160 On Theories oj Association 
Mr Yule has invented a series of statistical methods which are in no case based 
on a reasoned theory, but which possess the dangerous fascination of very easy and 
ready application, and therefore are at once seized upon as applicable to all sorts 
of problems by those who are without adequate training in statistical theory, 
or without the mathematical knowledge requisite to weigh cautiously their logical 
basis. The methods to which we refer are these : 
(i) the use of the so-called " coefficient of association " to measure the 
relationship of two attributes ; 
(ii) the use of a new coefficient, which Mr Yule terms a " coefficient of 
colligation," apparently to be used in like cases with the coefficient of association ; 
(iii) the development of a method which first appeared in a paper by the late 
Mr John Gray * ; in this method each group of a contingency table is considered 
as a cell of unit subrange for both variates. This assumption being made, Mr Yule 
calculates the coefficient of correlation by the product-moment method, and on 
the basis of this procedure terms his coefficient the coefficient of correlation and 
uses the customary letter r for it. 
Such a terminology is absolutely unjustifiable and can only confuse the 
uninstructed and undiscerning reader. If the groups were extended from 5 or 8 
to an indefinite number, all Mr Yule would reach by this method would be a 
correlation of ranks, not of variates. As it is, he has obtained a correlation of 
ranks with enormous " brackets f." It does not seem to have occurred to him that 
the correlation of ranks may be quite different from the true correlation of variates, 
and that in cases where we do know the relationship the correlation of ranks 
is sensibly lower than that of variates. Further, he makes no suggestion that a 
very fundamental correction — that of the variate and class-index correlation — is 
needful before this method could possibly be applied to deduce a limit to the true 
correlation of variates. For these reasons we shall term Mr Yule's latest method 
of approaching the problem of relationship of attributes the method of pseudo- 
ranks. We are concerned principally therefore in this paper with the so-called 
method of association and the method of pseudo-ranks. In addition we deal 
incidentally with other coefficients and reply to certain criticisms, not to say 
charges, Mr Yule has made against the work of one or both of us. 
(2) History of Subject. 
In view of the misstatements made in the discussion at the Royal Statistical 
Society, with regard to the history of the subject, a few preliminary remarks of an 
historical nature may be fitly made here. Mr Sanger, for example, said that "all 
statisticians before Mr Yule had this passion for the normal curvej." This statement 
* Gray and Tocher, Journal of Anthrop. Institute, 1900, Vol. xxx. p. 111. 
t On the difficulty of "brackets" in the correlation of ranks, see Pearson, "On Further Methods 
of determining Correlation," Drapers' Research Memoirs, Dulau and Co., p. 36. 
X Journal Roy. Stat. Soc. Vol. lxxv. p. 045. 
