Andrew W. YouNfi and Karl Pearson 
TABLE III. 
= -14895, C'2 = ^ / = -36005. 
227 
Various formulae used 
1st Term of 
equation (xiv) 
1st and 2nd Terms 
of equation (xiv) 
All Terms of 
equation (xiv) 
cr^2 . . . 
•062006 
■079848 
•082317 
Probable 
error of (f)'^ 
•041822 
•053857 
•055522 
•16902 
•21765 
•22438 
Probable 
error of C 
•11400 
•14680 
•15134 
The relative importance of the three terms of equation (xiv) is not markedly 
different in this table of small total content from what it was in the case of the 
Handwriting-Intelligence table and we cannot base different conclusions on the 
two cases. 
Again, using the approximation given by selecting the large terms from the 
second bracket of (xiv), viz. 
we obtain a^^ = -0864, 
which as in the previous example is a reasonable approximation to the full expression 
result. 
(9) Second ApiMcation. Test for Zero Conlimjency. 
Suppose that we may expect in the sampled population an absence of contin- 
gency or correlation between the variates considered. In other words we will 
suppose 
A. 
N 
= "... 
If, however, we take a sample from that population, the quantity 
which is the mean square contingency in the case of a population with zero 
correlation, would certainly not vanish. The problem then arises: How great 
may the quantity <f)'^ be without making it highly improbable that the sample 
in question is really a sample from a population of uncorrelated material? 
First of all, the mean value of cp^ as determined from a large number of samples 
would be 
= Xi ^ (c 
1) 
..(XVI), 
15—2 
