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On Theories of Association 
says it is "very small." It may according to the percentage difference be 5*15 or 
0 - 96 ; thus the percentage difference might be higher than in the very " high 
association indeed" case in the partial universe of those without nerve signs. 
Finally in the "high association" case of the total universe, the percentage 
difference might be 1'91 or 5T03. Clearly in judging by percentages the con- 
clusion will depend on which percentage is worked out first. Is it not clear 
that, however Mr Yule may have reached his judgments of no, small, high or very 
high association, the percentage difference is not his actual measure and could 
only confuse the tyro in statistics, for whom he introduces this "simple" method? 
But if difference of percentage has obviously no correlation with Mr Yule's 
judgment of these grades of association, what weight can possibly be given to the 
coefficient of colligation in determining' association ? The chief merit of that 
coefficient according to Mr Yule is that it has — what Q has not — a physical 
meaning; but for him percentage differences of 1*91 and 36'96 alike mark "very 
high associations" and differences of 0'9G and 10 88 alike mark very small or no 
association. We have no standard and clearly Mr Yule has none of how such 
differences of percentages are to be interpreted. Mr Yule has b)' his treatment 
of percentages a priori destroyed any rational meaning that could be given to 
his own coefficient of colligation as a measure of relationship. Is not Professor 
Edgeworth's question answered ? The coefficient is a "colligation," not a "profound 
truth." Mr Yule obviously lays no consistent stress whatever on percentage 
differences in practice. 
(d) Mr Yules use of Pearsons "Transfer" (ab — cd)jN as a, 
Measure of Association. 
Among Mr Yule's many means of testing association — no two of which give as 
a rule the same result — perhaps the most striking is his use of the "Transfer" 
(ab — cd)jN, to which he gives a new name and letter, the "common difference" S*. 
One of us had already suggested that the " transfer" per unit of the total frequency 
might be used as a coefficient of association of an inadequate character-f-. It is in- 
adequate because it makes no correction for class-indices and none for the centroids 
of the quadrants. Thus it does not lie between 0 and 1, and is largely affected by 
the position of the dichotomic lines. Mr Yule has preferred to use instead of the 
transfer per unit of total frequency simply the transfer, his "common difference 
8," and the results add further evidence of the vagueness of the whole of his 
conceptions of association. He tells us, to begin with, that " the difference of the 
cross-products may be very large if N be large, although 8 is really very small... 
the difference should be compared with N, or it will be liable to suggest a higher 
degree of association than actually exists" (loc. cit. p. 37). To illustrate his 
* Theory of Statistics, p. 36. 
t Phil. Trans. Vol. 195 A, p. 14. 
