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On Theories of Association 
we knew nothing about the frequency and for which the dichotomic lines gave 
marginal frequencies having any continuously ascending order. 
Such invalid discussions as to the " apparent law that associations were on 
the whole higher where populations were healthier or more defective " and on 
the relation of change of association between two defects with age had actually 
been attempted by Mr Yule*. Heron criticised, it will be seen, not the laws, if 
they be laws, but Mr Yule's attempt to investigate them by " association." He 
wrote"f" : "For precisely similar reasons his discussion of the change of association 
with age must be dismissed as entirely fallacious. There may be, and probably is, 
some decrease of association with advancing age, but the enunciation of such a 
law on the basis of a number of coefficients of association is purely idle." Heron 
then proceeded to show that the proportions of blind and of mentally deranged 
both increased steadily from infancy to age, and this signifies that if the frequency 
surfaces were of the same type and really had the same correlation at each age 
the Q would steadily decrease with age. It will be seen that Heron's criticism 
applied solely to Mr Yale's methods ; it was an unanswered and, we believe, 
absolutely unanswerable criticism of the absurdity of trying to deduce laws from Q. 
How does Mr Yule meet it? He writes j: "Dr Heron also objects to my con- 
clusion that association decreases with age. His objection appears to be that the 
product sum correlation does not decrease so markedly or regularly with age in 
one of my cases that he examined... and that no evidence has been given that 
the normal coefficient decreases." 
The destructive criticism that Q for the Gaussian and for all surfaces of which 
we have any practical experience increases the more one-sided is the dichotomy — 
and Mr Yule thinks nothing of '02°/ o dichotomies — is not met at all. The criticism 
was of the method of forming an inference, and not as to whether the inference 
led to a law which could be otherwise substantiated. " There may be, and 
probably is, some decrease of association with advancing age," wrote Heron, "but 
the enunciation of such a law on the basis of a number of coefficients of association 
is purely idle." The truth of the law or its falsity is of no great importance, but 
that Mr Yule should reach it by a fallacious method is of fundamental importance. 
Mr Yule seeks by the words "Dr Heron also objects to my conclusion that 
association decreases with age" — an objection never raised — to confuse the really 
destructive criticism, that Q, unlike tetrachoric r t , having no intelligible correction 
for the one-sidedness of its dichotomies is a function of the dichotomic percentages 
and therefore two Q's based on different percentages are wholly incomparable. 
* Phil. Tram. Vol. 194 A, pp. 309 et seq. 
f Biometrika, Vol. vm. p. 119. 
X Loc. ext. p. 037. 
