THEORY OF STATISTICS. 
Here the important question is, How far does inoculation 
protect from attack? The most natural comparison is therefore— 
Percentage of inoculated who were not attacked . 98:9 
z not inoculated ow LLB 
or we might tabulate the complementary proportions— 
Percentage of inoculated who were attacked . aide] 
2 not inoculated . a . a J 92 
Either comparison brings out simply and clearly the fact that 
inoculation and exemption from attack are positively associated 
(inoculation and attack negatively associated). 
We are making above a comparison by rows in the notation of 
the table on p. 26, comparing (4B)/(4) with (aB)/(a), or (48)/(4) 
with (af)/(a). A comparison by columns, ¢g. (4B)/(B) with 
(4B)/(B), would serve equally to indicate whether there was any 
appreciable association, but would not answer directly the 
particular question we have in mind :— 
Percentage of not-attacked who were inoculated . 30:8 
ps attacked ¥ py ; . 43 
Example vi—Deaf-mutism and Imbecility. (Material from 
Census of 1901. Summary Tables. [Cd. 1523.]) 
Total population of England and Wales . . 32,528,000 
Number of the imbecile (or feeble-minded) x 48,882 
Number of deaf-mutes . ‘ : : 15,246 
Number of imbecile deaf-mutes 451 
Required, to find whether deaf-mutism is associated with 
imbecility. 
We may denote the number of the imbecile by (4), of deaf- 
mutes by (B). A comparison of (4B)/(B) with (4)/N or of 
(AB)/(4) with (B)/N may very well be used in this case, seeing 
that (4)/N and (B)/N are both small. The question whether to 
give the preference to the first or the second comparison depends 
on the nature of the investigation we wish to make. If it is 
desired to exhibit the conditions among deaf-mutes the first may 
be used :— 
Proportion of imbeciles among deaf- 
= AEE) }20 6 per thousand. 
Proportion of imbeciles in the whole 1'5 
population = (4)/& . : : 
32 
29