164 Oil Criteria for the Existence of Biferential Deathrates 
Eeturniiig to our deathrate symbols we have 
0/ r. G/ o 1 
s 
dg 
.(viii) 
Hence the age classes of the standard population must be taken proportional to 
^d\ d„\ , /'d', d. 
a gag l^-^- 
id's 
or very approximately to 
, fd's dg\ 
\a g agj 
d\ + d. 
d'g + dg 
a'g + a.g 
We note at once that this method would give irrational values for As in the 
case of any material for which the age deathrate was not invariably greater for one 
district or class. On the other hand Q the ratio of the difference of corrected 
deathrates to the standard deviation of that difference is always real and given by 
Q' = S 
= S 
.(ix), 
d'g + dg j 
approximately. 
If for every value of s, d'gja'g is either greater than dg/dg, or, on the other hand, 
is always less than dg/a^, then the odds are about 50 to 1 if § be as great as 2 that 
there is significant divergence of the two corrected deathrates. On the other hand 
if Q has no significant magnitude, the deathrates will not be significantly different. 
Supposing the condition as to the relative magnitude of d' gja g and djag be not 
satisfied, then if Q has no significant magnitude for these irrational age classes, 
it will certainly have no significant magnitude for any other size of age classes, 
and accordingly we conclude that the difference of the deathrates is not significant. 
But if Q be of significant magnitude for the irrational age classes, it does not follow 
that it will be significant for rational age classes, and further discussion is needful. 
Of course any case in which for the bulk of groups d' gja' g is greater than dgjag, 
but for one or two groups dgjttg is the greater, will have Q = {M' — M)jaM'-M 
lessened by the inclusion of these cases, for the numerator of Q is decreased and 
the denominator increased. We should therefore be at liberty to consider only 
the groups where the deathrate goes one way. for the age groups are actually 
independent, and it is really a fictitious balancing of the corrected deathrates 
which arises, when one age class with deaths in excess compensates for another 
age class with deaths in defect, and so tends to equalise M and M'. This is of 
course a grave difficulty which must arise when we deal with any corrected 
