ON A NOVEL METHOD OF REGARDING ASSOCIATION 

 For the case of the fourfold table for example 



we find that G,= -707. 



Mr G. U. Yule in his recent Introduction to the Theory of Statistics, p. 66, 

 suggests that the coefficient of contingency should not be used when m is less than 

 5 or so. But such advice could only result from wholly overlooking the essential 

 nature of a contingency coefficient. The true position is that it is not comparable 

 with a coefficient of correlation for like tables assumed to be Gaussian unless we 

 use a 5x5 or finer classification. It actually measures the probability that the 

 observed results arise from independent material, whatever be the classification. 



A very little consideration will show that the table 



d 



ought not, in the absence of knowledge as to the finer classification of a and d, to 

 give a unity coefficient. In my conception of contingency Cj = 1 marks absolute 

 dependence, i.e. every individual A is associated with its own individual B. But 

 a table of the above kind gives us no information with regard to the distribution 

 of the a group of A^'s associated with B^'s, or of the d group of A^'s associated 

 with B^'s. Such a coefficient as Mr Yule's coefficient of association seems to me 

 absolutely misleading on this very account, because it gives such tables a complete 

 association of the variates, or a unity value for their coefficient. It is perfectly 

 true that if we assume the Gaussian distribution of frequency, then a wasp- waist 



is impossible unless the correlation is perfect. But the 



distribution like 



a 



d 



very essence of any theory of contingency or association is to proceed from purely 

 logical grounds and avoid any assumption that our distribution is quantitative 

 much less that it is Gaussian. Hence when the coefficient of contingency gives for 

 a fourfold table with only entries in the diagonal cells 707 and for a 10 x 10 fold 

 table with only entries in the diagonal cells "949, while a Yule association coefficient 

 gives 1*0 in both cases, this is not as Mr Yule seems to argue a disadvantage of the 

 contingency method, but one of its chief merits. It indicates how we pass to closer 

 and closer relationship as we classify more finely, and any coefficient which neglects 

 this essential is to that extent, I hold, defective. There ought to be no attempt 

 to modify the coefficient of contingency so as to raise mxm tables when m is 

 small up to correlation values, for such values assume some further knowledge not 



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