258 On Theories of Association 
Diagram XV. 
(ii) 
0-10 _ 
10-25 
Haemorrhagic. Confluent. Abundant. Sparse. Very Sparse. 
Severity of Attack. 
of sex, or in the use of a spear or a sword in negro tribes as alternatives, although 
even in these cases it is hard to understand why the male is a unit in excess or 
defect of the female or why a spear is a sword plus or minus a unit. But if we 
admit this, then cf> is the appropriate coefficient to use, and not Mr Yule's 
association or colligation, and it should be applied to the original data and not 
to the adjusted or equalised table. Personally we should never use <f> in such 
cases ; we should measure the probability that the variates were independent, 
i.e. deduce the P from nty 2 by Elderton's tables, and this would guide our judg- 
ment in the matter*. 
* We can get rid of the main effect of influence of total number of cases considered, and of the 
inequality of the marginal grouping, by adopting the method proposed by Pearson and thinking on a 
correlation scale : see " On a Novel Method of regarding the Association of two Variates classed solely 
in Alternate Categories," Drapers' Company Research Memoirs, Biometric Series VIII, Dulau & Co. 1912. 
In that paper the values of the correlation on the probability scale r P were only tested against tetra- 
choric r t for such totals and divisions as occur most frequently in everyday practice. A caution must be 
given here against the extension of that method without fuller investigation of such cases to divisions 
giving small percentages in the marginal frequencies. For such cases we know that tetrachoric r t gives 
poor results. 
