Average Intelligence Quotients of Children of Different Ability. (From Chotzen's Tables X & XI.)
| Life-Age | Not Feeble-Minded | Doubtful Defect | Morons | Imbeciles |
|---|---|---|---|---|
| 8 | 0.92 | 0.84 | 0.76 | 0.71 |
| 9 | 0.85 | 0.81 | 0.77 | 0.67 |
| 10 | (0.80) | (0.80) | 0.74 | 0.62 |
| 11 | (0.73) | (0.68) | 0.71 | (0.64) |
| 12 | (0.75) | (0.75) | (0.73) | (0.61) |
| 13 | (0.73) |
The Jaederholm data with his form of the Binet scale, as treated by Pearson, shows a straight regression line for the backward children which falls below the normal development line on the average four months of mental age for each additional year of life from 7-14 ([167]). Accepting Pearson's interpretation that a year of excess or deficiency and a year of growth is a constant unit, we find that the deficient group from special classes was falling continually behind the normals with increase of age a relatively greater distance from any rational reference point. Pearson accounts for this change in the distance between the two groups of normal and backward children, as I understand his paper, by supposing that with increase in age more and more normal children become deficient. It would seem that this data would be more easily explained by supposing that the distributions became skewed toward deficiency for the older ages, rather than that the distributions remained normal and became flatter.
The best evidence as to the relative positions of the curves for deficients and those for average ability would be provided by using psychological tests that could be adequately scored in terms of equal physical units for the same task. The position of various lower percentiles relative to the average or to an assumed reference point could then be compared on the same objective scale. I have reviewed studies of this type in discussing skewed distributions in Chap. XIII, A, c. I there reached the conclusion that the weight of the evidence was that the distributions were slightly skewed in the direction of deficiency, although the evidence was not conclusive. We are now raising the further question whether this skewness increases with age.
On account of the difficulty of determining the points for zero ability in terms of the physical scales used, let us see what conclusion might be reached if we calculated the relative distance of median and low ability of equivalent degree from the scores of the same higher degree of ability assumed as a reference point at the various ages. There seems to be no reason in the theory of measurement why the highest score instead of the lowest score in random samples might not be used for a reference point for comparing the distances between normal and deficient children at different ages. Instead of using the highest single score, it would be better to use the upper quartile or quintile since it would be less affected by a chance error in giving the test.
Applying this method to determining the relative position of median and retarded ability I have calculated the data for the form board test cited previously from Sylvester ([191]) and from Young ([227]). This affords the only adequate evidence of which I know, derived from tests scored in equal physical units given to sufficiently large groups to indicate whether or not the retarded group changes its relative position from the normal group at different ages. The comparison is shown in Fig. 9. With Sylvester's data the distance of the lower quartile in ability from the median is compared with the distance of the upper quartile from the median, the latter distance being taken as a unit. With Young's data for Witmer's form board the quintile is used instead of the quartile and each sex is given separately. Since Young's table shows the scores for half ages, it was necessary to take the average of the two scores, thus giving the approximate score for the middle of the complete age group. The graph discloses no pronounced tendency for the retarded group to fall relatively farther behind the median with increase in age. There are, however, notable fluctuations in the relative positions of the groups so that at 7 years with Young's data for boys and at 13 years for Sylvester's curve the retarded group is twice as far from the median relative to the distance between the median and the corresponding better group as it is at some other times. It is possible that the curves for the older groups of those of poorer ability are too high since it is likely that more of the actually deficient children tend to be dropped from the public school classes with increase in age. Nevertheless, so far as the evidence at present goes it is not sufficient to determine whether the backward and the corresponding better group show a general change in their relative distances from the median with approach to maturity.
Fig. 9. Relative Positions at Each Age of the Median and of Corresponding Bright and Retarded Children with the Form Board Test.
On the other hand the curves indicate the tendency for the distributions to be skewed toward deficiency and for the relative distances to fluctuate as we should expect if the accelerations in growth occurred at different ages for those of different ability. The data of Young suggest that there may be sex differences in the age of acceleration, the backward girls showing accelerations, relative to the upper group at ages 7 and 12, a year or more before the boys. For Sylvester's data the ratio of the distance between the median and the lower quartile divided by the distance between the median and the upper quartile for each of the age groups is as follows: 5 yrs. 1.8, 6 yrs. 2.4, 7 yrs. 3.0, 8 yrs. 2.0, 9 yrs. 2.2, 10 yrs. 2.4, 11 yrs. 2.0, 12 yrs. 1.8, 13 yrs. 3.0, 14 yrs. 2.1. For Young's data the corresponding ratios are—Boys: 6 yrs. 1.5, 7 yrs. 1.9, 8 yrs. 1.5, 9 yrs. 0.8, 10 yrs. 1.6, 11 yrs. 1.2, 12 yrs. 1.4, 13 yrs. 1.0, 14 yrs. 1.3. Girls: 6 yrs. 1.7, 7 yrs. 1.0, 8 yrs. 1.5, 9 yrs. 0.9, 10 yrs. 1.0, 11 yrs. 1.3, 12 yrs. 0.9, 13 yrs. 1.5, 14 yrs. 1.4. Changes in the rate of growth causing asymmetrical distributions are to be expected throughout the periods of growth. A fundamental skewness toward deficient mental capacity, therefore, would be indicated only if it were found at maturity or at ages when the average rate is decreasing, when the more capable individuals would theoretically approach relatively nearer the deficients if the latter accelerated later.
So far as physical growth is concerned Baldwin (74, 75) has shown with repeated annual measurements on the same group of children that the period of adolescent acceleration shifts from 12½ years for the tallest boy to 16 years for the shortest boy. For the tallest girl the maximum height was attained at 14½, for the shortest at 17 years, 3 months. Maturity may be reached at 11 years by a tall well nourished girl, while with a short girl light in weight it may be delayed until 16. “Children above medium height between the chronological ages of 6-18 grow in stature and in physiological maturity in advance of those below the medium height, and they may be physiologically from one to four or five years older than those below the medium height. Those above the medium height have their characteristic pubescent changes and accelerations earlier than those below; there is a relative shifting of the accelerated period according to the individuals' relative heights” ([74]).