172 Oil Criteria for the Existence of Differential Deathrates 
or, the chance of a deviation so great as this appearing is only 4-73/10^, or the 
"corrected" cancer deathrates for males are significantly different in Dundee and 
Edinburgh. 
Using the General Population of Scotland, 1891-1901, as a standard population, 
we find 
[M' - M)laM'-M = 4-7399. 
Using the General Population of England and Wales (1901, males) as a standard, 
we find 
[W - M)/aAf'-M = 4-7630. 
These again both mark significant deviations in the corrected deathrates, but 
fail to give the maximum of significance. 
Now let us apply the test of distribution of squares of differences. We have 
(1^2 _ _ 4-24:186/a/10 
= 1-3414. 
Such a deviation would occur about once in ten trials and is not necessarily 
significant. 
Again applying the test of mean value, we have 
Wi = - -1564, 
and accordingly /// j \^^^y=^ = -6994, 
and this is an insignificant ratio of the deviation to its standard deviation. 
We now turn to the Xo' test, where we have = 28-0393. The Tables of 
Goodness of Fit provide for n' = eleven : 
P = -00178, 
or the odds are nearly 500 to 1 against such a deviation on random sampling. 
We conclude that there is a significant difference between cancer mortality in 
Dundee and Edinburgh. It is noteworthy that the corrected deathrates criterion 
which when analysed seems so very unsatisfactory gives here as in the case of the 
Liverpool and Birmingham General Deathrates far greater significance to the 
observed differences of mortality. 
We have not considered it worth while to investigate for this case the test 
of the significance of the mean of the 2u deathrates. It is we believe inadequate 
and further is laborious to calculate. It is, we hold, sufficient and more enlightening 
to calculate Xo^> and, what is almost deduced in the same process, the quantity Q^. 
There is a further point which may be illustrated on the Liverpool-Birmingham 
and Dundee-Edinburgh data. We have supposed in the course of our work that 
{d^ + d\)/{ag + a's) is an extremely reasonable value to give to p^. If we assume 
