Special talents and defects

I. THE COEFFICIENT OF CORRELATION

The question is: How are mental capacities mutually related, with regard to amounts of each found in given individuals?

Before verifiable facts can be established in a field of knowledge, it is necessary to introduce therein methods of enumeration and measurement. The question above propounded has waited long for answer, because of the great difficulty of applying mathematics to mental phenomena. The answer required first that single functions be accurately scored, and then that a measurement be obtained of the relationship between and among the single functions.

It seems well agreed that the quantitative determination of the relationship between and among mental characteristics began with Galton, about 1885. Various scholars have presented discussions of the subject since then, notably Baerwald in 1896, Spearman in 1904, Stern in 1911, Meumann in 1913, and Thorndike in 1913, each of whom summarized the findings up to the time of writing, with original interpretations.

The methods of quantitative measurement used to study the constitution of mental abilities, or functions, as related to each other, are chiefly those of correlation—simple correlation, multiple correlation, and partial correlation.

It is not within the scope of the present volume to give consideration to these methods as such. Highly technical instruction in the theory and practice of measurement is necessary for complete understanding of them. The results may be comprehended for our purposes, without complete knowledge of the methods. Much of the evidence we now have in the matter of relationships among mental functions has been obtained by the method of simple correlation. A brief exposition of how a relationship is established between two variable functions within a group, by simple correlation, will suffice to give a general understanding of the term coefficient of correlation, which is used here, and which frequently appears in modern texts of educational psychology. The interpretation of coefficients of correlation should not, however, be undertaken independently without full knowledge, as competent interpretation for practical purposes must take into account all the conditions under which they have been derived.

Below are listed fourteen school children, each of whom has been measured in each of two mental functions: (1) mental age, determined by a standard scale for measuring general intelligence (Stanford-Binet), and (2) spelling ability, as measured by a standard spelling scale (Ayres’ scale). These children were selected for study, because they appeared to be characterized by special discrepancy between the two functions.

We wish now to know whether and to what extent the child who falls high in the distribution of mental ages also falls high in the distribution of spelling ability. According to the formula which is most useful in this case,^[1] we arrange these pupils in their order of merit for one of the functions measured, e.g. for mental age. We then find the rank for each, within the group, in the second function, which is here spelling ability. The difference in rank between the paired functions is then found for each pupil, and the correlation formula is applied.^[2]

If there is in fact perfect correspondence, so that each pupil holds the same rank on the distribution in both functions, a perfect positive correlation is obtained, the coefficient of correlation being expressed as 1.00. If no relationship at all exists between the two functions measured, so that nothing whatever can be predicted of either from knowing about the other, the coefficient of correlation will be 0.00^[3] If there exists a perfect negative relationship, so that the person who stands highest in one stands lowest in the other, and so forth through the series, in a perfect inverse standing of all members, then a coefficient of correlation expressed by −1.00 is obtained.

In the sample given, the coefficient of correlation obtained is .081, which not being reliably greater than zero (because of possible error due to the smallness of the group and other conditions) tells us that the two functions are in this case related to each other only very slightly, if at all. The child who stands above the average of the group in mental age, may or may not stand above the group average in spelling. With a relationship so far from unity as is expressed by a coefficient of .081, we may expect to find in this group comparatively intelligent children who are very poor spellers, and good spellers who stand low in mental age. Among children taken at random, however, a different relationship exists between spelling ability and general intelligence, as represented by mental age. The positive correlation is much higher among children not selected, as these were, for an observed discrepancy.

At the present time the more elaborate methods of partial correlation and multiple correlation are being applied to the study of relationships, where more than two functions are involved. Into the intricacies of these we shall not enter, except as concerns their results.

II. GENERAL INTELLIGENCE vs. SPECIAL APTITUDES

The original attempts to apply mathematical formulæ to the study of relationship among mental traits eventuated in divergent hypotheses. In England, Spearman, with his students and collaborators, interpreted his researches to mean that there is in mental constitution a “general factor,” which shows itself in all the performances of a given individual. This would render relatively predictable the quality of performance in all functions, from knowledge of performance in one function. “All branches of intellectual activity have in common one fundamental function (or group of functions), whereas the remaining or specific elements of the activity seem in every case to be wholly different from that in all others.... The function almost entirely controls the relative position of children at school (after making due allowance for differences of age), and is nine parts out of ten responsible for success in such a simple act as Discrimination of Pitch.... Its relation to the intellectual activity does not appear to be of any loosely connected or auxiliary character (such as willingness to make an effort, readiness in adaption to unfamiliar tests, or dexterity in the fashion of executing them), but rather to be intimately bound up in the very essence of the process.”

Spearman noted that, though all functions seemed related to this “common factor,” they were not all equally related in his results; wherefore he formulated the concept of a hierarchy of relatedness. Discussion as to the essential nature of the fundamental factor was reserved, but it was predicted from the correlations made that “general intelligence” could and would be measured for practical purposes. This interpretation was based upon the fact that among abilities which yielded to his measurement, Spearman could find only positive coefficients of correlation, when the groups were large and the human beings non-select.

In the United States, Thorndike and his collaborators were most struck by the fact that the coefficients obtained fell short, in many cases far short, of unity. They laid stress upon the imperfection of the relations revealed, and were able to show that between some functions, such as discriminating among the lengths of lines, and others, such as naming the opposites of words, the correlation dropped in groups investigated to approximately zero.

As a result of interpretation from their point of view, they wrote as follows: “One is almost tempted to replace Spearman’s statement by the equally extravagant one that there is nothing whatever common to all mental functions, or to any half of them.” They maintained that mental functions are specialized, and that when excellence in one is correlated with excellence in another, “this is due chiefly to the fact that the two involve identical elements in their execution. It is not due to one and the same ‘faculty,’ which presides over their activities.”

These two divergent interpretations of the same array of data have been cited, because the controversy involved is of first rate importance for mental measurement, for the understanding of individuals, and for education. The controversy now appears to have been one of emphasis. To recapitulate, Spearman stressed the positive aspect of the coefficients found, and declared mental traits to be distributed so that status in one is predictable from status in another. Thorndike emphasized the reduction from unity of the coefficients, and formulated the hypothesis that there is no absolutely predictable coherence among mental functions, that each is special to itself within an individual. No laboratory scientist has ever found reason for adding a third side to the controversy, by advocating seriously that mental traits are compensatory in relation to each other. Negative coefficients of correlation have never been found, except occasionally by chance or selection.^[4] All know that the correlations among amounts of traits are positive. It is the reduction from unity which has caused the disagreements of interpretation.

During the twenty years which have elapsed since the first interpretations were set forth there have been modifications of each hypothesis, in the direction of mutual reconciliation. This has come about through extended researches by many inquirers, furnishing additional data.

III. CORRELATION OF ABILITIES IN VARIOUS GROUPS

Some of the significant studies of correlation made since Spearman and Thorndike proposed their conflicting interpretations, have been cited in the appended list of references. Two samples of the results of these studies are herewith presented. The first is from Simpson’s study of mental tests given to two groups of adults, chosen respectively from the opposite extremes of competency, as shown by social-economic success. One group was composed of successful professional educators. The other was composed of unskilled laborers and unemployed men. The table on page 18 shows how the traits measured cohere among these individuals. The coefficients are positive, in the majority of cases highly so.

The second sample is from Weglein’s study of standing in school subjects, among high school pupils.

Bearing in mind that, if no mutual relationship exists among the abilities considered, coefficients of correlation will approach zero, it is clear that there is decided positive, but not perfect, correspondence. The wider the range of competence tested, the greater the correspondence found. High school pupils (from among whom those having very little ability for the subject matter taught have already been eliminated) show smaller coefficients than do the persons measured by Simpson. If all adolescents in existence were obliged to study the subjects listed by Weglein, and if the resulting grades were then correlated, the coefficients would be notably higher than those recorded.

These are fair samples of the results of studies in correlation, among mental functions, in groups of individuals more or less select. Even physical traits, like height and longevity, have been found to give slight positive correlation with mental traits. Evidently there is a general organic quality, which shows itself to some extent wherever the individual is fairly tested or “sampled.”

IV. STUDIES OF DISORGANIZING MINDS

Another series of attempts at the solution of this problem has been made through observations upon deteriorating minds. The question is, Do mental functions deteriorate together or separately in dements? When a person is “losing his mind,” is the impairment general or selective in its progress?

The study of demented persons had been carried on by a few investigators in the hope that the decay of capacities might throw light upon their relationships. The chief obstacle to study from this approach has been that the investigators have never been able to know the original mentality of their subjects. They have always been obliged to make assumptions. It is difficult to see how this factor may be controlled, short of filing careful mental analyses of great sections of the population in youth. The chief conditions in which decay of ability is most probably present, as distinguished from decay of effort and attitude, are senile dementia, dementia paralytica, and alcoholic psychosis; and it cannot be known beforehand which persons are destined to represent these conditions. It cannot be predicted who will live long enough to become senile, who will contract syphilis, eventuating in general paresis, or who will be a chronic alcoholic. It is true that original mental status may be inferred with a moderate amount of accuracy from school status attained. If the dements studied had all been high school graduates, for instance, then we could be certain that the performances shown in the recorded studies really represent deterioration.

Unfortunately, the subjects of study have been, with rare exceptions, persons of elementary education and humble social status. They come from those sections of the education-occupation distributions, where very limited capacity is found. Therefore, we are rather uncertain as to how much deterioration from original status has really taken place. So far as actual figures go, it is not shown that there has been decay of intellect.

However, assuming that these segregated persons had actually deteriorated in their ability to perform tasks, let us inquire what the researches show. Binet and Simon worked with forty adults, classified as senile dements or as victims of dementia paralytica. They conclude that “Every dement has an intellectual level below normal,” as measured by tests of general intelligence. The limitations of dements are, nevertheless, qualitatively different from those of other incompetents (children and the feeble-minded); and the reactions of the senile differ from those with dementia paralytica. Of the victim of dementia paralytica they say, “He has not tumbled down the ladder of development, rung by rung. His is a difficulty of functioning.” “It is characteristic in these losses of functioning that the subject knows how to meet the problem submitted to him; he has the knowledge, but from time to time the power fails him.” This inertia of comprehension is general, and has the effect of lowering the total level of performance, though the particular items of failure and success may vary markedly from occasion to occasion. It is hardly the same thing as actual decay of a structure. Thus one cannot predict the responses of these dements, as one can those of other incompetents, like children and imbeciles, because their errors and failures have a remarkable degree of inconsistency. “In a general way, one can hardly foresee how such a one is going to conduct himself, for special failures and successes are at such variance with the general level.” “General paralytics are hardly able to perform the hundredth part of what they know.”

Senile dements are different, in that they actually no longer know. The structure itself has been demolished, not merely has it been paralyzed as to function. According to the observations of Binet and Simon the abilities of senile dements as a group are by no means equally impaired. They cannot remember events nor learn new things, yet they retain the power of auto-criticism, many complaining that they no longer “know anything.” They may be degraded to the level of early childhood in ability to repeat digits, yet retain use of the vocabulary of a superior adult.

These observations are extremely suggestive, but they lack statistical validity, being limited to narrative descriptions. It is true that one who has worked much among dements in a practical way, recognizes the pictures drawn by Binet, of persons decayed in some functions, yet “surprisingly preserved” in others. Proof of the extent to which this characteristically happens would necessarily be derived from tests of large numbers of cases, treated mathematically, and not by the method of narrative.

Hart and Spearman more recently presented a study of sixty-one insane persons,^[5] asking the question, “Does an insane person present, as a rule, much greater inequality of performance than a sane one?” Recognizing the error from not knowing the original status of the presumably deteriorated minds, in all the various functions to be tested, the attempt was made to allow for this by testing in the same way thirty-three sane persons, selected presumably to represent what the insane were like before they became alienated. Nineteen mental functions were thus tested, and the results were then treated by the method of correlation, the assumption being that if there were greater inequality among mental functions in the insane (that is to say, among deteriorated minds) than among the sane, this would show itself in diminished coefficients of correlation.

It is interesting to consult the original tables of data, which, however, will not be presented here. The conclusion reached is that “The inequality between the powers of the same person for different kinds of performances does not appear to be appreciably greater in insanity than in health, nor in one of the forms of insanity tested than in another. Thus, in the main, the mental injury appears to be of a perfectly diffuse character, or to constitute a lowering of the whole intellectual level.... Over and above this general impairment, elaborate methods can also detect certain damages characteristic of particular maladies. These are very narrow and specific in kind, but probably may be correspondingly grave in intensity.”

Spearman thus again maintains his “two factor” theory of endowment—the “general factor” conditioning performance as a whole, and “specific factors” conditioning certain mental functions to a much greater extent than others. To determine what these special mental functions are, Spearman leaves to further research.

This careful investigation is nevertheless imperfect for the purpose, which is to learn whether there is selective enfeeblement of abilities. It is really impossible to know that deterioration has occurred, unless there have been measurements made beforehand. Sane persons, selected from the same social stratum, are not entirely reliable as a control, because those who are of the psychic constitution destined for insanity undoubtedly differ originally from those who remain sane, and this difference may involve a difference in mental abilities, either of amount or of relationship. The degree of deterioration calculated by Hart and Spearman may be merely a matter of original differences in central tendency between the two groups.

Here, too, it should be noted that Hart and Spearman mixed a variety of psychoses (even including an imbecile not deteriorated so far as known), both those that do involve actual decay of ability, and those that involve only disturbances of general auxiliary functions, like attitude and effort. Just what would be the effect of this mixing upon the correlations could be told only if we knew how each form of disorder characteristically affects the relationship among mental functions, which is unknown. If mental functions are differently selected for impairment in the different forms of psychosis, then we should expect diminished coefficients of correlation among the insane, because mixing the psychoses would produce inconsistency of rank within the group. If, however, certain functions were deteriorated in all or nearly all of the insane, others remaining intact, or relatively so, this selective enfeeblement would not appear in correlation coefficients. Facts like those observed by Binet and Simon might be obscured by the methods of Hart and Spearman.

Moore, working subsequent to Hart and Spearman, limited his investigation to those cases believed by psychiatrists to be characterized by real loss of abilities, the dementias: dementia paralytica, senile dementia, and alcoholic dementia. He tested thirty dements, laborers and tradesmen, and, as controls, six young men from the same occupational group, in the following mental functions: (1) perceiving eight each (in a series) of real objects, pictures of objects, printed words, and spoken words, referring to real objects of ordinary everyday experience; (2) repeating after one exposure of the series as much of it as could be remembered without regard to sequence; (3) after a minute of mental work at calculation, repeating again what could then be remembered of the series. Moore then correlated performance within the group in each of these functions with that in each of the others. The coefficients thus resulting are interpreted as follows: “The average of all correlations of perception with the various memories is .538.... That the average correlation for memory and perception is as high as .538 shows that there must be a common factor present. But its presence does not exclude the existence of special forms of mental ability.” Moore also correlated perceiving with remembering in the functions separately, and remembering immediately with remembering after a minute of distraction. These coefficients are positive, and mostly high, but not perfect.

The work of Moore does not seem to go beyond knowledge already obtained from study of sane persons. The coefficients do not prove that the amounts of deterioration in the functions had been equal; or even that deterioration had taken place. Moore’s six sane subjects were too few to constitute a control, and are not referred to as such in treating results. Instead, Moore refers the reader to the records of subjects in preceding monographs to show that “the low values of these subjects (the insane) are distinctly pathological.” This comparison is seen to be invalid, for the subjects referred to as establishing the criterion of intactness are professors and university students, almost certainly much higher in ability by original nature than the insane group.

Assuming, nevertheless, here also that the subjects really had deteriorated, the method of correlation must again be brought under criticism as ill adapted to answer questions concerning selective enfeeblement. A group of senile dements, all high school graduates, might, for instance, be not at all deteriorated from their original status in the mechanics of reading, but greatly deteriorated in the ability to tell what has been read. Yet correlation might result in a positive coefficient as high as that found among typical high school graduates, if the decay in repeating matter took place in proportion to the degree of ability originally present in each individual. There might be marked selective impairment, which would be hidden in coefficients of correlation.

The problem of selective enfeeblement must be investigated by computing deviation in various functions from a known norm or standard in each; and the person’s original status in that function must be known. For such investigation senile dements would seem to be the best subjects, since in them there is natural decay of functions. It is, however, difficult to find very aged deteriorated persons, whose original status is known (known, at least, to have been generally high), and who have not some sensory or motor handicap to complicate performance, such as deafness, failing vision, or palsy.

The net result, for our purposes, of studies so far made of mental decay is not very helpful, because (1) the original status of the subjects is never known, (2) the psychoses have been mixed in experiment, without preliminary test-knowledge of the characteristics of each, if any, and (3) the method of correlation, which has been used, is not suited to show selective enfeeblement of mental functions. Every study made has suffered from one or more of these hindrances to interpretation. The information gleaned from them is much the same as that already gleaned from studies of the undeteriorated, namely, that among people (whether sane or insane) those who hold a certain rank within a group in one function tend also to hold a similar rank within that group in other functions. The question of selective enfeeblement of a function within a group of the insane remains unanswered. The investigators of the demented have, however, made a particular contribution in pointing the way to a new source of light. For the study of mental decay, when carried on by adequate methods, extremely difficult of attainment, is sure to throw light on the relationships among mental functions. From it we shall learn whether some functions remain intact, with impairment of other functions.