198 
Correlation of Cancer and Diabetes Deathrates 
The accompanying Table II gives under each year the total male population, 
the total deaths from cancer and from diabetes, the crude deathrates, the corrective 
factors and the corrected deathrates. From the latter the first six differences, 
Aj^ to Ag, were found and these were correlated for the two diseases. The following 
correlations were found : 
Correlation of Differences of Corrected 
Corrected Deathrates 
First Differences 
Second 
Third 
Fourth 
Fifth 
Sixth 
Deathrates. 
+ -958 ± -008, 
+ -058 ± -113, 
+ -043 ± -130, 
+ -047 ± -143, 
+ -051 ± -154, 
+ 050 i -164, 
+ -045^1 -173. 
It will be seen that with the first differences we get an enormous drop in the 
correlation of the cancer and diabetes deathrates, i.e. from + -958 to + -058, and 
that very rapidly the correlation becomes steady* and insignificant. Thus with 
the removal of the time factor there appears to be no organic relationship between 
the prevalence of diabetes and cancer. A year in which there is an excess of diabetes 
deaths is not a year which will probably have an excess of cancer deaths. 
Now this result although absolutely conclusive as far as it goes, must not be 
stretched beyond its exact hmitation. There is nothing to show that an increase 
of cancer at any given epoch will be accompanied by an increase of diabetes. 
It might be argued that it is conceivable that an increase of diabetes will be 
followed at an interval by an increase of cancer. I have not directly tested this, 
but it is to some extent indirectly tested by the method of variate differences. 
The sixth difference correlation correlates functions of the deathrates for seven 
years in the case of two diseases, and would be likely to indicate if there were any 
such related succession. At the same time it must be remarked that previous 
investigators have all dealt with the contemporaneous deathrates of cancer and 
* This steadiness can be illustrated also by the method discussed in Biometrika, Vol. x. p. 272 and 
illustrated on p. 346. 
2 
Values of cr^^m ,./ff^^„i-ix their approach to 4: . 
m 
2 
Theoretical Ratio =4 
m 
Cancer 
Diabetes 
Mean 
1 
2-000 
0-655 
0-830 
0-742 
2 
3-000 
2-689 
2-969 
2-779 
3 
3-333 
3431 
3 386 
3-409 
4 
3-500 
3-446 
3-549 
3-497 
5 
3-600 
3-719 
3-627 
3-673 
6 
3-667 
3-653 
3-669 
3-661 
It will be seen that there is a rapid approach to the theoretical values of the ratio. 
