108 On Criteria for the Existence of Differential Deatlirates 
Illustrations, (i) We have for Birmingham and Liverpool the following data 
for all Males in 1911 : 
Age (jrroup 
Birmingham 
Liverpool 
Population 
Deaths 
Population 
Deaths 
0— 
32,552 
2003 
45,889 
3117 
5— 
58,053 
161' 
78,518 
326 
15— 
48,431 
162 
()2,751 
309 
25— 
47,212 
252 
58,216 
476 
35— 
37,897 
382 
47,711 
632 
45— 
25,431 
454 
32,664 
775 
55— 
15,384 
575 
20,198 
944 
65— 
7,535 
511 
10,215 
904 
75— 
1,944 
321 
2,194 
335 
85— 
173 
58 
191 
62 
Totals 
275,212 
4879 
358,547 
7880 
Our problem is to discover whether there is actual differentiation between these 
two systems of deaths, and if so, what is the measure of it. We work with ten 
age groups. 
The actual arithmetical work is indicated on the following page. It leads 
M' — M 
to = 165-5031 or Q = 12-8648. Hence applying first test — = 12-8648. 
Or : the difference of the two deathrates corrected to the population of maximum 
ratio is no less than 12-86 times the standard deviation of the difference. We 
conclude that the chance of such a difference arising from random sampling is 
enormous*, or the two deathrates are most certainly and markedly different. 
There is no difficulty in correcting the deathrates to the population of maximum 
difference as standard, but it is of interest to note what happens, if the standard 
population has other values. 
For example, when we correct to the male population of all England and Wales 
for 1901, we find using the formula of p. 161 
M' - M 
- = 10-0198. 
If we use the general male population of England and Wales in 1911 we find 
M' - M 
— = 10-1567. 
* The chance is approximately 3-3508/1038. xhis test is practical]}^ valid in tliis case for the general 
deathrate of Liverpool males is greater at all ages except 75 onwards than that of Birmingham and the 
age groups above 76 contribute nothing of importance to the value of Q^. 
