220 On the Probable Error of a Coefficient of Contingency 
With these formulae we can now proceed to discuss the mean value of 0^ and 
its variability. 
(4) Mean Value of (f>^ {continued). 
At the end of (2) we had arrived at the equation 
and substituting from («) we now obtain 
We can usually put Xi = 1 write 
In the particular case of the contingency table 
(l -.\\ S{^'\ + ~ S( (x). 
Now S (j^^ ) ^ ^ where (/)p^ is the mean square contingency for the whole 
population, so that the mean value of cf)^ as determined from a large number of 
samples is in excess of the true mean square contingency by 
(5) Standard Deviation of Non-npjiroximatii^e Formulae. 
From the equations 
and l + 
we have NS4.' - S (^^-"f^) + 2S (^f-) ^ x.S {| (l " |)} ("i)- 
Squaring, slimming for a large number of samples and dividing by the number of 
samples, we have 
N^g\. = Mean (8</.2)2 
= Mean 
