Deficiency and Delinquency: An Interpretation of Mental Testing

by James Burt Miner

5. Compared as to their popular significance, there is no doubt that the lowest 0.5% of the individuals of a particular age has very much more significance to those not familiar with detailed statistical practise than a coefficient or a multiple of the standard deviation. A statement that an adult has only the tested ability of a child of 7 years is certainly much more impressive than his score in other quantitative terms. It will probably always be desirable, therefore, to supplement any other method of scoring by a statement of the individual's test age.

D. Theoretical Advantage of the Percentage Method with Changes in the Form of the Distributions

With our present series of tests, the percentage method will best provide a concept of the equivalence of the borderlines at different ages provided the form of the distribution does not remain uniform. I discussed this question briefly in connection with units of measurement. In considering curves of development, I assembled some of the evidence which makes the assumption of normal distribution or even of a constant skewness at least uncertain. In my opinion the weight of the evidence is against the hypothesis that the distributions retain a constant form during the period of development. If this were clearly demonstrated, both the ratio methods and deviation would fail to express equivalent borderlines for the different ages with the Binet scales. A fixed multiple of the standard deviation or a fixed quotient would exclude different percentages of the population at each age when the skewness varied. By reference to Figures 3 and 5, it can be seen that, if our physical units in which we expressed the measurement were uniform and ability always extended to the same absolute zero point, it is true that .01 of the physical units reached by the best at each age would be the same relative amount of ability of the best at each age, stated in physical units, regardless of the form of the distributions. Such a concept, however, has an unknown biological or social significance so far as I can see, except for a constant form of distribution. The same relative physical score compared with the highest at each age, theoretically might exclude the lowest 40% of one age group, for example, and only 10% of another group provided the distribution varied enough in form. The concept of the same relative amount of ability measured in physical units, so soon as the form of distribution varies from age to age, thus loses significance in terms of the struggle for existence. In that struggle, a vital question is—do the individuals at different ages have to struggle to overcome the same relative number of opponents of better ability at their age? If they do, the individuals might properly be regarded as in equivalent positions in the struggle for social survival, disregarding how far the next better individual is above them on the objective scale. This is the concept accepted by the percentage definition of the borderline as the best available under uncertain forms of distribution.

The recent rapid perfection of objective scales to measure educational products, like ability in handwriting, etc., in equal units running to an absolute zero of ability, suggests that it might be possible ultimately to state the borderline of deficiency in terms of the same relative objective distance between the best and zero ability at each age on a scale of general ability. This ideal could be approached, for example, with the Sylvester form-board test in which the units are seconds required to complete the same task, if we could agree upon a maximum number of seconds without success which should mean no ability, and if this zero should remain the same at each age. It would only be necessary to take, for example, the best position or the median or the upper quartile at each age as the other point of reference. We could then say that a borderline in physical units was always, for example, .01 of the median record at each age above zero. Such a method would provide relatively equal objective borderlines at each age and it would afford a measure which would take into account the ability of the individuals to be competed against instead of merely counting them as the percentage method must. It would be better than a description in units of the standard deviation in that its significance would be more easily understood if the form of distribution varied with age.

To demonstrate its worth, however, this method of defining the borderline in terms of the same proportion of the physical difference between zero and the median at each age, would also have to provide a better prediction of ultimate social failure. It would have to be shown that individuals below the relative objective borderline at maturity were below the same relative objective borderline during immaturity. Moreover, it would have to be shown that this relationship was closer than it would be with percentile records. It is a form of this relative objective measurement which Otis advocates in his “absolute intelligence quotient,” which he proposes as logically the best measure of ability. It consists of the ratio of the score of the individual measured in equal absolute units of intelligence, divided by his age ([163]).

While a relative objective borderline might under certain circumstances afford a better criterion than the same lowest percentage of individuals, there are two very serious practical difficulties which at present make it impossible. In the first place, with the exception of a few motor tests, there are no test results with children of different ages measured in terms of equal objective units for the same task. Even if the Binet year units are equal, as applied to the same task, there is no accurate means of dividing the year units into smaller physical units on the basis of scores with the tests. This makes the use of the Binet scale impossible and we should be forced back upon such tests as the form-board, the ergograph, etc., for which we should have to agree upon an absolute zero of ability. Moreover, mental tests do not lend themselves to measurement in terms merely of rapidity in doing the same task or in terms of other equal physical units since the quality of the work also has to be evaluated and this is usually done in units assumed arbitrarily to measure equivalent degrees of perfection.

The second practical difficulty which at present makes a relative objective borderline impossible is that we know nothing as to the prediction of social failure and success from relative positions on the objective scale used even with the few isolated tests that might be made available. Until we have data on this question, as well as scales of tests for native ability that are measurable to zero ability in objective terms, the percentage method affords the only available way of stating equivalent borderlines when the form of distribution changes.

If the age of arrest of development shifts either earlier or later with different degrees of capacity, then there seems to be no logical escape from a change in the form of distribution. Stern recognized this when he concluded that idiots reach an arrest of development earlier than those better endowed, so he stated that his quotient would not hold for them. He said:

“The feeble-minded child, it must be remembered, not only has a slower rate of development than the normal child, but also reaches a stage of arrest at an age when the normal child's intelligence is still pushing forward in its development. At this time, then, the cleft between the two will be markedly widened.

“From this consideration it follows that the mental quotient can hold good as an index of feeble-mindedness only during that period when the development of the feeble-minded individual is still in progress. It is for this reason that there is no use in calculating the quotient for idiots, because, in their case the stage of arrested development has been entered upon long before the ages at which they are being subjected to examination” ([188]).