Karl Pearson and J. F. Tocher 
179 
confirms the view already expressed that but little is to be gained from its use. 
The fact is that each test measures a different feature of the difference of the 
distributions and the worst test will be that which measures the least important 
characteristic. There is little doubt that the deviation from zero of the mean of 
all the deviations measured in terms of their S.D.'s is this characteristic. The 
second test measures the significance of the "corrected" deathrates for the standard 
population of maximum significance gives results which are most closely in accord 
with the p^o^ but it suffers from two rather serious defects: (i) it is conceivable 
that M might be very close to M' and yet the actual distribution of deaths very 
different, (ii) the standard population which gives the maximum significance to 
the difference of the corrected deathrates may, as we have indicated (p. 164), be 
an impossible one. Hence the values of the significance may be very considerably 
exaggerated. It has been our experience, that when we have taken other standard 
populations, we have found the Q- considerably less than for the population of 
maximum significance, but not always most markedly less. 
On the whole we think a test which considers the general distribution of 
deviations more likely to show definite results, than one which considers only 
a mean, and from this standpoint we hold that the xo' and HQ^ - u)/V u are the 
better criteria. The main assumptions on which these tests are based are for the 
latter : that the distribution of squared deviations (each measured in terms of 
its own S.D.) will, even if each deviation be selected from a non-normal frequency, 
give a second moment distribution which follows the normal law ; and for the 
former: that the Gaussian curve accurately enough describes the frequency given 
by a binomial. This assumption would be more closely fulfilled by a general 
than by a special disease deathrate, but is probably more valid than the previous 
assumption. Hence we believe that while the three first tests have all a certain 
value, the first and third are to be preferred and the first is best of all. 
Judged by the first, second and third tests we conclude that significant 
differences can be definitely said to exist between all these cancer mortalities. 
Urban and Rural Districts showing the least but still a very weighty significance ; 
that London and the County Boroughs other than London have significantly 
different cancer mortality, while both London and the County Boroughs dift'er 
conspicuously from the Urban and Rural Districts. 
It is clear that the degree of significance is closely associated with some variate 
which increases with difference of position in the scale (a) London, (b) County 
Boroughs, (c) Urban Districts, (d) Rural Districts, i.e. with some factor which 
increases with the city character. The increase during the past fifty years in the 
cancer deathrate has been associated by some with improved diagnosis. Is the 
variate correlated with the above order that of better diagnosis ? It may, perhaps, 
be doubted whether the general practitioner is much more competent in cancer 
diagnosis in London now-a-days than in the Rural Districts. But an examination 
of the terms of or Xn^ shows that nearly half of the significant difference arises 
from the terms and Xs" corresponding to the 45 to 55 group and nearly a third 
