1 70 On Criteria for the Existence of Differential Deathrates 
These values of course lead to the same conclusion but show that the ratio 
{M' — M)jaM'-M varies from standard population to standard population, and 
may be increased more than 20 % when we pass to the population of maximum 
difference as standard. Such an increase might be of considerable importance in 
our estimate of differentiation if the ratio (M' — M)/aM'-M lay between 1-8 and 
2-2, say. 
Our third test is given by the formula on p. 165 : 
ihQ^ - u)/Vu = 72-7515/\/l0 = 23-01. 
The probability of a deviation as great or greater than this arising is immense. 
Thus we see that the distribution of the squares of the actual deviations is 
excessively improbable. 
Proceeding to our second test we find 
m = - -16625, 
and accordingly ifi / = -745, or Wi does not differ significantly from zero. 
/ \V2u/ 
Thus by this test no essential difference would be indicated. This does not show 
that it does not exist, but only indicates the inadequacy of the test. In fact since 
ds - Psas + d's - PsCi's = 0, 
and there is no great difference between V cisPsIs Va'sPsqs' tends to be zero, 
even with considerable differences between and p^ag or d'^ and pstt'^. 
We have seen that the value of in the Liverpool and Birmingham case is 
165-5031. We will now investigate the value of the factors 
\p p' ) / \ V + p ) 
for the ten age groups. They run 
Age 
Factor 
Age 
Factor 
0—5 
•98817 
45—55 
1-00182 
5—15 
•99626 
55—65 
•99895 
15—25 
b00071 
65—75 
■99440 
25—35 
1-00652 
75—85 
1-01376 
35—45 
1-00422 
• 
85 and over 
1-01510 
It will be seen that the factors differ very little from unity and introducing them 
into the several terms of Q'^ we find 
Xo^ = 165-4695, 
or xo^ only differs by 0-02 % from Q^. Applying the test for goodness of fit to 
for n' equal eleven groups* we find 
P = 2-40/1030, 
* See Table.i for Statisticians, p. xxxiii. 
