556 A Study of the Effects of Diphtheria Isolation 
because a wide-spread epidemic means a mild epidemic. All four coefficients are 
significant, and pair and pair they are quite consistent but in no case are they 
of any marked importance. They enable us, however, to correlate the isolation- 
rate and the case-mortality for a constant total attacked, i.e. to find the partial 
correlation „rj,„. We have the following results : 
whil 
(Correlation of Isolation-rate \ 
and Case mortality iov r 
constant number attacked J 
we have already found : 
i Congelation of number isolated 
J with number of deaths for 
I constant number attacked 
a' id 
First Period 
1904-1908 
- -4741 -056 
4- -066 ±-077 
Second Period 
1909-1912 
- -512-1- -057 
•220 ±-072 
Correlation of Total Numbers Isolated and Total Registered Deaths. 
Total Numbers Isolated. 
I 
1 
1 
0 1 
1 i 
1 
1 
—1250 
—1500 
—1750 
^1 
] 
i 
—3000 
®>! 
SO 
1 
Totals 
■=) 
■•O 
o 
o 
?^ 
§' 
^} 
55 
0— 75 
(U 
27 
2 
1 
94 
75 — 150 
16 
9 
3 
5 
2 
1 
36 
150—325 
1 
1 
2 
2 
2 
1 
9 
225—300 
7 
2 
1 
4 
300—375 
1 
2 
1 
1 
1 
6 
375—450 
2 
1 
1 
1 
5 
450—525 
1 
1 
525—600 
] 
1 
600—675 
0 
675—750 
750—825 
1 
0 
1 
Totals 
81 
37 
6 
7 
10 
6 
4 
2 
1 
0 
1 
0 
2 
157 
. , ' 
Means 
54-2 
59-8 
112-5 
133-9 
232-5 
312-5 
382-5 at 2125 isolated 
103-4 
a; 
be 
P2 
It will therefore be clear that removing the variation in number attacked has 
made only slight reductions in the values of the correlation coefficients between 
isolation-rate and case-mortality. The discrepancy between the absolute numbers' 
and the rates' correlations is not to be accounted for by " spurious correlation " 
involved in the use of total numbers attacked in both rates. It must therefore be 
due to : (i) lack of linearity in certain of the rcgres.-ions, (ii) high values in the 
coefficients of variation in certain of the quantities under discussion, or to a com- 
bination of these causes. With the small size of the populations under discussion 
it is by no means easy to test the true linearity of the regressions, even if we do 
what appears legitimate in this case, namely pool our data for the earlier and 
