566 
A Study of the Effects of Diphtheria Isolation 
of variats differences we should free ourselves from the influence of the time 
factor, if attack-rate and isolation-rate increase simultaneously in the more 
prosperous towns, but without organic association. We have nine years' returns, 
but the epidemic nature of diphtheria in many cases does not give one great 
confidence in applying the method of variate differences to individual years. 
We considered that it would not be wise to deal with smaller intervals than 
three-year periods, and should have preferred had the data been available to work 
with five-year intervals. As it is, we cannot with three-year intervals for each 
town go beyond the second differences. We have accordingly 228 isolation-rates 
and attack-rates obtained from 76 towns for each of three three-year periods, 
152 first differences, and 76 second differences. We may symbolise them as /' and 
A', Sj/' and S^A' and and SoA'. We found the following results: 
' z'^' = + '332 + -040, 
%rs,A' = + -^'^Q ± -075. 
The first of these results compares reasonably with the previous results for the 
first and second periods on p. 552, i.e. 
1904-1908 : ? = + -427 + -063, 
1909-1912 : = + -290 + -069, 
with a mean value of + "358. And this is the more true because the values of 
were found by the product moment method without grouping, while rj>j^, was 
obtained from grouping in a correlation table*. 
Now the above values bring out very markedly that when we endeavour to 
remove the influence of the time factor and to obtain a purely organic relationship 
between / and A, we more than halve the correlation between them by proceeding 
to the second difference only. If we might suppose that a hyperbola would give 
the asymptotic value of j'g^' from the above three known correlations we should 
have 
VV=8-105+.-'^^"2' 
which indicates, although no stress can be laid on actual numbers, that at about 
the fifth difference rgj'g^' would tend to become negative. All we think it 
possible to say would be that if the time factor be eliminated there is very little 
positive organic association between high isolation-rate and high attack-rate to be 
cleared up, — certainly not more than is indicated by the correlation on p. 565 : 
W3^Z_j, = + -147± 076, 
* It may be noted that p was also found from a correlation table, but I'g as having only 
7G cases by product moment without grouping. 
