CHAPTER II

THE RELATIONSHIPS AMONG CAPACITIES

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]

TABLE FROM HOLLINGWORTH Showing rank in each of two mental functions, within a group of fifth grade children, selected for special disability in spelling. The coefficient of correlation obtained is .081. ═══════════════════════╤═══════════════════════╤═══════════════════════ NAME │ MENTAL AGE │ SPELLING ABILITY │ YRS. MOS. │ PER CENT CORRECT │ (STANFORD-BINET) │ LISTS Q AND R (AYRES) ───────────────────────┼───────────────────────┼─────────────────────── RL │ 13 7│ 90.1 JP │ 12 5│ 95.2 HA │ 12 2│ 81.7 MG │ 11 6│ 31.7 LK │ 10 10│ 80.2 SSh │ 10 10│ 77.9 SSc │ 10 9│ 81.8 MS │ 10 9│ 34.1 PJ │ 10 4│ 32.6 HL │ 10 1│ 58.9 RH │ 9 8│ 93.1 MU │ 9 8│ 57.0 BN │ 9 6│ 92.1 HR │ 8 3│ 81.8 ═══════════════════════╧═══════════════════════╧═══════════════════════

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.

TABLE FROM SIMPSON

PEARSON COEFFICIENTS OF CORRELATION (CORRECTED FOR ATTENUATION)

Correlations of abilities in two selected groups, and in the two treated as one group. In the case of each test the heavy-face figure given first is for the Good and Poor together, divergences being measured from the median of the 37 individuals. The second figure is for the Good group, divergences being measured from its median. The third figure is for the Poor group.

═══════════╤══════════════════════════════════════════════════════════ │EBBINGHAUS HARD MEMORY EASY A MEMORY ADDING │ TEST OPPOSITES OF OPPOSITES TEST OF │ WORDS PASSAGES ───────────┼────────────────────────────────────────────────────────── │ =92= =92= =75= =68= =91= =71= Ebbinghaus │ 66 67 48 03 42 55 test │ │ 90 78 90 76 61 63 │ │ =92= =92= =81= =76= =86= =74= Hard │ 66 75 93 15 45 79 Opposites │ │ 90 77 78 65 64 51 │ │ =92= =92= =68= =70= =89= =56= Memory of │ 67 75 52 −13 41 20 Words │ │ 78 77 70 88 100 23 │ │ =75= =81= =68= =71= =69= =70= Easy │ 48 93 52 05 05 45 Opposites │ │ 90 78 70 51 58 50 │ │ =68= =76= =70= =71= =60= =67= A Test │ 03 15 −13 05 14 59 │ 76 65 88 51 48 39 │ │ =91= =86= =89= =69= =60= =66= Memory of │ 42 45 41 05 14 20 Passages │ │ 61 64 100 58 48 15 │ │ =71= =74= =56= =70= =67= =66= Adding │ 55 79 20 45 59 20 │ 63 51 23 50 39 15 │ │ =54= =64= =67= =54= =94= =60= =44= Geometrical│ 00 07 06 38 68 −30 13 Forms │ │ 36 33 56 34 91 41 19 │ │ =72= =72= =82= =43= =44= =63= =46= Learning │ 22 14 53 −04 −16 −26 12 Pairs │ │ 73 66 44 64 72 22 51 │ │ =50= =70= =51= =50= =84= =38= =77= Completing │ 67 100 100 100 04 35 86 Words │ │ 71 49 43 49 88 13 70 │ │ =26= =25= =06= =53= =27= =12= =27= Drawing │ −17 10 −23 00 −10 −24 −49 Lengths │ │ 27 13 −09 43 08 09 05 │ │ =52= =55= =59= =56= =57= =58= =17= Estimating │ 28 −08 44 −02 −11 −36 04 Lengths │ │ 01 −02 16 16 13 35 −40 ───────────┴──────────────────────────────────────────────────────────

═══════════╤══════════════════════════════════════════════════ │GEOMETRICAL LEARNING COMPLETING DRAWING ESTIMATING │ FORMS PAIRS WORDS LENGTHS LENGTHS │ ───────────┼────────────────────────────────────────────────── │ =54= =72= =50= =26= =52= Ebbinghaus │ 00 22 67 −17 28 test │ │ 36 73 71 27 01 │ │ =64= =72= =70= =25= =55= Hard │ 07 14 100 10 −08 Opposites │ │ 33 66 49 13 −02 │ │ =67= =82= =51= =06= =59= Memory of │ 06 53 100 −23 44 Words │ │ 56 44 43 −09 16 │ │ =54= =43= =50= =53= =56= Easy │ 38 −04 100 00 −02 Opposites │ │ 34 64 49 43 16 │ │ =94= =44= =84= =27= =57= A Test │ 68 −16 04 −10 −11 │ 91 72 88 08 13 │ │ =60= =63= =38= =12= =58= Memory of │ −30 −26 35 −24 −36 Passages │ │ 41 22 13 09 35 │ │ =44= =46= =77= =27= =17= Adding │ 13 12 86 −49 04 │ 19 51 70 05 −40 │ │ =40= =61= =30= =35= Geometrical│ −23 00 40 −14 Forms │ │ 39 32 14 07 │ │ =40= =34= =04= =54= Learning │ −23 74 −38 61 Pairs │ │ 39 34 20 36 │ │ =61= =34= =17= =22= Completing │ 00 74 −04 06 Words │ │ 32 34 00 −28 │ │ =30= =04= =17= =55= Drawing │ 40 −38 −04 −41 Lengths │ │ 14 20 00 34 │ │ =35= =54= =22= =55= Estimating │ −14 61 06 −41 Lengths │ │ 07 36 −28 34 ───────────┴──────────────────────────────────────────────────

TABLE FROM WEGLEIN │ │ Coefficients of correlation between school subjects (teachers’ marks) in the case of 59 high school pupils. │ │ ACADEMIC GROUP ╒════════════╤══════════╤══════════╤══════════╤══════════╤══════════╕ │ │ ENG. I │ ALG. I │ HIST. I │ LATIN I │ DRAWING │ ├────────────┼──────────┼──────────┼──────────┼──────────┼──────────┤ │English I │ │ .22│ .20│ .19│ .37│ │Algebra I │ .22│ │ .42│ .65│ .09│ │History I │ .20│ .42│ │ .57│ .13│ │Latin I │ .19│ .65│ .57│ │ −.22│ │Drawing │ .37│ .09│ .13│ −.22│ │ ╘════════════╧══════════╧══════════╧══════════╧══════════╧══════════╛

COMMERCIAL GROUP ╒═══════════════╤═══════╤═══════╤═══════════╤═══════╤═══════╤═══════╕ │ │ENG. I │ BKK. │COM. ARITH.│STENOG.│TYPEWR.│DRAWING│ ├───────────────┼───────┼───────┼───────────┼───────┼───────┼───────┤ │English I │ │ .69│ .52│ .54│ .50│ .15│ │Bookkeeping │ .69│ │ .66│ .48│ .50│ .50│ │Com. Arithmetic│ .52│ .66│ │ .38│ .52│ .53│ │Stenography │ .54│ .48│ .38│ │ .51│ .21│ │Typewriting │ .50│ .50│ .52│ .51│ │ .31│ │Drawing │ .15│ .50│ .53│ .21│ .31│ │ ╘═══════════════╧═══════╧═══════╧═══════════╧═══════╧═══════╧═══════╛

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.

V. IS INTELLECT INHERITED AS A UNIT?

There are still other approaches to the study of the constitution of intellect. One is through the investigation of heredity. The question is whether intellect is inherited as a unit, or whether some different formula is indicated. If intellect is a unit character, subject to but one determiner in the germ-plasm, then it should act as an “all or none” capacity in its appearance among offspring of given matings. Children should be separable into distinct groups, each having a different median with respect to intellect, _i.e._ those who have intellect and those who lack it.

The methods of mental measurement teach us plainly that intellect is not inherited in this way. Instead of a broken curve, indicating a division of children into those who inherit and those who fail to inherit a unit character, we obtain the curve already demonstrated, which is continuous and symmetrical. There is but one diversified group of children, with respect to intellect—not distinct groups.

The inheritance of intellect does not, therefore, follow the simple formula of unit characters, as does the shape of peas, the color of rabbits’ coats, or eye-color in man. The trait we measure and name as general intelligence is a complex, resulting from the incidence of a great number of functions, acting together in a great number of ways, yet cohering in respect to amounts found in given individuals.

Possibly each of the indefinitely numerous functions, which thus appear to act together as man’s intellect, may be a unit character, inherited according to Mendel’s formula. Such a possibility is at present purely speculative.

The puzzle is that a given individual should “hit,” as it were, at approximately the same point in the distribution of nearly every function.

VI. CAN AN INTELLECT BE TRAINED AS A UNIT?

Studies of the learning process also give light upon the organization of capacities. The question here is as to whether training in one function spreads equally to all other functions. Is it possible to “train the mind” as a whole? Will it raise the proficiency of all performances fifty per cent, if a fifty per cent gain is achieved in Latin composition?

Numerous attempts have been made to determine the extent to which skill acquired in one performance increases skill in other performances. The conclusion which emerges from these studies is that _intellect cannot be trained as a unit_. Transfer of training from one function to other functions is far from complete. Apparently, there is spread of improvement from practice in a function only to such other functions as have elements in common with it. If two performances differ in any way, there is something in the second that remains _untrained_ by the practice given to the first. If two performances differ in all respects, the second seems not to derive any benefit at all from training in the first.

To a very highly intelligent individual, nearly all situations and performances tend to have some identical elements, no doubt. To a very dull person, relatively few situations or demands present identical elements, for the dull perceive only gross similarities and differences. Thus, spread of improvement is without doubt greatest for the innately gifted, and least for the innately inferior minds. In connection with the present discussion, however, the chief point of interest is that no mind, of whatever degree of innate integrity and sensitivity, can be trained as a unit. Each function has elements special to itself, and some functions are very highly specialized, as regards the amount of transfer of training from them to others, or from others to them.

The evidence from learning, therefore, substantiates the evidence from heredity, indicating that intellect is not a unit, but a complex of many capacities, coinciding mysteriously in amount to a very marked extent in an individual.

VII. THE HIERARCHY OF ABILITIES

It has been stated that though all, or nearly all, mental functions so far measured and correlated, yield positive coefficients, all do not show an equal amount of positive correlation. Certain mental functions, for example, are shown to yield coefficients of as much as .80, for a total correlation with others of a series; while some yield coefficients as low as .10, approaching absence of relationship. To explain these facts, Spearman formulated the concept of a hierarchy of relatedness to a “general factor.” Those abilities showing slight correlation with others in series of tests, were thought of as but loosely related to “general intelligence,” and as constituting “special abilities.” They might be displayed by persons inferior in general, or might be lacking in persons otherwise superior.

Here again, the facts are not in question. It is admitted by all that functions show different amounts of positive correlation with one another, and of total correlation with members of a series. Not all experts agree, however, with Spearman’s theoretical explanation of the phenomena. Thomson has recently shown, by tossing dice of various colors, that in this game of chance (in which there is no “general factor,” but only many independent factors), hierarchical order of correlation coefficients is almost sure to be obtained, for combinations resulting from throws. Thomson, therefore, holds that the theory of a “general factor,” participating in all the separate performances of an individual, is not proved from the facts about correlation coefficients. He proposes the following, regarded by him as an alternative: “The mind, in carrying out any activity such as a mental test, has two levels at which it can operate. The elements of activity at the lower level are entirely specific, but those at the higher level are such that they may come into play in different activities. Any activity is a sample of these elements. The elements are assumed to be additive like dice, and each to act on the ‘all or none’ principle, not being in fact further divisible.”

It is not quite easy to see that this theory, finally proposed by Thomson, which might be termed the “two level” theory, is very different from Spearman’s “two factor” theory, nor why the terms “higher” and “lower” should be introduced. But demonstration of the probability of obtaining a hierarchy of correlations simply from the tossing together by chance of independent factors, as with dice, adds new data for consideration. It might be that non-biological principles of probability are sufficient to explain the hierarchical order of correlations, among many tests administered to a given group, just as they are apparently sufficient to account for the particular form in which ability in any single test is distributed through the human species.

But if this is so, how account for the _consistency_ with which certain abilities, like ability to draw, are repeatedly shown to correlate but slightly, while others, like completing sentences, repeatedly yield high total correlation? How account for the fact that there is marked coherence among certain groups of tests, such as “tests dealing with words only,” and “tests dealing with numbers only,” as contrasted with the relative lack of coherence among “tests, some dealing with number, and some with words”? It would seem that these phenomena must be at bottom _biological_. It cannot, for instance, be demonstrated that yellow dice and red dice thrown, wherever and by whomever cast, tend always to correlate high, while green and maroon dice tend always to correlate low with each other, and with yellow and red dice. Nor can it be demonstrated that dice colored, let us say, from one end of the spectrum tend always to correlate high among themselves, but much lower with the dice colored from the other end of the spectrum, wherever and by whomever cast.

Furthermore, die-casting will not give a relationship in which throws resulting in low scores are paired with low scores, and so on, from low through high, high scores being also paired with high scores, as when organisms are tried. The correlation among throws of dice arises from _a different form of relationship_, in which the improbable throws, resulting in either very high or very low scores, are paired indifferently,[6] this indifference not being able, however, to produce zero correlation, because of the infrequency of extreme scores. The frequently occurring, mediocre scores in both series are, however, very similar, the most frequently occurring score for both being, indeed, the same. Since the mediocre scores tend to occur _both frequently and together_, because of the laws of chance, they produce positive correlations, differing in amount from series to series (also because of the laws of chance). But when organisms are tested, as has been repeatedly demonstrated, the serial relationship between two functions holds through high and low, and this, also, must be _biological_, and not explainable by laws of chance.

The demonstrations from die-casting are extremely significant, as warning us not to depend wholly for our inferences upon the amount of positive coefficients of correlation, nor the possibility of arranging them in hierarchical order. Both of these features of apparent relationship may come of chance, within a single series. Other features of relationship must be examined in the attempt to infer biological law, especially the _consistency_ with which given traits correlate to a given degree with others, when investigated by different examiners, in various groups; and the _form_ of the relationship, whether all the way from highest to lowest, or only in central tendency.

VIII. PRESENT STATUS OF THE PROBLEM

Whatever may be the ultimate cause of the manifestations, educators are practically concerned with the facts. The practical implications for education of knowledge gleaned up to the present time, concerning the coherence among mental functions, have been well stated by Burt, in his recent discussion of _Mental and Scholastic Tests_: “The examiner should always discriminate between children who are backward in most subjects, and children who are backward in one subject, or limited group of subjects, alone. A child, for example, who suffers merely from a specialized disability in reading and spelling, such as so-called ‘word blindness,’ is to be carefully distinguished from one who is in every respect mentally defective.

“As I have shown in memoranda previously published, educational attainments depend largely upon capacities of two kinds: first, a common or general capacity, entering into every subject in different degrees, but best exhibited in those that need thought-processes of a higher order, such as the comprehension of reading matter among young children, and, among older children, problem arithmetic and literary (or rather logical) composition; secondly, specific capabilities—such as arithmetical ability, linguistic ability, manual ability, and musical ability—entering into a small group of subjects. A child who is deficient in the former will be backward in all subjects—most backward in those subjects most dependent on this central capacity (such as the subjects first named), least backward in those subjects least dependent on it (such as manual and musical subjects). A child who is deficient in one of the specific capacities alone will be backward in the limited group of implicated subjects, and in none but these.”

McCall writes as follows: “There is an objectively and practically measurable something, which constitutes the core of most aptitudes. It is overlaid with various incidental abilities, and furthered or retarded by emotional or physical characteristics of the individual. This something is general intelligence. If an individual’s intelligence is all that is known, some mistakes will be made in attempting vocational guidance, but if only one thing can be known, general intelligence is perhaps most important.... A pupil’s intelligence score is an approximate measure of the diameter of an approximate general ability circle, and is hence an approximate basis for vocational guidance.

“But any individual who assumes that all the spokes in an ability-wheel are of exactly equal length, or that instances of marked special aptitudes do not exist, or even that most individuals do not possess some tendency toward a special aptitude, would make as egregious an error as one who assumed that all individuals are markedly lopsided.”

These two summaries of the present status of this problem from the practical point of view, coming as they do, the one from a student of the British school, the other from a student of Thorndike, show how the two originally conflicting interpretations have been approaching middle ground. There is found to be a quality of the individual, which results in generally superior, mediocre, or inferior performances in his case—a positive coherence in the amounts of all traits possessed, extending even to appreciable coherence between mental and physical. General intelligence is now measured, for practical purposes, as Spearman long ago predicted. Nevertheless, there are, as Thorndike maintained and maintains, mental functions, standing in which is hardly predictable from knowledge of other capacities. In rare cases there may be complete discrepancy in rank between performance in one task and performance in other tasks, with equal training. These are the cases of special talents and defects, to which this volume is devoted.

IX. MEASUREMENT OF GENERAL INTELLIGENCE: THE IQ

We now see that the “general” factor in intelligence may be defined simply as the positive coherence which exists among the multitudinous abilities of an individual, as respects their amounts. The first to obtain a quantitative measure of general intelligence, for the practical purpose of classifying school children, was Binet. Binet concluded from reflection on the research done, that failure or success in one mental function may be of slight significance for the classification of an individual, because correlation is imperfect; but that failure or success in a score of different functions must be of very great significance, because correlation among mental functions tends strongly to be highly positive. Working on this basis, he devised a large number of mental tests, intended to sample the individual’s performance in many different functions.

A mental test may be defined as a standard stimulus, which provokes a response capable of quantitative interpretation. Binet devised numerous standard stimuli, and a method of interpreting the responses elicited, in terms of a context of scores made by children of various ages, throughout the period of immaturity. His measurements were thus in terms of “mental age,” a phrase now somewhat familiar in education.

The science of mental measurement is rapidly progressing to more exact usage. The concept of “mental age” when applied to persons who vary in birthday age is in some respects misleading, and in other respects quite inapplicable (as with superior adults). General intelligence is at present usually scored in terms of points achieved, percentile attained in total distribution, or of mental ratio. The most reliable scales now available for the measurement of general intelligence in school children, score in terms of mental age and intelligence quotient (IQ). This measure (IQ) signifies the ratio borne by the intellectual level attained by a given child in tests, to the level attained by the typical child of his birthday age. For instance, a child 9 years 6 months old has an IQ of 100, if his score in tests equals that made by the average child of 9 years 6 months. If he is inferior to the average child of his age, the amount of such inferiority will be expressed by a ratio less than 100. Thus, if his performance equals only that of the average child of 5 years 2 months, his IQ will be 62 months ÷ 114 months, or 54 (dropping fractions less than .5). On the other hand, if he is superior to the average, attaining, let us say, the performance of the average child of 14 years 0 months, his IQ will be 168 months ÷ 114 months, or 147. An IQ of 100 may thus be thought of as “par” in general intelligence for a school child, while anything less may be thought of as “below par” to the extent indicated; and anything greater than 100 may be thought of as “above par.” The IQ shows the point of focus, for amounts of performance in a variety of mental functions. It derives its value for educational procedure from the positive correlation, which has been demonstrated to exist among performances in mental operations.

Scales at present available will measure general intelligence, in terms of IQ, about as low as IQ 10, and about as high as IQ 190, at certain periods of development. No doubt human intelligence ranges somewhat below and above these limits, but adequate methods of establishing the two extremes have not yet been devised. It is by no means usually realized that the range of individual differences in general ability is so wide that it is extremely difficult to invent methods of discovering its full extent. However, for practical purposes, available scales are adequate to cover the range for young school children, because intelligences that fall below IQ 25 or above IQ 175 are so rare as to be dealt with very seldom.

Within the limitations named, the general intelligence of school children can now be determined by a competent examiner, with a very small margin of error. The average error made by such an examiner will not exceed ± 5 IQ.

Not all scales for the measurement of general intelligence are scorable in terms of IQ. Some have been standardized in terms of “raw” points achieved, and some in terms of percentile status. There is at present much variety of usage in scoring, the ideal being to find _units_ of measurement. It does not lie within the scope of this volume to treat the problem of establishing units for the measurement of mental traits. The general intelligence of the children to be discussed here has usually been determined in terms of IQ, which will be comprehended from the brief description given.

An ideal of students of mental measurement is to devise a scale which will measure any intelligence, from the lowest to the highest existing, after maturity, in units every one of which is equal to every other; and to devise a scale fulfilling the same requirements for each 12-months interval of the period of immaturity. This ideal is far from being realized at the present time, but the future will see it achieved.

In the meantime scales for the measurement of special talents, which are not measured by the scales for measuring general ability, are being worked out. What these special talents are we shall now consider.

X. THE MEASUREMENT OF SPECIAL ABILITY

Although much further research is required before we can identify all the mental functions which are incoherent with general intelligence, we already have some knowledge of the matter, useful for the welfare of school children. Certain abilities are shown repeatedly by different investigators to be relatively independent. Success in music and in representative drawing is very slightly correlated with success in other school subjects. Spelling is far from perfectly predictable from grades in schooling generally. Mechanics is relatively independent. Whereas ability in reading and in arithmetic is highly, but not perfectly, correlated with general competence.

These facts mean that from knowledge of a pupil’s general intelligence we can make very reliable predictions as to his capacity for reading and for arithmetic, somewhat less reliable predictions as to his aptitude for spelling or mechanics, and that our predictions concerning his ability to draw, sing, or play musical instruments should be given without confidence in their reliability, if given at all.

Other kinds of performances, like the management of people, appreciation of a joke, dancing, the management of wild or domestic animals, have not been thoroughly studied in their relation to general intelligence, though these and scores of others which will occur to the reader, might be of great significance for practical psychology, if shown to be somewhat independent talents.

As we have already said, most of the functions performed by human beings are very complex, and capable of analysis. To read, understand, and execute a page of any musical composition is a very complicated performance. The attempt to measure special ability has been the attempt first to scale total performance in the function, and second to scale performance in the various coördinating functions contributing to total result. Thus in the case of musical talent, Seashore has found by analysis a large number of contributing factors, and has actually devised scales of measurement for five of these subsidiary functions.

Measurement more or less adequate can now be made of ability to read, spell, draw, write, put mechanical contrivances together, and calculate. This list does not by any means exhaust the possibilities of measurement in particular functions at present, but exemplifies them. Slowly we are approaching the point of being in position to tell not only how a child stands in general intelligence, but also to indicate his status in regard to special abilities. The “picture” of the total relationship among a person’s abilities is called a psychograph.

XI. THE PSYCHOGRAPHIC PICTURE OF INDIVIDUALITY

A psychograph may consist merely of numerical statements of the individual’s standing in various mental capacities respectively; or it may be presented in the form of a graph drawn from the figures. No standard graph has been agreed upon. Sometimes the method is to present points of deviation from a horizontal line representing the typical performance; sometimes to present the deviations from a vertical line, representing the typical; sometimes to present deviations along the spokes of a “wheel,” the typical being taken as a circumference drawn midway between the center and the perimeter of the circle.

[Illustration:

FIG. 3.—The psychograph of a school boy, showing his standing in various mental functions; illustrating use of the horizontal line to denote typical performance. The scores are in terms of mental age. (From Hollingworth’s _Judging Human Character_. Reproduced by courtesy of D. Appleton and Company.) ]

Figure 3 is an illustration of the first mentioned mode of presentation. It shows the status of a school boy in various mental functions measured. This boy is 18 years old. In interpreting the psychograph, which is platted in terms of mental age, it must be borne in mind that many of the capacities here included are matured by the age of 16 years. The individual is not, therefore, subnormal with regard to them. This case illustrates some of the difficulties of treating adolescents and adults in terms of mental age.

[Illustration:

FIG. 4.—The psychographs of three school girls, showing their standings in various mental functions, measured to determine mathematical ability; illustrating use of the vertical line to denote typical performance. The scores are in terms of weighted deviations. Scores to the right are above, and scores to the left are below, average. (From _Tests of Mathematical Ability and Their Prognostic Value_. Reproduced by courtesy of Agnes L. Rogers.) ]

Figure 4 shows the use of the vertical line as the “type” or “norm,” picturing the extent to which the individual measured departs from or corresponds to the typical, in the functions tested.

Figure 5 illustrates the use of the circle, with radii to show standing in the various mental functions. The adolescent presented is near the typical (the 50 percentile) in nearly all functions measured.

Which of these forms of graph is best adapted to its purpose has not been determined. All are simply different methods of picturing the same facts.

The chief obstacle to the platting of psychographs, for such capacities as are now measurable, is that scales for measurement have been standardized in different terms. To plat a lucid psychograph, some traits on which have been measured in P.E., some in IQ, some in percentiles, some in “raw” points, some in values of a T Scale, some in terms of school grade achieved[7] is now impossible, because of the difficulties of equating all these “steps” of difference. The psychographs here presented will, therefore, be understood to be crude, merely approximating the lucidity of those which will be made in future, when the science of mental measurement has made greater progress. Each of the methods of standardization has some advantages and some disadvantages, as compared with the others. Only experience and discussion can finally determine which is best. It is desirable to achieve uniformity as soon as possible, in order that the psychographic study of individuals may be facilitated.

[Illustration:

1. General Intelligence (Stanford-Binet) 2. Completion Test (Trabue) 3. Cancellation (Pinter) 4. Digit Symbol (Pinter) 5. Opposites (Pinter) 6. Mechanical Ability (Stenquist) 7. Tonal Memory (Seashore) 8. Pitch (Seashore) 9. Time (Seashore) 10. Intensity (Seashore) 11. Pictoral Completion (Healy) 12. Grip in Hand (Smedley)

FIG. 5.—The psychograph of a school boy, showing his standing in various mental functions; illustrating use of the circle as a diagram, the median circumference denoting the performance of typical persons of his age. The scores are in terms of percentiles. ]

XII. AT WHAT AGE IS MENTAL ENDOWMENT EVIDENT?

The question arises as to when special talents and deficiencies become evident in growing individuals. We know almost beyond any doubt that the degree of general intelligence is manifested from the beginning of life, and could be measured then if our instruments of precision were fine enough. With present methods we cannot undertake with confidence the measurement of general intelligence much before school age. Extreme deviations may be reliably identified as early as 3 years of age, or earlier, but slight amounts of deviation cannot be reliably determined by available methods before the age of 5 or 6. The inadequacy of method with very young children arises, partly because it is so difficult to obtain non-select children under school age for purposes of standardization, partly because of the coarseness of the “steps” at present used to measure. The most refined and reliable scales we have are cast in terms of “mental age,” and some do not allow for any difference of less than “2 months of mental age.” An error of only two misscorings in the same direction would therefore result in a considerable error in the IQ of a child 3 years old; since 4 months is a large percentage of 36 months.

As early as 6 years, however, even by present methods, we can determine objectively the individual’s status in general intelligence. The indications are that when the measurement of special talents has made similar progress, we shall find that these become evident just as early as general ability does. These special talents are gifts, innate in the organism, and manifested no doubt from the beginning of life, just as general intelligence is.

In the discussion of special gifts for music, drawing, and calculation we shall see that investigators have been particularly struck by the very early age at which these were manifested in the persons studied. It is common for those who later became historical prodigies in these performances to have shown symptoms of their ability as early as 3 or 4 years of age.

On the other hand, special deficiencies in these functions are not commonly noted until after school has been entered, usually long after. This is inevitable, because no one is likely to suspect a child of tone deafness, for instance, until his music teacher has worked with him for some time. But conspicuous aptitude for melody and rhythm is likely to be noticed.

The question arises: Can these special talents be acquired, or the special deficiencies be overcome, by any course of training? Scientific psychology tends more and more strongly to the conclusion that psychology and education can do nothing to alter the amounts or relationships of innate mental endowment. They can but measure endowment and give it training suited to its requirements. The history of Seguin’s form-board seems to illustrate the evolution of the point of view on this question. About sixty years ago this form-board was hopefully used as a supposed _means of altering_ original endowment. Feeble-minded children were given exercises in placing and replacing the blocks in it, in order that they might become more intelligent. To-day this form-board is used as a _means of gauging_ original endowment. Psychology cannot create endowment; it can merely measure and describe it. Education cannot bestow mental gifts; it can only utilize such as are innately present within the organism. Talent and genius can be created in children only by the procreation of parents, who are the biological carriers of extraordinary endowment.

XIII. THE FREQUENCY OF MARKED SPECIAL TALENTS AND DEFECTS

No census of special talents or defects of given degree has ever been taken. Surveys have been made showing the distribution of musical sensitivity, of ability in drawing, spelling, calculation, and so forth. These distributions tell us the frequency of extreme deviations in these functions, but they do not tell us to what extent the deviations are _special_. From them we cannot learn whether or not the extremely fortunate deviations are identified with great general superiority, and whether the unfortunate deviations represent the work of generally stupid children. What we require is a survey of children of uniform age, educational opportunity, and IQ, in respect to music, drawing, spelling, and so forth.

Although we cannot state with precision the frequency with which marked special gifts occur among the stupid, or marked special deficiencies occur among the highly intelligent, we know that such cases are quite rare. It is necessary to remind ourselves constantly of this fact, because it would gratify the demand for justice and fair play to find that special gifts are freely distributed among the generally inferior, and special defects frequently found among the superior. The truth which satisfies our desires need be stated but once, to be apprehended and remembered. The truth which offends kindliness, self-interest, or cherished beliefs, and is hence unsatisfying, requires emphasis. Therefore we must take particular care to bear in mind throughout the whole of our discussion of special talents and defects, that we are dealing with comparatively rare phenomena. The distribution of abilities, as determined by biological law, does not correspond to our concept of fair play. Nearly all stupid persons are inferior in all capacities. The great majority of gifted persons are superior in nearly all their abilities. The majority of human beings are neither markedly inferior nor markedly superior, but are “typical” (not far from the median or average) in all respects.

XIV. POSSIBLE ORIGIN OF THE DISSOCIATION OF CERTAIN CAPACITIES

Why should certain capacities, like musical sensitivity and ability in representative drawing, be so loosely correlated with general ability, throughout the species? Why should other capacities, like ability to name opposites and to complete sentences, give such high and positive total correlation? We do not know with assurance the answers to these questions. Perhaps the evolutionary explanation is adequate. Those variants lived to transmit their hereditary constitution, whose functions were so correlated that life was well sustained. Perhaps functions are, therefore, loosely correlated, where nothing would be added to the probability of survival by high correlation.

It makes little difference in a world like ours whether an intelligent man can or cannot sing. It is of small moment whether one who can easily detect absurdities of statement can also produce fine representative drawings. It is very important for survival, on the other hand, whether one who can detect similarities can also detect differences, in the objects which surround him, and whether he can at the same time anticipate incomplete meanings in the sentences and gestures of those whom he meets.

The suggestion also arises as to whether those performances which do not cohere closely with performances in general are such as involve the sensori-motor apparatus to a special degree, as distinguished from the central nervous system. Those functions which depend relatively little upon equipment of eye, ear, or hand, but essentially upon the sensitivity and integrity of the cortical neurones, might be expected to cohere closely, constituting what we should properly call intelligence. Where performance depends largely on sense organs and muscles, the correlation with functions largely independent of sensori-motor apparatus might be expected to be only as great as the tendency to general organic quality would bring about. Certainly drawing, music, and mechanical ability, for example, involve eye, ear, and muscle to a much greater extent than does the detection of absurdities in life situations, or the learning of symbolic significances. The mechanical technique of reading clearly involves the sensori-motor apparatus to a much greater extent than does the comprehension of what is read.

It would be valuable to determine to what extent a hierarchy of correlations would be consistently maintained in the use of tests, selected for graduated degrees of involvement of equipment accessory to the central nervous system.[8]

REFERENCES

BAERWALD, R.—_Theorie der Begabung_; Reisland, Leipzig, 1896.

BINET, A., and SIMON, TH.—“Théorie nouvelle de la démence”; _L’année psychologique_, 1909.

BROWN, WM.—“Some Experimental Results in the Correlation of Mental Abilities”; _British Journal of Psychology_, 1909–10.

BURT, C.—“Experimental Tests of General Intelligence”; _British Journal of Psychology_, 1909–10.

BURT, C.—_Mental and Scholastic Tests_; London County Council, 1921.

HART, B., and SPEARMAN, C.—“General Ability, Its Existence and Nature”; _British Journal of Psychology_, 1912.

HART, B., and SPEARMAN, C.—“Mental Tests of Dementia”; _Journal of Abnormal Psychology_, 1915.

HOLLINGWORTH, H. L.—_Judging Human Character_; D. Appleton and Co., New York, 1922.

MCCALL, W. A.—_Correlation of Some Psychological and Educational Measurements_; Teachers College, Columbia University, 1916.

MCCALL, W. A.—_How to Measure in Education_; The Macmillan Company, New York, 1922.

MOORE, T. V.—“The Correlation between Memory and Perception in the Presence of Diffuse Cortical Degeneration”; _Psychological Monographs_, 1919.

RÉVÉSZ, G.—“Ueber das frühzeitige Auftreten der Begabung”; _Zeitschrift für angewandte Psychologie_, 1919.

RUGG, H. O.—_Statistical Methods Applied to Education_; Houghton Mifflin Co., Boston, 1917.

SIMPSON, B. R.—_Correlations of Mental Abilities_; Columbia University, 1912.

SPEARMAN, C.—“The Proof and Measurement of Association between Two Things”; _American Journal of Psychology_, 1904.

SPEARMAN, C.—“General Intelligence Objectively Determined and Measured”; _American Journal of Psychology_, 1904.

SPEARMAN, C., and KRUEGER, F.—“Die Korrelation zwischen verschiedenen geistigen Leistungsfähigkeiten”; _Zeitschrift für Psychologie_, 1906.

TERMAN, L. M.—_The Measurement of Intelligence_; Houghton Mifflin Co., Boston, 1916.

THOMPSON, J. R.—“The Rôle of Interference Factors in Producing Correlation”; _British Journal of Psychology_, 1919.

THOMSON, G.—“The Proof or Disproof of the Existence of General Ability”; _British Journal of Psychology_, 1919.

Thomson, G.—“The Hierarchy of Abilities”; _British Journal of Psychology_, 1919.

THORNDIKE, E. L., and AIKENS, H. A.—“Correlation among Perceptive and Associative Processes”; _Psychological Review_, 1902.

THORNDIKE, E. L.—_Heredity, Correlation, and Sex Differences in School Abilities_; Columbia University, 1903.

THORNDIKE, E. L.—“On the Organization of Intellect”; _Psychological Review_, 1921.

WEGLEIN, D. E.—_The Correlation of Abilities of High School Pupils_; Johns Hopkins University, 1917.