162 On Criteria for the Existence of Differential Deathrates 
(2) Two points, however, arise in this work. We do not know jp^ and qs 
nor have we yet selected the standard population, i.e. the values of ratios 
like AsjA. 
With regard to jjg it may be held by some that the value obtaining in the 
general population shovUd be given to it. This might be reasonable if that popula- 
tion were immensely large as compared with either group under consideration, 
but very often the group dealt with is quite considerable as compared to the 
remainder. Thus in Scotland for certain administrative purposes we consider 
Scotland [Clyde), and Scotland {excluding Clyde). In England for similar purposes 
we find nine official districts* selected, so that if we were comparing the North- 
western district with the London district, it would be curiously difficult to demonstrate 
why if these are samples, we take them plus the remainder to be more representative 
and fixed than either alone. We doubt very much whether the material we 
suppose we are sampling is to be considered as the general population. Rather 
we look upon that general population as the indefinitely large group who might 
be considered as living and dying under the same environmental conditions, if 
they continued indefinitely in force. 
Again, is it quite correct to take from the general population of the country 
when the problem is to discover whether the two districts are themselves random 
samples from some population which may not be the same as that of the general 
population of the country? Thus Aberdeen and Inverness might both well be 
random samples of a population which is not that of Scotland as a whole f. Hence 
as in cases of probable error it will usually be best to calculate from the observed 
material itself, i.e. if our two groups be really samples of the same population, 
then probably the best thing we can do is to take 
d, + d\ , ^ d^ + d\ 
= ^ ^ and (/c = 1 ~ — 
^ a, + a s + a s 
If be small, as it usually is, then it will be sufficient to take 
''(Zo + d s\ Af.^) 
f ds + d'A 
\ a,a\ ) 
A 
It remains to consider AJA. Here again it is not unusual to take A^jA as 
given by the general population. Or if the "corrected deathrates" for a series 
of years are being compared, it is not unusual to reduce the age distributions to 
that of a certain year, e.g. in the manner of the English Registrar-General for 
tuberculosis and cancer deathrates to the population of 1901. For the same 
reasons as in the case just discussed we might, perhaps, find it fitting to take 
AsjA as given by the material under discussion, i.e. =-- {a^ + a's)/{a + a'). Or, 
again, we might reduce one district to the population of the other, i.e. take 
AgjA = aja, or a'Ja'. It is of interest to see practically what differences such 
divergent reductions make. 
* By the Board of Trade for example. 
t Or again lawyers and the clergy may have or may not have significantly different mortalities, 
but the mortality of both differs essentially from that of all England. 
