A. Ritchie-Scott 
119 
Summing these four latter expressions we have 
7n.-,m 
K 2 
+ 
.(126), 
Annnn A 
m.-itu 
m 
III 
III. 
111- 
III 
m' .2 
(127 
When the table is symmetrically divided in both categories and r = 0 we have 
m^. = wi'i., = ZTgj = /I2, etc. and the above reduces to 
2 ^22 ^22 ^11 
and 
\mi. I \iii.i I 111. n.i 
4^2 ^2 ^2 
2NHK 
.(128). 
§ 10. Comparison of the Standard Deviations of Polychoric r 
AND Enneachoric r. 
We may now compare the standard deviations of and r^. 
~ iXll - X12 - X2I + X22) = - - 8P, 
21 "T ^^22 
.(129), 
- (^^11 + + C'21 + C'22)§r, = 8P„ 
Xii Xi'i 
(1 c r p 
"^n rs^ ^12 ST) "-^21 , <^22 
SP12- — SP2I+— - 22 
X21 
X22 
.(130), 
from which it appears as before (p. 108) that the enneachoric r is equivalent to a 
polychoric r in which the weights of the r's are ~ Xn^ ~ X21) X22; i-®- 
^ Xll^ll - Xl2yi2 - y21^21 + X22y22 
(131). 
Xu - X12 - X21 + X22 
Hence also the standard deviation of the enneachoric r may be written 
c^r^ = (- dPu + rfPi2 + dP2i ~ aP22? «n + etc (132). 
Upon expansion this reduces to 
„Pn + N {A,, + P„ - 1) + ,Pi2 - N (A,, + B,, ~ l)n2 
_+ „P2i - N (^21 + P21 - 1) - aP22 + N (^22 + P22 - 1) 
-iV{(^22 - ^21) - (^12 - ^11) + (P22 - P12)? 
{B,, - B,,)} - {P,, - P12 - P21 + P.22) 
etc. 
«ii + etc. 
N ]a22 - ai2 + ^22 - ^21 - ^" Pi2^P2i + P22 
+ etc. ...(1.33) 
(using a, /3 in the sense of p. 99), which is identical with the corresponding 
coefficient in ct^^ as given in equation (30). 
