A quantitative definition of intellectual deficiency would certainly be much simpler if it could be assumed that the percentage of deficients at each age is practically constant during the time when a diagnosis of deficiency is most important, say from 5 to 25 years. Otherwise the objection might be raised that it is impracticable to determine different percentages for each year of immaturity or to formulate our borderlines of ability for a particular age. When the general instinctive origin of intellectual deficiency is considered along with the incurability of the condition, we seem to be theoretically justified in assuming that the variation will be slight from one year of life to the next. This assumption is tacitly made by all those who use Stern's quantitative description of deficiency in terms of the mental quotient. On the other hand, there is a feeling among some of the investigators that there is a sudden influx of feeble-minded at particular ages and this position should be examined. Probably more important than this possibility of increase is the question of a decrease in frequency with age on account of the excessive death rate among the deficients.

It is a natural supposition that there is a sudden increase in the proportion of feeble-minded at adolescence. On account of the increased rate of growth at this period we might expect to find greater instability for a few years. It may well be that there is a rather sudden influx of the unstable type of feeble-mindedness at this period. Such an increase may occur without being detected by a series of brief intellectual tests such as the Binet scale. It would be of the conative type of feeble-mindedness that cannot at present be diagnosed by objective tests, the type that requires diagnosis by expert opinion. It is to be noted, however, that Binet, who paid much attention to the unstable type, says: “Since the ill-balanced are so numerous at ten years of age, and even at eight, we conclude that in many cases the mental instability is not the result of the perturbation which precedes puberty. This physiological explanation is not of such general application as is sometimes supposed” (77, p. 18).

Only when an emotional disturbance is so great as to be detectable by mental tests will this influx need to be taken into consideration in stating the borderline for objective tests. The evidence that few cases of feeble-mindedness are not detectable until after ten years of age is all the other way. With the Stanford measuring scale, Terman and his co-workers did not even find a noticeable increase in the variability of the groups at the ages of adolescence (57, p. 555). It is to be remembered also that we are not concerned here with mere instability which corrects itself with more maturity, such as has been described by Bronner among delinquents. This does not, of course, amount to an incurable conative deficiency and is not classified under feeble-mindedness.

Goddard has suggested that possibly the moral imbecile group comes into our class of feeble-minded suddenly with a common arrest of development at about the stage reached by the nine-year-old. He notes that “of the twenty-three cases of this sort picked out for us (at Vineland) by the head of the school department, fifteen are in the nine-year-old group, five in the ten-year-old, two in the eleven, and one in the twelve” ([113]). He regards this evidence, however, as meager and only suggestive. Doll has given evidence of late appearance of retardation in rare cases (100 and 99).

It is to be noted that if a sudden change is found in the percentage of children falling below a certain test standard it is perhaps more likely to mean that there is a change in the difficulty of the tests at that point. For example our Table V shows 1.3% of the nine-year-olds test two or more years retarded, while 18.9% of the ten-year-olds are retarded two years or more. This presumably indicates a change in the relative difficulty of the tests for VII and VIII rather than a change in the frequency of retardation at ages nine and ten. When we turn to Goddard's norms for VII and VIII we find that 81% of the seven-year-old children pass the norm for VII while only 56% of the eight-year-old children pass the norm for VIII.

The Jaederholm data ([167]) obtained by applying the Binet tests to pupils in the regular school classes and in special classes for the retarded may suggest a possible influx of intellectual deficiency at about 12 years of age or else “more mental stagnation in the intellectually defective” at this life-age and after. If one were to define intellectual deficiency in terms of the standard deviation of the regular school children, this data suggests that there is a marked increase in the number of children sent to the special classes at 12 years of age who are -4 S. D. or lower. Roughly speaking it amounts to 36 children at 12 years of age, 36 at 13, and 21 at 14, as compared with 11 at 11 years and 13 at 10 years. On the other hand, this may as well mean that intellectual deficiency becomes greater in degree rather than in frequency at these ages. The latter interpretation is adopted by Pearson for the Jaederholm data, so that it is perhaps not necessary to consider this evidence further. On the average the pupils in the special classes fall about .3 S. D. months further behind regular school children with each added year of life from 5 to 14 inclusive. A third possible interpretation of the greater number showing the degree of deficiency measured by -4 S. D. with the older ages should be mentioned. It is possible that 1 S. D. has not the same significance for 5-year-olds as for 12-year-olds. The distribution of abilities at succeeding ages may be progressively more and more skewed in the direction of deficiency. We shall return to this point in Part Two as showing the advantage of the percentage definition over a definition in terms of the deviation. In connection with the Jaederholm data on special classes one should also consider the fact that younger children are not as likely to be detected by the teachers and sent to the special classes. It is possible also that the difference in difficulty of the tests for different age groups is somewhat obscured by using a year of excess or deficiency as a constant unit as Pearson has in treating this data. The bearing of this difference in difficulty was pointed out above for Goddard's data.

The investigations by Pearson of children in the regular school classes indicate that there is no important shift with maturity in the frequency of those with different degrees of ability, when the ability is measured either in terms of years of excess or deficiency with the Jaederholm form of the Binet scale or in terms of estimates of ability relative to children of the same age (166 and 167). In both these studies the correlation of ability with age was shown to be almost zero. For tested ability for 261 school children “r” was .0105, P. E. .0417; with the estimated ability, the correlation ratios were for 2389 boys, .054, P. E. .014; for 2249 girls, .081, P. E. .014. Until we have better data this is certainly the most authoritative quantitative answer to the question of the shift with age in the frequency of the same relative degree of mental capacity.

The best method of empirically settling this question of the early appearance and constancy of deficiency would be to test the same group of children again after they had reached maturity and find out how many of those who tested in the lowest X per cent. still remained in the same relative position. This is, of course, not possible at present, but it certainly should be done before we are dogmatic as to the permanent isolation of the lowest X percentage at any age. The nearest approach to this sort of evidence is Goddard's three annual testings of a group of 346 feeble-minded children with the Binet scale (117, p. 121-131). Among these 109 showed no variation, 123 gained or lost 0.1 or 0.2 year, 18 lost 0.3 or more, and only 96 gained 0.3 or more of a year. With so small a change in absolute tested ability the probability of a change in position relative to normal children seems to be slight. Only one of the 76 who had tested in the idiot group gained as much as a half year in tested age in three years.

It is not possible to settle this question of the constancy of the percentage of intellectual deficiency from one life-age to the next by considering the frequency of different ages of children among those who are sent to special classes for retarded pupils. This is evident from the fact that these classes contain a considerable proportion of those who are feeble mentally mainly because of conative disturbances. These would not be detected by our present tests and would not be classed as intellectually deficient. In the second place the pupils for the special classes are usually selected mainly on the advice of their teachers, who cannot, of course, without tests select those who are intellectually deficient except by trying them for a number of years in the regular school classes. This means that a smaller percentage of pupils in the special classes at the younger ages is to be expected.

The figures of the U.S. Census as to the ages of inmates of the institutions for feeble-minded are also of little significance in connection with the question of the variation from age to age. That the number of inmates at the different ages is affected most largely by the pressure of necessity for shifting the care from their homes to the institution is shown by the fact that three-fourths of the admissions are of persons over 10 years of age. It is also indicated by the fact that for the period from 15 to 19 the males are over 20% more frequent than females, while from 30-34 the females are nearly 20% more frequent. Considering those ages most frequently represented in the institutions, 10-24 years, the average variation for the three five-year periods in the percentage of the population of the corresponding ages who are in these institutions is only 0.01%. The middle five-year period has the most, but even if there were a cumulation of feeble-mindedness with age, which is not shown, we would anticipate a change of not more than 0.05% for these 15 years. This would be clearly negligible in considering the general problem.