III. —ASSOCTATION. "1 
It will be evident from §§ 1 and 2 that a large number of such 
comparisons are available for the purpose, and the question arises, 
therefore, which is the best comparison to adopt? 
10. Two principles should decide this point: (1) of any two 
comparisons, that is the better which brings out the more clearly 
the degree of association ; (2) of any two comparisons, that is the 
better which illustrates the more important aspect of the problem 
under discussion. 
The first condition at once suggests that comparisons of the 
form 
(4B) _ (48) ) 
®) ~ ®) “ 
are better than comparisons of the form 
(48) (4) 
@ F 0) 
For it is evident that if most of the objects or individuals in the 
universe are B's, i.e. if (B)/N approaches unity, (4B)/(B) will 
necessarily approach (4)/N even though the difference between 
(4B)[(B) and (4B)/(B) is considerable. The second form of 
comparison may therefore be misleading. 
Setting aside, then, comparisons of the general form (), the 
question remains whether to apply the comparison of the form (a) 
to the rows or the columns of the table, if the data are tabulated 
as on p. 26. This question must be decided with reference to the 
second principle, 7.e. with regard to the more important aspect of 
the problem under discussion, the exact question to be answered, 
or the hypothesis to be tested, as illustrated by the examples 
below. Where no definite question has to be answered or 
hypothesis tested both pairs of proportions may be tabulated, 
as in Example vi. 
Example v.— Association between inoculation against cholera 
and exemption from attack. (Data from Greenwood and Yule, 
Table II1., ref. 6.) 
Not attacked. Attacked. Total. 
Inoculated . . : 276 279 
Not inoculated . 473 539 
cL... 
5 
3 
66 
L0LalL 749 69 318