no. 2.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 387 



Obviously this is not a satisfactory situation, from the practical point of view, since 14 of 

 the 36 cases recalled are not within the range which it is desired to recall, whereas 13 cases under 

 9 years, who are probably at least questionable cases whom the examiner should see, are missed. 

 Reference to the scatter table for beta with Stanford-Binct made it clear that no way of shifting 

 this line would make the situation satisfactory. Any adjustment would be a compromise be- 

 tween the desire to secure more low-grade cases and the intention to escape recall of cases above 

 the questionable range. 



That it may be clear that the situation as above described is not dependent upon the fact 

 that the usual elimination on the basis of alpha had not been made, the following facts are sub- 

 mitted showing the results which would have been secured had an application of the usual 

 system of recall been applied to this group : 



Number recalled for beta from alpha, 118. 



Number of recalled cases testing below 40 in beta, 30. 



Mental ages of these 30 cases, by Stanford-Binet: 



Below 8 years, 3 cases (75 per cent of all cases below 8 years). 



8-9 years, 9 cases (40.9 per cent of all cases between 8 and 9 years). 



9-10 years, 7 cases (11.3 per cent of all cases between 9 and 10 years). 



Above 10 years, 11 cases (1.9 per cent of all cases above 10 years). 



These results indicate that the same situation exists as that previously outlined, with 

 merely a trivial reducing of numbers by the elimination accomplished by alpha. 



For this situation there is no satisfactory solution, unless the relationship between Stan- 

 ford and beta at the lower end of the scale can be improved. The best that can be done is to 

 establish the dividing line arbitrarily to meet the exigencies of the situation in the camps, know- 

 ing that a shift in either direction would increase or decrease its efficiency, according as this is 

 measured by the adequate recall of low-grade cases, or by the absence of excess recall of cases 

 beyond the questionable range. 



Section 4. — Possibility of increasing the correlation between beta and Stanford-Binet. 



Since, therefore, the immediate practical need seemed to be for a higher degree of corre- 

 spondence between results in beta and results in individual examinations for cases in the lower 

 ranges of the scale, an attempt was made to determine, by means of a multiple correlation, the 

 maximum possible correlation between beta and the Stanford scale, assuming appropriate 

 weighting. If evidence could be found that an appreciable gain could be made by weighting 

 of tests in accordance with results thus obtained, the intention was to determine the necessary 

 weights of the various tests and also to ascertain what tests, if any, could be eliminated from the 

 series without reduction in the degree of correlation. 



Table 52 shows the correlation arrays for Stanford-Binet with the separate tests of beta. 

 Table 53 presents the Pearson product-moment coefficients of correlation for each beta test 

 with Stanford-Binet and with the other beta tests. From these figures partial coefficients were 

 computed making possible application of Yule's formula for determining maximum correlation. 1 



Application of the formula gives the following results : 



R s (12345678) = 0.74, where R s(i 2 34567s) indicates the maximum correlation which might be 

 obtained between Stanford (s) and the beta tests, indicated by the numbers in the subscript, by 

 the best possible weighting. The above value (0.74) applies only to the present body of data. 



Further application of the formula showed that considerable reduction in the number of 

 tests used was possible without appreciable reduction in the amount of correlation, as indicated 

 in the following figures : 



Rs/(34567)=0.74. 

 Rs/<457>=0.73. 



' Yule, G. U., Introduction to the Theory of Statistics, p. 24S, formula 15. 



