no. 3.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 



641 



the sum of all alpha and beta scores, plus mental age rating. Since this sum is an unweighted 

 one, we can calculate these correlations from the correlation coefficients of table 155 and the 



appropriate standard deviations of table 156. 

 variables the basic determinant is: 



Thus, for the equation including all eight alpha 



Rn, 



The basic determinants for the shorter equations will of course be portions of the above 

 determinant, i. e., what is left after the rows and columns corresponding to omitted variables 

 are struck out. 



We thus obtain the following equations : 



(7= J/ C + 2 C (.32840) 

 = J* O +2 C (.23490 



'4 



-Jt+Z.. 21061 



= .¥ C + Z C {. 15990 



= 34 + 2< 



1358 



c- 



+ .6396 " 2 



(7) 



)+. 25990)+. 35250)+. 23960)) (8) 



)+ .23330)+ .16830)+ .17760)+ .29540)1 (9) 



)+.18520)+.177O0) + .21120)+.17370)+.2O26(^))(lO) 

 )+ .13900)+ .13620)+ .19590-;)+ .18440;)+ .17970) 



(7=if e + 2 oj.H830)+.13920) + .12O10)+.17550)+.O9790)+.14O20 : ) 

 + .16630) + .16160) 



(ID 



(12) 



Having located the center of each subgroup of the total score distribution on our combi- 

 nation, we need to consider the variability of these subgroups. It is evident that they are not 

 equally variable, for combination scores can be predicted from scores in two tests less precisely 

 than from scores in eight tests. For, by means of the formula 



R- 



•V 1 



Rp, 



Re 



the maximum correlation between combination scores preaicted from the various sets of variables 

 by the above equations and actual combination scores can be calculated. We find 



Equation (7) R = 0.9076 

 Equation (8) R= .9473 

 Equation (9) R= .9574 

 Equation (10) R= .9707 

 Equation (11) R= .9721 

 Equation (12) R= .9770 



