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MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XV, 



Proceeding in this manner for each class interval we obtain a table of deviation values 

 (table 158) for the complete range of alpha total scores: 



Table 158. — Deviation values for every class-interval of the alpha scale and every alpha test. (See text.) 



With the aid of this table we treat each class interval exactly as we should have treated 

 individual cases if that procedure had been possible. Thus the lowest class interval, 0-4, is 

 treated as an individual case with scores of 0.66S5 and 0.9315 in tests 1 and 2, respectively, and 

 zero scores in all other tests, and the probable score on the combination scale is calculated by 

 means of a multiple regression equation connecting these three variables. Similar procedure is 

 followed for the remaining class intervals. We thus require six different equations to fit the 

 six different typical combinations of variables — the variables shown in table 158. If we desig- 

 nate by C a combination scale score, the regression equations will be of the form 



C-m = -S c 



#C1 Oj , ;Rc2. «!,^CJ_ 



JXqq (Tj -ffco O 2 **cc 



«3 



+ 



Rcc o; 



where R cc , R 01 , R C2) R 03 , etc., are the minors corresponding to the elements in the first row and 

 first column, first row and second column, first row and third column, etc., respectively, taken 

 with the signs corresponding to these elements, in the determinant : 



R a 



. 1 



Now r 10 , r 20 , r 30 , r 40 , etc., are the correlations of tests 1, 2, 3, 4, . . . respectively, with 

 combination scores, or, in other words, according to the definition of the combined scale with 



