Karl Pearson and David Heron 
259 
But the cases of approach to discrete differences are exceedingly few in number 
compared to the mass of cases with which we have to deal ; they exist as a rule 
only in the class-names, not in the things classified. Personally we have rarely 
found them except as already stated in theoretical Mendelian investigations, and 
to such cases the method of ranks, i.e. use of a ranks coefficient whether for four- 
fold or manifold tables, was first and rightly applied by Pearson. The Biometric 
School criticise not the application to Mendelian theory of these methods by Dr 
Brownlee and others, in which they only followed what had already been done, but 
Dr Brownlee's applying tetrachoric r, to such theoretical tables and then supposing 
that he had got at the root of the difference between theoretical and actual heredity 
correlation tables ! Mr Yule nowhere distinguishes between a theoretical Mendelian 
table and what we can absolutely demonstrate not to be theoretical Mendelism, 
e.g. Pearson's pigmentation tables. He writes : " As regards Dr Snow's recent 
comments in Biometrika on the use of the normal coefficient for Mendelian 
tables in Dr Brownlee's paper, he really thought that those comments were a 
much stronger condemnation of Professor Pearson's than of Dr Brownlee's work. 
Professor Pearson had repeatedly used the normal coefficient for inheritance 
tables, that were in all probability representations of Mendelian inheritance, as 
if it were an approximation to the product-sum correlation" {loc. cit. p. 651). 
It is a pity Mr Yule has not the courage of his opinions, and did not assert that 
the eye-colour data had a correlation of the Mendelian value ^ because they were 
Mendelian. Instead of that lie throws the sop of J to the Mendelian Cerberus, 
having carefully produced it not from the proper fourfold Mendelian table, but by 
applying the method of pseudo-ranks, which involves just the same assumption 
of continuous variation and regression beyond the Mendelian divisions into unit 
characters, as is involved in the tetrachoric r t . What Mr Yule means by "in all 
probability representations of Mendelian inheritance " is eloquently demonstrated 
by our discussion of the case — eye-colour in father and son — which he has himself 
selected to illustrate the Mendelian §. 
If we leave the Mendelian theoretical table and any other truly discrete 
fourfold classifications, which are indeed difficult to find, and pass to the fourfold 
classification in general, what method are we to use ? We assert that the four- 
fold or tetrachoric r, is a coefficient of association infinitely superior to Mr Yule's 
old Q or new &>. 
Mr Yule says he attaches no importance to the fluctuations of Q and a> for 
different divisions of the same table. If so, how can he usefully compare the 
values of Q or w found from two tables with different divisions ? If so, on 
what ground can he complain of the use of tetrachoric r, because in certain 
cases it fluctuates for different divisions of the same table ? He admits that 
"the coefficients of association and of colligation for different divisions of the 
same table in many cases fluctuate more largely than the normal coefficient" 
{loc. cit. p. 651), yet the only illustration he gives in his paper is that of the 
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