Irregularity on a Binet Examination as a Measure of its Reliability
- Author:
Sidney L. Pressey, Ph.D.,
Indiana University.
The writer became much interested, while serving as Assistant Psychologist at the Boston Psychopathic Hospital in the summer of 1916, in “irregularity” on a psychological examination as shown by insane patients. The results of a special study of this subject, using the Point Scale, have already appeared,1 and were summarized briefly in a paper at the annual meetings of the Psychological Association in December, 1917. In this paper a method for stating “irregularity” on the Binet scale was also suggested. Briefly, this method consisted in adding together the number of months failed below the mental age (each failure being multiplied by the number of years away from the mental age at which the failure occurred) and the number of months passed above the mental age (each success, again, being multiplied by its distance, on the scale, from the mental age). The present paper is a brief report of results obtained, using this method of figuring the “scatter,” with the Stanford Binet scale. A word should first be said in explanation of the method. The method for stating “scatter” most in the spirit of the Binet scale would, the writer believes, be simply to add together the failures below the mental age and the successes above. This gives, as a matter of fact, results of not a little interest. But it is obvious that a failure one year below the mental age is not of the same importance as a failure four years below the mental age; a success one year above the mental age is of much less significance than a success four years above. To put the situation concretely, a child with a “mental age” of ten years, who fails a six-year test and passes a sixteen-yearold test, is much more interesting material for further study than the - child with a ten-year mentality who fails nothing below the nine-year group of tests and passes nothing above the twelve-year group. The expedient was, therefore, adopted of multiplying the value of each test appearing in the irregularity by the number of test groups which that test was away from the mental age. In the case of the ten-yearold child first mentioned, the failure of “two months’ worth” of test at six would be multiplied by three (this being the number of test groups away from the test group in which the mental age appears). 1 IYessey, S. L.: “Distinctive Features in Psychological Test Measurements made upon Dementia Praecox and Chronic Alcoholic Patients,” J.of Abn. Psychology, June, 1917,and ” Irregularity as a Measure of Deterioration,” same Journal December, 1918.
And the five-months’worth of success in the sixteen-year test group would be multiplied, again, by three?the number of test groups away from that test group in which the mental ages falls. We will suppose that the mental age of this child was 9-8, that he failed one test in the six-year group, one test in the seven-year group, two tests in the eight-year group and one test in the nine-year group. The number of successes or failures in the ten-year group is of no interest; if the examination were perfectly even the child might fail any two of the ten-year tests without its being possible to consider him other than typical. The two months of failure at nine would be counted as two months of irregularity, the four months at eight as eight months’ irregularity, the two months at seven as six months’ irregularity, and the two months of failure at six as eight months’ irregularity. In similar fashion we may suppose this extraordinary child to pass one test or “three months’ worth” at twelve,to fail all the tests of the fourteen-year group, but to pass one test of the sixteen-year group. The irregularity in the twelve-year group (one test group away from that test group in which the mental age falls) would be counted as three months in making up the total of irregularity, and the five months’ worth of success in the sixteen-year group would be multiplied by three?the number of test groups which this last success is away from the test group where this child should, if the examination had been perfectly even, have stopped succeeding.1 The total irregularity, as thus figured, would be forty-two.
The present brief study is based on irregularities, thus figured, from 141 white children, 51 colored children and 16 adults. The white children have, of course, been the basis of comparison. They range in age from four through fifteen. The distribution by I. Q. will be given shortly; many were tested as special cases?either sub-normal or brilliant. The group is thus not a representative one, but does well enough for the rough comparisons here presented. The number of cases and median irregularity at each age are as follows:
A<re 4 5 6 7 8 9 10 11 12 13 14 15 No 1 1 12 13 18 10 24 25 17 12 4 4 141 Median 8 10 8 12 9 13 9 8 10 10 10 1 The question will naturally be asked as to why this success at sixteen was not multiple by six, the number of years which this success is away from the mental age. This procedure was tried; it was found, however, that since the tests above ten are already progressively weighted, the handling of the scores in this fashion tended to double-weight irregularities above ten and increase excessively the amounts for the older children. The method can best be understood by clearly grasping its purpose. What is being sought, of course, is a statement of total variation of successes and failures about the mental age which shall give an expression simply, and solely, of the consistency of a subject’s responses to the different parts of the examination, and which shall make possible a direct comparison of the consistency shown by different subjects, and at different ages. And the difficulties encountered are due to the fact that the mental age is not an average but a sum, and that even the Stanford scale is not sufficiently systematized for any very satisfactory statistical treatment. The small number of cases at certain ages permits only tentative conclusions from these results, but the medians would suggest that the irregularity was fairly constant over the range of these ages.1 If we may suppose irregularity to be at least roughly constant over these ages, it will be permissible to lump the cases of different ages in studying possible relations of irregularity to “brightness.” The results, when the cases are grouped according to I. Q., are as follows: I. Q -7G 76-90 90-110 110-125 125No 23 37 42 24 15 141 Median 9 8 9 10 14 Clearly irregularity is, as thus stated, not distinctive of subnormality.2 A greater scattering of scores in examinations from superior children might seem suggested. But the increase is slight, individual differences arc great; the slightly greater irregularity can hardly, when everything is considered, be thought of any practical importance. In fact, it is hard to see any value in such a measure of irregularity?unless, possibly, as a special method in the study of examinations from insane patients.
The results from the colored children and the adults put a different light on the situation, however. The 51 colored children referred to in the beginning of the paper make up all the pupils (except some few who dodged the examination) in a small colored school. The number is too small for tabulation by age; but the group as a whole gives a median of 14 units irregularity. The 1G feebleminded adults show a median irregularity of 26. Such findings surely suggest that though irregularity may not vary with “brightness” it may, nevertheless, be indicative of some factor of importance in the examination. To see whether some further understanding of the situation might not be given by intensive study of extreme cases, the children showing the highest ten per cent of irregularity were especially considered. Only 15, or about 11 per cent, of the total 141 white children, show irregularities of 20 or over. The girl who shows the greatest irregularity (71 units, as compared with the average of 10) is the child of a university professor. Although twelve years old she has never attended school, never plays with other children, spends most of her time in reading, has been educated by her mother. The girl is thus distinctly abnormal in mental make-up and training. Another girl, with an I. Q. of 94, has an irregularity of 27. Her * Similar results were found for irregularity on the Point scale, as described in the writer’s papers above referred to. 2 The results are thus in accord with Dr Wallin’s interesting paper, dealing with this subject in a slightly different way. Wallin, J. E. Wallace, “Irregularity and Feeble-mindedmss,” Ptycholociccd Clinic 11; 179-195, 1917, and with the results of the writer already mentioned.
vision is so defective that her teacher says she can “scarcely see even with glasses;” the teacher also says that home conditions are “dreadful.” A third girl with an I. Q. of 72 and an irregularity of 22 has been out of school much, and is just recovering from pneumonia. A boy with an I. Q. of 101 and irregularity of 26 was, the examiner notes, impatient of the examination, wished to get through with it as quickly as possible, and did not give satisfactory attention. Another boy?thirteen and a half years old, and in the fifth grade? gave an I. Q. of 91 and irregularity of 34. It was found after making the examination that the boy had been tested before. The second examination was made toward the close of the school year, after a large number of his classmates had been “Bineted.” There was good reason to believe that the results of the first examination (which had been for practice), along with talk among the pupils, had influenced the examination; the scale rating was much higher than was expected by either examiner or teacher.
In fact, of the fifteen children of irregularity 20 or over there were only three who were not known to have some marked peculiarity of mental make-up or training, or whose examinations were not qualified by some such special circumstances. Something the same situation appears in the case of the adults. They were all, with two exceptions, inmates of a county poor asylum. Again, with two exceptions, they were over forty years of age. A number had more or less defective vision, several showed illiteracy beyond what would be expected from the amount of their mental defect. That is, most of the cases were old enough so that some affects of maturity1 (or, perhaps, of senility) upon the make-up of the examination might be expected. And the majority suffered from special handicaps of one sort or another which might be expected to affect the consistency of their showing in the examination.
The slightly greater irregularity of the colored children the writer is inclined to explain in analogous fashion. Previous work has shown negro children to give a somewhat distinctive “pattern” of scores on a group of psychological tests.2 An innate difference in abilities is naturally suggested. Anyhow, the average colored child surely comes from a total environment very different from the mental environment acting upon the white child; standards of living, 1 The writer has already presented some evidence to show that individuals over twenty give examinations distinctly different from the examination given by a child of the same “mental age.” See Pressey, S. L. and Cole, L. W. “Are the Present Psychological Scales Reliable for the Examination of Adults?” J. of Abn. Psychoogy December, 1918.
2 See, for instance, Pyle, W. II. “The Mind of the Negro Child” School and Society 1: 357-G0,1915; Ferguson G. 0., Jr.: “The Psychology of the Negro: An Experimental Study,” Archives of Psychology, No. 3G, 1916 p. 138, Sunnc, Dagny: “A Comparative Study of White and Negro Children,” J. of Applied Psychology, 1: 71-83, 1917;; Loades Redfern, H., and Rich, S. G. “Binet Tests on South African Natives?Zulus,” Ped. Sem. 24: 373-83, 1917. moral and social attitudes, sentiments and ideals and interests and ambitions, are all subtly but powerfully different. And it would seem not unreasonable to expect the sum of such influences to have some effect on the reactions to a psychological examination. The conclusion is, of course, that a high irregularity indicates the presence in the examination (and in the score) of some more or less irrelevant factor, preventing a standard measurement of the “general intelligence” of the individual. A very unusual education or environment, marked sensory defect,physical illness,poor co-operation, possibly age and racial peculiarity, may thus operate to prevent a satisfactory rating. And when they do thus operate, they show their presence most distinctively by increasing the irregularity. Irregularity might thus be said to give a measure of the reliability of an examination?of its freedom from such factors.1 And a statement of irregularity would seem of little less importance than the mental age and I. Q. in summarizing the findings of an examination. These are obviously very far-reaching conclusions from a very small amount of data. The present paper has been intended only as a suggestion of methods and problems?and beyond this has tried only to demonstrate that there is in this subject of “irregularity” somewhat more promise than has ordinarily been supposed. A priori it would seem as though we needed, as a matter of ordinary statistical precaution, some measure of the dispersion, as well as of the average or sum, of the scores obtained with a composite group of tests on a given individual. And the few results above presented surely suggest an actual value for such a measure in the use of the Binet scale. The writer hopes further studies may be made of the subject.
1 It might be said that the writer believes the irregularity shown by mentally diseased individuals should be interpreted in the same way. Irregularity need not, in such instances, be the result of deterioration. It may be simply the result of absorption in a delusional system, of distraction by hallucinations, of negativism, retardation, or other relatively temporary conditions. But it is always the result of some factor which makes the examination unreliable as a measure of the patent’s intact mentality.
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