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 r.e.t.a.r.dates and are below average in intelligence.

[Ill.u.s.tration: 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 const.i.tutes mental deficiency. Similarly for genius. It is exactly as we should undertake to cla.s.sify 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 r.e.t.a.r.dation 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.)

s.e.x DIFFERENCES. The question as to the relative intelligence of the s.e.xes 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 s.e.xes 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 inst.i.tutions 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.

[Ill.u.s.tration: 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 s.e.x 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 s.e.xes, 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 s.e.x differences."

3. Apart from the small superiority of girls, the distribution of intelligence in the two s.e.xes 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 s.e.xes.[24]

[24] For an extensive summary of other data on the variability of the s.e.xes 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 pa.s.sing. 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 CLa.s.sES. Of the 1000 children, 492 were cla.s.sified by their teachers according to social cla.s.s 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 cla.s.s is about 7 points above, and that of the inferior social cla.s.s about 7 points below, the median I Q of the average social group. This means that by the age of 14 inferior cla.s.s children are about one year below, and superior cla.s.s children one year above, the median mental age for all cla.s.ses taken together.

2. That the children of the superior social cla.s.ses 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 cla.s.ses in terms of the same objective scale of intelligence. This scale should be based on the median for all cla.s.ses taken together.

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

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 h.o.m.ogeneous 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 r.e.t.a.r.dation problem is exactly the reverse of what we have thought it to be. It is the bright children who are r.e.t.a.r.ded, and the dull children who are accelerated.

The remedy is to be sought in differentiated courses (special cla.s.ses) for both kinds of mentally exceptional children. Just as many special cla.s.ses 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.