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



431 



ALPHA CORRELATIONS. 



Group. 



Alpha before beta (Meade) 



Beta before alpha ( Meade) 



Alpha before a (Meade) 



MacArthur (all alpha) 



Beauregard (all alpha) 



Company H, Fifth Battalion, Infantry Replacement Camp (MacArthur) 



BETA CORRELATIONS. 



Group. 



Alpha before beta (Meade) 



Beta before alpha (Meade) 



MacArthur (all beta) 



Beauregard (all beta) 



Company H, Fifth Battalion, Infantry Replacement Camp (MacArthur) 



0.647 ±0.025 

 .588± .033 

 .379± .§33 

 .320± .031 

 .379± .047 



5.3454 

 5.2706 

 4.1353 

 4.6909 

 4. 0403 



None of these groups can be regarded as even approximately unselected. Induction into 

 the Army was "selective" to an unknown but probably high degree. Further, the continual 

 sifting and transferring of men within the Army itself produces in even short periods of time 

 groups (companies, e. g.) of varying but high degrees of " selectedness. " A glance at the 

 standard deviations of scores, which are relatively objective measures, shows that the groups 

 listed above vary widely in "selectedness." It is well known that selection affects a coeffi- 

 cient of correlation for any pair of measures of the selected group, and that the higher the 

 degree of selection the lower will be the correlation. It follows, therefore, that correlation 

 coefficients calculated for two groups which differ in degree of "selectedness" are not directly 

 comparable. 



Pearson 1 has shown that if r iy be the correlation between two variates for an unselected 

 group, in which the standard deviation of the variate x is <r x , the correlation between the vari- 

 ates x and y in a group in which the standard deviation of the x variate has been reduced by 

 selection to s x , is given by the formula — 



M„ 



a?. 



b-m 



where (r) XT is used to denote the coefficient of correlation in the selected group. Or if (r) Iy is 

 given, and also the values of the two standard deviations, we can solve the above equation 

 for r lv and thus find the degree of correlation in the unselected, or relatively less stringently 

 selected, group. The formula is — 



_ _ (r)xr 



NV-3] 



(r)\ 



i 



By means of this formula, using the alpha before beta group as the standard, since the 

 standard deviations of scores of both alpha and beta for this group are the largest values 

 obtained, the correlations for the other groups can be adjusted to the degree of "selectedness" 

 of this group and thus made comparable. The results of such an adjustment are as follows: 



ALPHA CORRELATIONS. 



Group. 



Alpha before beta (Meade) 



Beta before alpha (Meade) 



Alpha before a (Meade) 



MacArthur (all alpha) 



Beauregard (all alpha) : 



Co. H, Filth Battalion, Infantry Replacement Camp (MacArthur) 



' K. Pearson, Trans. Roy. Soc, Series A, vol. 200, pp. 1-06. 



Raw r. 



Adjusted r. 



