Schmidt urges that the deficients are qualitatively different in being “unable to plan”, and then suggests tests which most markedly bring out this distinction between deficient and normal children ([178]). As I have said before, however, this seems rather to be a failure to recognize that such an attempt to find tests which “qualitatively” distinguish the two groups is only an effort to pick those tests which best make measurable the differences between individuals at the extreme of mental ability. As such it is a valuable contribution to this problem. If it is intended as an attempt to set up a qualitative distinction in a mathematical or biological sense, between deficient and passable ability, it seems to me wholly to fail. As I take it, a “qualitative” distinction with Schmidt is only a bigger quantitative distinction and is intended only to mean this.
None of those who advocate quantitative definitions would contend, I believe, as some of their opponents seem to think, that such definitions afford a final diagnosis for particular cases. In attempting to place the borderlines on a scale of tests, this is always done with the clear recognition that such borders are only symptomatic of deficiency. The diagnosis of “social inefficiency,” to use Pearson's term, rests upon many facts among which the test result is only one, albeit the most important.
Other characteristics which each of the above quantitative definitions, except that of a constant absolute amount of deficiency, have in common, or might easily have if they were stated in their best forms, include the possibility of adaptation to any developmental scale, the suggestion of borderlines for both the mature and immature, the distinction of a group which might be regarded as presumably deficient from one that was of better but doubtful ability and of this from a still better group which was presumably socially efficient.
Perhaps the most curious and important thing about these definitions is that they are all substantially identical, except in their terminology so long as general mental capacity is found to distribute in the form of the normal probability curve and to extend to absolute zero ability at each age. This can easily be seen by comparing the distribution curves in Fig. 3. The position of the percentage borderline would always represent the same distance from the average in terms of the standard deviation of each age and the same ratio when the life-age of arrest of development had been determined as the largest divisor. Under these conditions, therefore, these main statements of the quantitative definition agree in supposing that the same proportion of the individuals of each life-age would test deficient. Those who advocate any of these quantitative definitions logically commit themselves to assuming that the percentage of deficients at each age is practically constant, unless they suppose the symmetry of distribution varies or does not extend to the same zero point.
If the distributions do not extend to the same zero points of lowest ability on an objective scale (see Fig. 5), the ratio is clearly at a disadvantage compared with either of the other methods, since it assumes that the same percentage of average ability is an equivalent measure. This does not hold when the lowest ability at different ages is not at the same point on the scale of objective units. For example, .7 of an average 100 units above 0 is not equivalent to .7 of an average 150 points above a zero ability of 30 points on the objective scale. The idea of regarding percentages of averages as equivalent is therefore generally avoided in mental measurement. In case the position of the absolute zero points of ability may be different, the distance from the average should be stated in terms of the deviation. In this respect the method of the deviation or the lowest percentage are equally good so long as the form of distribution does not change.
C. Practical Advantages of the Percentage Method
1. With the percentages fixed at the lowest 0.5% as presumably deficient and the next 1.0% doubtful, these borderlines for tested deficiency have the advantage of being more conservative than those at present advocated. On the basis of our empirical knowledge this is an important reason for urging borderlines on the scales at least as low as those suggested herein. Disregarding the extremely high borderlines which have fallen into disuse, we still find that social deficiency is often presumed for those testing above the lowest 1%. With the new Stanford scale, Terman presumes “definite feeble-mindedness” below an Intelligence Quotient of .70, below which he finds that 1% of 1000 unselected children fell. I Q's from .70 to .80 would include his uncertain group, which he describes as “border-line deficiency, sometimes classified as dullness, often as feeble-mindedness” (57, p. 79). His tables show 5% below an I Q of .78. We have no results with a random group of adults by which to judge how many would be below these borders. When the I Q has been applied to scores with other scales a larger percentage has often been found to be excluded. Fernald has shown that Haines' suggestion of a coefficient of .75 with the Point scale would exclude 16% of 100 Cincinnati girls selected at random from among those who left school at 14 years to go to work ([16]).
Unless the examiner wishes to assume that social inefficiency is more frequent than it has been demonstrated by the practical tests of life, the success of those who have low quotients should make him exceedingly cautious about accepting the various borderlines which have been suggested by those who have not tested their criteria by the percentage method. It is not merely that the borderlines should be lowered, but that they should be lowered under some consistent plan so that we should know as much as is possible about their significance in the prediction of ultimate social inefficiency, and that we should be able to readjust them on the basis of new data or to new scales.
With the Point scale Yerkes and Wood say regarding “the coefficient of intelligence .70, which we accept as the upper limit of intellectual inadequacy or inferiority”: “Our data indicate that grades of intellectual ability measured by the coefficient .70 or less are socially burdensome, ineffective, and usually a menace to racial welfare” ([226]). With the most reliable part of their data, that for children from 8-13, this coefficient excludes the lowest 8.39%. Moreover, the lowest group for which they suggest a borderline, the dependents, falls at .50 or below and includes 1.05%.
2. A second practical advantage of the percentage borderlines on the scale is that they make no assumption as to the uniformity of the norms for the different ages. Except for the Stanford and the Jaederholm scales, there is little evidence that the age norms exclude equivalent portions of the children at the different life ages.