118 The Correlation Coefficient of a Poli/choric Table 
1 
^ 
1 
m^.m.^ni i.m 
N 
.(114), 
a 
'22 
lm.^.m.^m\.m' -L^ (115) 
Since /Hi.w'.i = jh-i. (iV — m-^.) = iVa,,,/ 
1 '^mx'^m' 
and similarly for the others 
= -^21 -22 ~ 
■^11 '21 ~ -^12 -22 = 
^11'22 = ^12'21 
With these values we have 
A = 
m.^m .2 
(= ^) 
m ^.m 2-^ -2 
.(117), 
.(118), 
.(119). 
1 
In 
'?12 
221 
222 
1 
e 
e 
f 
ee 
'7l2 
e 
1 
ee 
e 
?21 
/ 
6 
r 
ee 
1 
e 
?22 
/ 
t 
6 
e 
1 
.(120). 
Aooon IS S}' 
1 + ee' e + e' 
e + e' 1 + ee 
nnmetrical with respect to the centre of the square, hence* 
1 — ee c — e 
e - e' 1 - ee' 
= {(1 - e^) (1 - e^)f 
m j.m .{m2.m.2 
(121). 
The remaining minors are easily reduced and we have after reduction and sub 
stitution 
Annii 
(122), 
(123), 
^''^^ SH2.m'2. U'l. Vw-l^ -lV »»-2 / 
(124), 
'22 
(1 - e'^) (1 - e"2) ("X- - e\ ("t^ - A2) 
(125). 
* See Scott and Mcathews, Thtory of Detenninants (2nd ed.), p. 89. 
