, executing three commissions, naming colors, giving number of fingers, describing pictures, naming the months, making change, giving superior definitions, finding similarities, reading for memories, reversing hands of clock, defining abstract words, problems of fact, bow-knot, induction test, and comprehension questions.

A test which makes a good showing on this criterion of agreement with the scale as a whole becomes immune to theoretical criticisms. Whatever it appears to be from mere inspection, it is a real measure of intelligence. Henceforth it stands or falls with the scale as a whole.

The reader will understand, of course, that no single test used alone will determine accurately the general level of intelligence. A great many tests are required; and for two reasons: (1) because intelligence has many aspects; and (2) in order to overcome the accidental influences of training or environment. If many tests are used no one of them need show more than a moderately high correlation with the scale as a whole. As stated by Binet, “Let the tests be rough, if there are only enough of them.”