572 
Miscellanea 
Or, after some reductions 
where 
and 
Again we have o-^^a = o-^^ ; 
Now what we usually need is the probable error of the contingency coefficient 
But - <TC2 = <r0(l-(^2^)* = V(l+<^')*- 
Thus the probable error of the coefficient of mean square contingency 
•67449 X <rp - [WM±lz^\i 
This expression is much simpler than that for the probable error of the actually used value 
as given by Blakeman and Pearson*. It is not, however, asserted that it possesses greater 
theoretical validity. Those authors illustrate their formula by calculating the probable error of 
the contingency coefficient in the case of the association of handwriting and general intelligence 
in 1801 schoolgirls. They find 
6''= -2957 ±-0192. 
In the course of their work they deduce 
= -09580, 
(.^^) =-03268, 
t//„3 = . 14865. 
Using these values we have from (ix) 
It is clear therefore that (o-^^) does not differ very substantially from (o'^^^- Calculating 
from (x) the probable error of G^, we find it = -0217, while the Blakeman-Pearson process gave 
•0192. The two values only differ by '0025, which is unlikely to be of importance in the case of 
most inferences in practical statistics. 
Beyond the knowledge of (^^^ only ^^„3 jg required by the present process. 
This may be written 
^ n.„n„.\^ « « ^ 
[ N N 
In finding the mean square contingency c^a^, however, the three expressions 
Tir^ 4^ and 
N N 
N 
* loc. cit. p. 191. 
