Karl Pearson and David Heron 
301 
existence of huge brackets. We may, we hold, entirely dismiss from statistical 
practice this method of pseudo-ranks, except for the case wherein it has always 
been used, i.e. for discrete unit variates, classified by units, where it coincides with 
the usual product-moment method and needs no special name. 
We have only to note here that Mr Yule uses the method of pseudo-ranks, 
which we hold to be demonstrably false, to make very sweeping charges, which 
can be and have been met, against the pigmentation work of the Biometric School. 
He not only suggests that the workers on the pigmentation data were foolish, but 
that they were dishonest. That is the sort of attack which usually recoils on the 
head of the man who makes it, especially when he has for several years worked 
in the Department against which he prefers the accusation. As a matter of fact 
the non-Gaussian character, the variability of tetrachoric r t , for different divisions 
was recognised very soon after it had been applied. But the investigations then 
made and more amply illustrated in this memoir indicate that the values originally 
given were substantially correct, the inheritance of intensity of pigmentation 
between parent and offspring lies between - 46 and "50 ; it is not of the order J 
as Mr Yule asserts on the basis of a theory which we feel convinced he will have 
to withdraw, if he wishes to maintain any reputation as a statistician. 
We have shown in the course of this memoir that the coefficient of asso- 
ciation Q, if treated merely as an undefined measure of association, has not 
for varying dichotomies the stability of the tetrachoric coefficient and it appears 
to have no reasonable physical meaning even for the cases which he has selected. 
Mr Yule has deduced from it a second coefficient, that of colligation, which has, 
he says, a physical meaning, when the table has been dressed in an artificial 
manner, namely it signifies on this artificial table the excess of the percentage 
of A's that are also B's over note's that are also B's. We have shown from 
Mr Yule's own writings that such a difference of percentages has in his own 
practice no meaning at all from the standpoint of association. 
Mr Yule never tells us clearly when we are to use one or other of his co- 
efficients. He spends 16 pages of his memoir on discussing the application of 
his coefficients of colligation and association to the vaccination data; yet on p. 611 
he writes : " For discontinuous attributes — attributes proper, as we might term 
them — the true correlation is that given by formula (24) or (26) [i.e. the Boas- 
Yulean coefficient or Pearson's cf>] ; we are dealing with a variable in fact, which 
can only take two values as distinct from a variable exhibiting a normal or any 
other continuous distribution. Tables I, III and IV [i.e. the vaccination data], 
as it seems to me, represent precisely such a case." Here Mr Yule has given up 
colligation as applied to vaccination; if so why devote 16 pages to its discussion? 
But 20 pages later Mr Yule tells us that : " For investigations on smallpox and 
vaccination such as those of Brownlee and Macdonell and Turner, the use of Q or 
co would, in my opinion, have been more illuminating as well as simpler than the 
use of the normal coefficient" (p. 631). 
