A. RITCHIB-SCOTT 105 
N 
= ^^r" if 
Similarly n.,y + ^ n^^ = 2 (56). 
Hence substituting we have 
- ANHKKk,a/ = 2 m,. + m.,| (57), 
(/ij and yl'i are of course negative numbers) which remains finite when the extreme 
categories are equal to r = 0. 
(2) When we put /ig = ^2 = enneachoric table degenerates into a tetra- 
choric table and we have 
n,3 = 
— 
''^33 — 
n^i = 
*^33 ~ 
0, 
n.3 = 
0, 
X12 ---- 
X2I = 
X22 = 
0, 
and ni = 
But = '4^2 "~ ^11 
= 1- Al- 
Vl - rV Wl - r2 
Similarly ^21 = ^ ~ B^j^. 
Hence ^ d - -^xi) + d - ^n)^^^-x + N- n,. ~n^,^±n^ 
_ iV- U„%. + ^ji^., - n„) 
N 
iV • 
This form of the standard deviation of a tetrachoric correlation will be referred 
to again later, and will then be reduced to a still more symmetrical form. 
From the above it will be seen that we can determine the correlation coefficient 
from any frequency block, assuming a normal distribiition, but the accuracy of 
this determination varies with the position and size of the frequency block. The 
probable error {-GlUQo.) varies from cell to cell, and an unlucky choice of the work- 
ing cell may lead to a correlation coefficient with large probable error. A correction 
