554 A Study of the Effects of Diphtheria Isolation 
According to these correlations, when or where the isolation-rate is high, the 
case mortality is low. Further when or where the attack-rate is high the case 
mortality is low. Now we know that : 
/ = 100 X isolated cases all cases, 
A — 1000 X all cases population, 
m = 100 X deaths all cases. 
Hence if we selected the number attacked at random and chose the deaths to 
be simply some number less than this, we should expect to find a considerable 
negative correlation between A and m; and as we actually do find such a corre- 
lation, we cannot be certain that the actually observed values of r^,„ are not due 
to " spurious correlation." If they were " organic " we should interpret them to 
mean that a widespread epidemic {A large) was a less virulent epidemic (m small). 
On the other hand the spurious correlations of / and m would be positive in value, 
while the actual correlations are negative. Thus it would seem that while a high 
isolation-rate is associated with high attack-rate, it must be " organically " asso- 
ciated with a lessened case mortality. In other words while isolation does not, on 
the crude figures, appear to lessen the frequency of disease, it does appear to 
lessen the mortality among the attacked. This result appeared to be of such 
very great importance, if thoroughly established, that we determined to inquire 
into it further. It seemed reasonable to believe that the bulk of persons attacked 
might have better care in a hospital than in their own homes and thus isolation 
indirectly lessen the ill effects of the disease. 
We accordingly endeavoured to approach the problem from a somewhat 
different standpoint: Given two districts with the same total number of persons 
attacked (a), will that district with more isolated (i), have fewer or more deaths (d)? 
The answer to this question depends on whether the partial correlation coefficient 
of total isolated cases with total deaths for constant number attacked is negative 
or positive. We found : 
First Period Second Period 
Correlations 1904-1908 1909-1912 
Via = Isolated Cases and Deaths ... + -860 ± -020 + -867 ± -019 
= Isolated Cases and Attacked ... + -937 ± -010 + -968 ± '005 
r„a = Attacked and Deaths + -907 ± "014 + -918 ± -012 
= Isolated Cases and Deaths for con- 1 ^ .^^^ ^ .^^^ _ .^^^ ^ .^^^ 
stant number of Attacked J 
Thus in the first period for a given number of attacked more isolation was 
associated with more deaths, and in the second period for a given number of 
attacked, with fewer deaths ; but in both periods, having regard to the probable 
errors, we cannot assert any real significance, or be reasonably certain that where 
there is more isolation, there recovery is more likely to occur. 
We shall see later that the correlation between / and m for constant total 
number of attacks is not the same thing as the correlation of the total isolated and 
