558 
A Study of the Effects of Diphtheria Isolation 
Clearly these results are of miich interest; they show that the difference of r] 
for deaths on isolation over r is not as great numerically as, perhaps, the graph 
suggests, but they indicate the markedly high values for the coefficients of 
variation. Novv it is quite straightforward algebra to prove that 
//((, dla d> 
provided we may neglect terms of the square and product order in Vi and Va com- 
pared with unity, and this is perfectly legitimate when these coefficients of 
variation are, as is usual in anthropometric measurements, quite small quantities. 
But in the present case these quantities are greater than unity and their squares 
are not negligible as compared with unity, thus we need not be surprised at the 
marked inequality of «?',/„,,,/«* and a^,-, fo»ntl above. The values of the former 
show a marked relation between the case mortality and the isolation-rate, and the 
values of the latter indicate no appreciable betterment in the deaths due to 
increased isolation. Before we consider which of these coefficients gives us in the 
present case the better result as a guide to practical conduct, let us examine the 
correlation table for isolation-rate and case-mortality for the same 157 observations. 
Correlation of Isolation- Rate I and Case- Mortality m. 
Isolation- Rate. 
0 — 10 
10 — 20 
20—80 
SO— AO 
40—50 
50—00 
60 — 70 
70—80 
80—90 
Totals 
4— s 
1 
1 
7 
6 
5 
8 
28 
8—12 
2 
3 
3 
4 
8 
11 
9 
5 
45 
12—16 
5 
4 
3 
8 
3 
8 
6 
6 
1 
44 
16—20 
2 
1 
■2 
3 
3 
1 
2 
16 
20—24 
9 
2 
1 
2 
2 
1 
17 
24—28 
3 
1 
2 
6 
28— ,12 
1 
1 
Totals 
23 
1 
11 
15 
12 
26 
28 
22 
16 
157 
Means 
19-04 
14-00 
16-18 
15-60 
14-00 
11-08 
11-71 
11-09 
9-25 
13-26 
o 
O 
The following constants were found for this table 
Isolation-Eate 
Mean , 
Standard Deviation 
Coefficient of Variation... 
Correlation Coefficient and Ratio 
/ = 49-52 
o-/ = 25-52 
vi = 0-52 
rj„^= - -5291 ±-038 
Case Mortality 
m =13-26 
o-jn = 5'58 
v,„ = 0-42 
rimi= "5546 
The graph of the regression of case mortality on isolation-rate shows small 
evidence of skew regression (see Diagram II), and this is again confirmed by the 
difference between ?-j„, and 7],-^^ being fairly small. The marginal frequency dis- 
tributions show, however, considerable skewness, and that for the isolation-rate is 
lumped up at the end where there is no isolation : more than half the numerator 
of 77,„j being contributed by the towns with little or no isolation. It is desirable 
to consider these towns further. They have an attack-rate of -76, which is sensibly 
* This is the ^ »-^^^^ of our p. 556. ' f The values are given on our p. 554. 
