TABLE V.
Percentages of Mentally Retarded Children Tested with the 1908 Binet Scale. (From Goddard's Table.)
| Life-Age | No. of cases | Years Retarded | |||
| Two or more | Three or more | Four or more | Five or more | ||
| 5 | 114 | 5.3 | 1.8 | ||
| 6 | 160 | 2.5 | 0.6 | 0.6 | |
| 7 | 197 | 5.6 | 1.5 | 0.5 | 0.0 |
| 8 | 209 | 2.4 | 1.9 | 1.0 | 0.0 |
| 9 | 201 | 1.3 | 0.0 | 0.0 | 0.0 |
| 10 | 222 | 18.9 | 8.1 | 1.4 | 0.0 |
| 11 | 166 | 25.9 | 10.8 | 3.0 | 0.6 |
| 1269 | |||||
In the accompanying Table V Goddard's results are arranged so as to show the percentages at each life-age retarded two or more, three or more, four or more, and five or more years according to the Binet 1908 scale. The heavy black line indicates the upper borderline of the doubtful group according to our interpretation. In spite of irregularities, due mainly to insufficient numbers, the trend of the table is fairly plain. The column of percentages two or more years retarded and to the left of the heavy line suggests that the break comes at ten years of age. Using our tentative criterion of 0.5% presumably deficient and the next 1.0% uncertain intellectually, the outcome of this analysis is a rather striking demonstration of the feasibility of the percentage procedure even when the groups examined at each age are only composed of about 200 cases. I have preferred to take the empirical data at the lower extreme of each age distribution instead of projecting the tail of a smoothed distribution curve for each age.
Until better data are available we have adopted in practise, as a result of the study of this table, the procedure of considering any child who is ten years of age or over as testing of doubtful capacity if he is four or more years retarded below his chronological age, three or more years retarded if he is under ten years of age. If he shows one additional year of retardation we consider, in the absence of some other explanation of his retardation, that he is presumably intellectually deficient enough to justify a recommendation of isolation. Of course no such recommendation should be made without a complete medical examination, a full knowledge of the history of the case and a checking of the record by further tests at different times when there is any suspicion that the child has not done as well as he might under other conditions.
The fact that we have no data on random groups 12, 13 and 14 years of age leaves a gap which may mean that our criterion of 5 years retardation for presumable deficiency at these ages is too small. It is possible that the shift to 6 years retardation should be made before 15 years, which is the position where our criterion for the borderline for the mature automatically makes the shift. We say a 15-year-old testing X is above the group presumably deficient as he has entered the “doubtful” adult class.
It is also to be remembered that the standard error expected from the results of samples as small as these is 0.5% when the sample is 200 and 0.7% when it is 100. The limits thus might easily shift a year. The suggested borderlines for the immature can at best be regarded only as the most likely under the meager evidence available.
Whether the borderlines for deficiency on the Binet scale should be described in terms of years of retardation is doubtful except, as in this case, for practical convenience. It is certainly only a rough indication of the borderlines. When this method has not been followed the most common practise is to use some form of Stern's “intelligence quotient.” An extended discussion of this question is reserved for Part II of this book, to which the reader is referred. It need only be said here that the percentage procedure adapts itself to either method of description. Since the designation of the limits must be very rough until we have much further information from tests upon unselected groups, we have adopted the common method of description in terms of years of retardation, since it seems to afford for the 1908 scale the simplest expression of the borderline until the tests have been much improved. It happens that the empirical results for 5 years of age and over lend themselves to designating the lowest percentages in terms of years of retardation with only a single shift at 9 years of age. An equally accurate designation by the intelligence quotient would be quite complicated if it were adapted equally well to the different life-ages.
The fact that the Binet mental ages do not signify corresponding norms at each age has been frequently pointed out ([200]). Moreover it is probable that one year of retardation on the scale means a different thing at different chronological ages. With the new Stanford form of the scale, for example, “a year of deviation at age 6 is exactly equivalent to a deviation of 18 months at age 9, and to 2 years at age 12, etc.” ([197]) when measured in terms of the deviation in ability at these ages. This variation does not interfere, however, with our use of the “years of retardation” merely as a short method for describing empirically the positions on the scale which roughly and conservatively designate the same percentages of children of low ability at various ages. Besides its convenience in this respect, there is no question but that such a description does help better than a quotient to convince the public of the seriousness of the deficiency.
A more serious theoretical objection to describing the borderline for the immature in terms of years of retardation is that, when one changes from three to four years of retardation, it is clear that a moron who tests VI at 9 years of age would be supposed to be still only VI at 10 years in order to remain below the borderline, while it is known that there is some, albeit a small, amount of progress made by the higher class deficients at these ages. In the crude state in which the Binet scale still remains, however, we have preferred to waive these theoretical objections in favor of the prevalent custom which has the advantages of simplicity, practical convenience, popular significance and, in this case, equal accuracy.