Ethel M. Eldbeton and Karl Pearson 
555 
total deaths for constant total number of attacks. And this divergence, often in a 
marked degree, of partial correlations for rates and for absolute numbers is not 
unfamiliar to those who have had to deal with disease statistics. In the present 
case it renders still more obscure any argument drawn in favour of isolation from 
apparently lesser case mortality. 
(4) On the degree to which "spurious correlation" may he influencing the 
attack- and death-rates. It seemed desirable if possible to throw further light on 
this point and accordingly we correlated attack- and death-rates with the total 
population. It will be remembered that : 
A = 1000 X cases population, 
M = lOOO X deaths population, 
and accordingly if A and M be correlated with the population P, we might 
anticipate that if cases and deaths had no relation to population, there would be 
a high negative correlation arising from A and M both varying inversely as P. 
We were comforted by finding practically msigmfic&nt positive correlations. Thus : 
First Period Second Period 
Correlations 1904-1908 1909-1912 
?-p^= Population and Attack-rate -|- -137 ±-075 -|- -0541 -075 
r„/= Population and Death-rate + -131 ± -076 -f -1161 -074 
r,,, = Population and Isolation-rate -I--] 52+ -075 + -102+ -075 
The last correlation cofBcients show us that there is very little relation between 
the size of a population and the amount of isolation practised. Further these 
isolation coiTelations in which there is no obvious source of spurious correlation 
are as significant as those of population with attack- and death-rates where the 
possibility of " spurious correlation " is manife.st. We conclude accordingly that 
risk is more uniformly distributed over population than we had anticipated, and 
that the correlations between the three rates /, A and M are really open to 
" organic " interpretation. 
The next point which arises for discussion is whether the presence of the total 
number attacked (a) in the rates / and m can produce spurious correlation. If so 
we should anticipate that the absolute number a would be negatively correlated 
with both isolation and case mortality rates. We found : 
First Period Second Period 
Correlations 1904-1908 z""' 09-1912 
^ai = Total attacked and Isolation-rate -)--264±-072 +-226 ±-072 
>W= Total attacked and Case-Mortality --251 ±-072 --203 ±-072 
The first set of these coefficients are not even negative and therefore cannot 
be due to " spurious correlation," although such correlation may have reduced 
their organic values. They admit, however, of an easy interpretation, namely 
that : where the number attacked has been large the isolation has been more 
practised. The second set of coefficients might be due to spurious correlation, but 
they again admit of a simple interpretation as apart from "spurious correlation," 
namely that : when the attacks are numerous the deaths are relatively few, 
Biometrika x 71 
