RELATION OF VARIABLES. 



103 



TABLE I. 

 General Notation Employed. 



In determining the relation of w to x, let all values of tv be corrected 

 for the variable y to its middle value ys, and for the variable z to its 

 middle value Zg- Likewise, in determining the relation of iv to y, 

 let all values of w be corrected for x to its middle value X2, and fof z 

 to its middle value Zs. Similarly, in determining the relation of 

 w to z, let all values of ic be corrected for x to X2 and for y to ys. Cor- 

 rection to these arbitrarily chosen "standard" values requires the 

 following differences between the group averages: 



B-A=o,B-C=cf 



E*' - D^ = (/\ E - F' = f \ 

 E -D =(/,E -F =/ f 



H» - G' = (/, K' - V = i' 

 H -G =r7,H -I = i 



(4) 

 (5) 

 (6) 



Denote by A^ any observed value of iv in the {w, Xi) group; by B' 

 any observed value of w in the (w, X2) group, and so on to P for any 

 observed value of iv in the (u\ 29) group. Then one particular value of 

 A^ is identical with some particular value of w in the (w, y) series and 

 also in the {w, z) series, i: e., it is identical with a particular value of 

 D\ E\ or F\ and also of G'', H\ or I\ Suppose it is in the {ic, Xi), 



