The Significance of the Binet Mental Ages
The Psychological Clinic Copyright, 1914, by Lightner Witmer, Editor. Vol. VIII, No. 7. December 15, 1914 :Author: Edward L. Thorndike, Ph.D.,
Teachers College, Columbia University.
In view of the wide use that is being made of the Binet-Simon tests, in one or another of their varieties, it seems important to know how far their successive steps, labeled Mental Ages, 3, 4, 5, 6, 7, etc., really represent the normal or average or modal ability of children of those ages. It is recognized that the thirteen-year test represents an ability much above that of the normal or modal or average thirteen-year-old child. But Goddard has asserted that “the Binet Scale was wonderfully accurate”?that its questions are “well graded, at least from the ages of five to twelve, and that they Number of children of each chronological age who were rated by Goddard as of each Binet Mental Age; 1547 children were reported belonging to Grade VI or lower.
Chronological Age 4 yrs. 5 ” . 6 ” . 7 ” . 8 ” . 9 ” . 10 ” . 11 ” . 12 ” 13 ” . 14 ” . 15 ” . Totals. Binet Mental Age II III IV 17 2 40 29 81 VI VII VIII IX X XI XII XIII 3 40 48 15 1 3 1 111 16 69 114 87 27 15 4 4 1 337 (185) 50 86 54 24 13 10 5 1 256 0 4 16 56 19 25 13 6 1 3 143 1 3 12 58 124 50 42 30 6 0 326 3 4 27 60 36 19 5 1 155 12 39 21 4 2 Totals 114 160 197 209 201 222 166 144 89 20 6 1547
fit the ages to which they are assigned”;1 and others have accepted this conclusion.
I shall show that the very measurements whence Goddard derived this assumption of the exact correspondence of the Binet mental ages V to XIII, to the average ability of chronological ages 5 to 12, show in reality something entirely different, and that so also do the results of others who have used these tests.
Goddard’s facts are given in table I (a copy of table I on page 234 of the article referred to above).
If one reads this table down, asking “Does the Binet or mental age hit the corresponding chronological age?” the affirmative answer seems correct, unless one realizes that the numbers should first be turned into percentages of the total numbers examined of the age in question. But when one realizes this and replaces, say, the 3, 4, 27, etc., of the column under XI by:
Binet Mental Age XI Chronological Age Frequency 8 1.5 9 2 10 12 1 1 36 1 2 25 1 3 21 1 4 25 1 5 17 he at once sees the failure of the Binet standards to correspond with the ages whose names they bear. The Binet XI fits chronological 123^, the Binet XII fits chronological 133^. You must not test 166 eleven-year-olds and only 20 fourteen-year-olds and then use the gross numbers of 60 eleven-year-olds and only 5 fourteen-year-olds testing at Binet XI to prove that Binet XI fits the eleven-year-olds. The whole error becomes clear when the table is read horizontally. Take the line for the chronologically thirteen-year-old children, for example. There were 89 of them, of whom 1 tested at Binet VII, 5 at Binet VIII, 6 at Binet IX, 30 at Binet X, 19 at Binet XI, 21 at Binet XII and only 7 at Binet XIII. Of 144 twelve-year-olds, only 39 tested at Binet XII or higher, while Binet IX, X, and XI had 91.
The average and the median Binet ages for the four-year-olds, five-year-olds, etc., tested by Goddard were as follows (table II). 1 Pedagogical Seminary, June, 1911, Vol. 18, p. 232 and p. 523.
The Binet Test values corresponding to each chronological age, using the data of table I. Chronological Age 4 5 6 7 8 9 10 11 12 13 14 15
Median. Binet Age or so-called Mental Age 5.0 5.6 6.5 7.1 7.6 8.8 9.9 10.3 10.6 10.6 10.9 10.0 Average. Binet Age or so-called Mental Age 4.9 5.6 6.3 7.1 7.8 8.8 9.7 10.1 10.5 10.7 11.0 10.3
These figures however cannot be taken at their face value, for Goddard’s 1547 cases were all from grades VI or below, and represent therefore a superior selection of 4-, 5-, and 6-year-olds and an inferior selection of 13-, 14- and 15-year-olds (and to some extent of 12-yearolds) . We shall be able to make allowance for this more intelligently after examining some of the results obtained by other investigators. Dougherty1 tested children in grades 1 to 8 of a certain school, getting a fair sampling of children of each age from 7 to 14, and finding the facts shown in table III, columns 4 and 5.
As nearly as I can judge, Terman and Childs2 got approximately the facts shown in table III, column 6. They had a fair sampling up to 13, but had rather inferior pupils of ages 13 and 14 (pupils still in grade VII).
Strong3 testing about 30 of each age from six to twelve (how selected, I cannot be sure), found the facts shown in columns 7 and 8 of table III. It is clear from table III that eleven-year-old children do not equal the Binet XI standard, but a standard of about 10.6 (or X + f of the Binet X-XI step); that twelve-year-old children do not equal the Binet XII standard, but about 10.9 (X. + ttt of the Binet X-XI step). As to the older children, even if we make a very generous allowance 1 J. Of Ed. Psy., 1913, Vol. IV, p. 341. 2 J. of Ed. Psy., 1912, Vol. Ill, p. 69. ? Ped. Sem., 1913, Vol. XX, p. 489. 188 THE PSYCHOLOGICAL CLINIC. for the stupidity of Goddard’s thirteen and fourteen-year-olds in grades VI and below, and for Terman and Child’s thirteen and fourteen-year-olds in grades VII and below, Ave still find that they do not on the average pass the Binet XII. Probably 11.4 (or XI plus TV of the Binet XI-XII step) is as high as the general run of thirteen-yearold children would score. TABLE III. Median and average Binet scores found for each year of age. Chronological 9 10 11 12 13 14 Measurements by Goddard 2 Median 7.1 7.6 8.8 9.9 10.3 10.6 10.6 10.9 3 Average 7.1 7.8 8.8 9.7 10.1 10.5 10.7 11.0 Measurements by Dougherty 4 Median 7.3 8.0 8.8 9.8 10.6 11.0 11.1 11.7 5 Average 7.4 8.0 8.7 9.7 10.6 10.8 11.0 11.5
Measurements by Terman and Childs. 6 Median 7.5 9.25 9.0 10.0 10.5 10.8 11.3 12.0
Measurements by Strong 7 Median 7.1 8.1 8.9 9.4 10.9 11.1 Average 7.1 8.2 9.0 9.7 10.6 11.0
This means of course that the Binet X, XI and XII are not exact correspondents of the normal or modal abilities of children ten, eleven and twelve years old. The mental ages represented by the Binet scores for VII to XII seem to be about as shown in table IV. In all the foregoing I have used eight-year-olds to mean children 7 years 6 months to 8 years 6 months, and similarly for all other ages, adapting Terman and Child’s figures to this meaning. Such was the practice of all but Terman and Child as nearly as I can discover. Since this was written, the article by Brigham1 has appeared. All the children in grades 1 to 6 of a certain school were tested by Brigham with the result that the seven-year-olds had an average Binet age of 7.05; the eight-year-olds, of 8.08; the nine-year-olds, of 8.94; the ten-year-olds, of 9.49; the eleven-year-olds, of 10.30; the twelve-year-olds, of 10.62; and the thirteen-year-olds, of 10.79. Allowing generously for the fact that some of the brightest twelveyear-olds would have passed beyond grade 6, and that the brightest half of the thirteen-year-olds would have done so, these results agree fairly well with those used in this article and do not suggest any considerable change in table IV.
TABLE IV.
The true “mental” ages denoted by the Binet scores VII.O, VII.2, VII.4, XI.8. Score by Binet Test VII. 0 ” 2 4 6 8 VIII. 0 2 4 6 8 IX. 0 2 4 6 8 X. 0 2 4 6 8 XI. 0 2 4 6 The True Mental Age denoted thereby 6.8 7.0 7.25 7.5 7.75 8.0 8.2 8.4 8.6 8.9 9.1 9.3 9.5 9.75 10.0 10.25 10.5 10.75 11.0 11.6 12.2 12.6 13.0 13.4 13.8
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