A Comparison of the P.C and I.Q
The Psychological Clinic Copyright, 1930, by Lightner Witmer, Editor Vol. XVIII, No. 9 February, 1930 :Author: Gordon L. Riley, M.A.
Research Psychologist, The Training School at Tineland, New Jersey Dr Heinis, of Geneva, presented in the Journal of Educational Psychology (1926) a formula for describing mental growth. The index derived from this formula he calls the personal coefficient. x The formula is Y ?4.29 where e is the base of the natural (l-e6.675)
logarithm, x is the life age and Y is the test age. This is based upon three sets of test data covering almost the entire span of childhood. The tests used were group tests having unequal steps in contrast to the Binet metric system. The mathematical steps in the formation of the formula are omitted. While they would be of some interest in evaluating the coefficient, they are not necessary in the present study, which has to do with one phase of its application. For convenience in the use of this formula Heinis gives a double entry table whereby the P.O. can be directly obtained, given the life and test ages. One corollary of this formula is that the deviation of scores increases with age; in terms of the I.Q., the scores of inferior children decrease, while those of superior children increase; for the personal coefficient 011 the other hand they would remain constant. Heinis confirms these mathematical conclusions by the results of applying his formula to Kuhlmann’s retest data of subnormals. The present study is a further check upon this conclusion, a comparison of the predictive value of the I.Q. and P.C. for superior and subnormal children.
The data consist of 30 cases from Baldwin and Stecker’s “Mental Growth Curves of Superior and Normal Children,’’ 200 cases from Doll’s “Growth of Intelligence,” and 50 cases from the clinical files of The Training School. These children had 011 the Stanford Binet initial I.Q.’s outside the normal range of 90 to 110 with the excep262 THE PSYCHOLOGICAL CLINIC tion of a few ‘’ potential’’ feeble-minded from Doll’s study. In working with individual cases an initial test below 12.5 years and a final test at 14 years were taken to insure sufficient time interval. Otherwise no other basis of selection was used. These data were given the usual treatment to bring out the relative reliability of the two indices. This involved three methods, first, the constancy of the two indices, second, comparing the test score obtained with those predicted from the initial test indices and third, making graphic comparisons of individual cases.
Table I gives a summary of the test results. Column (3) gives the life ages at initial test, (4) test ages, (5) I.Q. from this test, and (6) the personal coefficient from it. Then the same data arc given for the final test.
Table I TEST RESULTS Author Cases Final Test L.A. M.A. I.Q. P.C. Doll 203 9.0 5.7 66 77 14.0 7.1 50 75 Doll 40 9.4 6.1 64 79 13.4 7.5 56 78 Baldwin 30 8.1 9.6 118 108 11.6 15.0 130 109 V.T.S. file … 50 11.0 6.5 61 77 14.0 7.6 54 77 From this table it is evident that while in each case the I.Q.
suffers considerable variation, 8 to 16 points, the P.C. remains constant or changes one or two points. The mean of the I.Q. difference is 11 points, and for the P.C. it is 1. This average change is just about twice that usually allowed in testing, while for all practical purposes the change in P.C. is not appreciable.
In Table II are given the arithmetic means of the final test, results and those mental ages predicted by the two indices from the Table II FINAL TEST RESULTS COMPARED TO THOSE PREDICTED BY I.Q. AND P.C. Difference Test and Author Test LQ; Ra MA. of I.Q. M.A. of P.C. Doll 7.1 9.2 7.4 2.1 .3 Doll 7.5 9.0 7.7 1.5 .2 Baldwin 15.0 13.7 14.8 1.3 .2 V.T.S 7.6 8.5 7.6 .9 0
initial tests. Column (1) gives the source of the data, (2) the final mental ages, (3) the mental age predicted by the initial I.Q., (4) the mental age predicted by the initial P.C., (5) the difference between the test age and that predicted by the I.Q., (6) the difference between the test age and that predicted by the P.O. In each case the results favor the prognostic value of the P.O. as against that of the I.Q. On the average for these cases the I.Q. prediction shows a discrepancy of 1.5 years, while that for the P.O. is .2 year.
Table III presents the constancy of the indices in somewhat more detail and for comparative purposes a similar summary on the constancy of the I.Q. for normals. Column (1) gives the author, (2) the index, (3) the number of cases, (4) the percentage of cases whose final index differs from the initial one by more than 10 points, (5) the range of the middle fifty per cent, (6) the arithmetical mean of the deviations, and (7) the correlation of the first and final indices.
Table III INITIAL AND FINAL INDICES COMPARED Author Terman Rugg .. V.T.S. . V.T.S. . Doll … Doll … Index I.Q. I.Q. I.Q. P.C. I.Q. P.C. No. Cases 435 137 50 50 40 40 Percentages 10 Points Difference 15 12 35 0 65 15 Limits Middle 50% -3.3 to +5.7 -2.3 to -j-5.6 -3.1 to ?12.0 -4.0 to -j-2.1 -5.9 to ?17.3 -5.3 to -f.8 Arithvietic Mean 4.5 4.7 7.5 3.0 12.7 5.2
In this table the I.Q. shows much greater variability by all the statistical methods employed. The P.C. also shows some fluctuations but its results are comparable to the normal studies and so shows what might be considered normal error. In fact, the P.C. measures show slightly less variation. This comes out most obviously in the percentage of cases showing more than ten points difference between the first and final index. For the normal I.Q.’s this is 13 per cent, for the subnormal I.Q.’s 40 per cent, and for the P.C.’s 7.5 per cent. From the tests of the feeble-minded a number of mental growth curves were drawn for individual cases. In addition to plotting the actual test results, curves based on initial I.Q.’s and P.C.’s were also drawn. A quantitative expression of this check is difficult. In most of the cases (over 80 per cent) the P.O. curves ran closer to the actual test results than the I.Q. The exceptions are the “improving” child and the “potential” type of feeble-mindedness.
Below are given tables giving life age, mental age, I.Q., and P.C. for two cases over a period of several years. These cases were chosen at random. Fourteen years is taken as the adult level in calculating the final I.Q. ‘s. The first case, C.F., shows that although the P.C. changes less than the I.Q., there is considerable and consistent change. This type, known as ‘’ potential’’ feeble-minded, may possibly be considered abnormal, involving either pathological or social causation, yet such etiology does not appear in the ordinarily complete clinical picture. In different studies of the feeble-minded this type presents a small but ever present group. They seem to be an exception to the successful application of the P.C. Case M.F. is an ordinary high-grade case, showing slight fluctuations, with the P.C. presenting less variation than the I.Q.
Table IV C.F. M.F. C.A. 8.6 9.1 10.0 11.4 12.0 13.0 16.4 M.A. 7.1 7.1 7.2 7.3 7.4 8.0 8.2 I.Q. 82 78 72 64 62 62 58 P.C. 90 88 85 82 80 80 78 C.A. 10.8 11.4 11.9 12.7 13.1 14.1 16.0 M.A. 7.3 8.1 8.2 8.3 9.0 9.2 10.1 I.Q. 68 71 69 65 69 65 72 P.C. 84 86 85 84 86 85 85
The quantitative results may be summarized as follows: 1. First and final P.C.’s correlate 6 to 12 points higher than those of the I.Q. 2. There are about 35 per cent more cases showing a difference of 10 points between the first and final I.Q.’s than for a similar difference in the P.C.’s. 3. The mental age predicted by the P.C. is about a year closer to the test result, on the average, than that predicted by the I.Q. 4. The limits of the middle 50 per cent and arithmetic mean of the differences between initial and final P.C. ‘s is less than the same for the I.Q.
5. The mean difference in I.Q.’s between the first and final test is 11 points and for the P.C. 1. In conclusion it may be said that although the number of cases is small and there are individual exceptions, all the methods of treatment consistently show the superiority of the P.C. over the I.Q. as an instrument of prediction for superior or subnormal children.
Bibliography
Anderson, Meta. A Study of the Data on the Results Gathered from Repeated Mental Examinations of ZOO Defective Children Attending Special Schools over a Period of Eight Years. Journal of Applied Psychology, Vol. 7, No. 1, 1923. Pg. 54. Baldwin, B. T. and Stecker, L. T. Mental Growth Curves of Superior and Normal Children. University of Iowa Studies in Child Welfare, Vol. II, No. 1, 1922. 61 pp. Doll, E. A. The Growth of Intelligence. Psychological Monographs, Vol. 29, No. 1, 1921. 130 pp. Heints, H. La Loi du Developpement Mental. Archives de Psychologie, Vol. 19, 1924. Pg. 97. Heinis, H. A Personal Constant. Journal of Educational Psychology, Vol. 17, 1926. Pg. 163. Kuiilmann, F. The Results of Repeated Mental Re-examinations of 639 Feeble-Minded over a Period of Ten Years. Journal of Applied Psychology, Vol. 5, 1921. Pp. 195-224. Rugg, H. and Colloton, C. Constancy of the I.Q. Journal of Educational Psychology, September, 1921. Pg. 315. Terman, L. M. The Intelligence of School Children. Boston, Houghton Mifflin Company, 1919. Chapter IX.
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