Karl Pearson and J. F. Tocher 183 
population of maximum difference, and (iii) the Test from Distribution of Squares 
of Deviations. 
Proceeding as in the case of Cancer we have the following table : 
Probability P of the two Groups being samples of the same Population. 
Paired Districts compared 
for Diabetes Mortality 
Goodness of Fit 
Test 
(ii) Test from 
DifEerence of 
Corrected 
Deatlirates 
1 M' - M\ lir 
= Q 
Distribution of 
Squares of 
Deviations 
{W-u)lJu 
Rural Districts and 
County Boroughs 
■0004 
•20/10' 
•0215 
Rural Districts and 
Urban Districts ... 
•0022 
•2.5/10« 
•1121 
London and County 
Boroughs ... 
•0:M4 
•000,02 
•4548 
Rural Districts and 
London 
•0801 
•000,04 
•3442 
London and LTrban 
Districts ... 
-.3520 
•000,7 
•0916 
Urban Districts and 
County Boroughs 
•7943 
•009,7 
•0184 
As before the order of significance, as we might expect, of the first two tests 
is the same*, but it is no longer as in the case of cancer the same as in the third 
test. The third test shows only significance between the members of the two pairs 
Rural Districts and County Boroughs and Urban Districts and County Boroughs, 
and neither difference is at all emphatic, while the last is out of accord with the -x^^^ 
test. The test shows distinct significance between Rural Districts on the one 
side and County Boroughs and Urban Districts on the other. The Rural Districts 
are not very significantly differentiated from London. Probably London and the 
County Boroughs have a different diabetes mortality. An examination of the table 
on p. 182 shows that the chief difference between the Rural Districts and the Urban 
and County Boroughs mortality is the much lessened deathrate after 50 years of 
age; while the difference between the Rural Districts and London lies in the 
much greater deathrate from diabetes under 45 in the Rural Districts. Such 
differences might be so balanced that there existed no significant difference in the 
corrected deathrates. No one could judge by the corrected deathrates of 10-948 
and 11-099 with a probable error of -60 that the Diabetes mortalities of Rural 
Districts and of London are as significantly differentiated as they are. 
We see that the second test enormously exaggerates the significances determined 
by the first test and this is precisely what we might anticipate. The second test 
* The order of significance in the third test will not now be the same as in the second, although 
it depends only on because (\Q- - u) can be positive or negative. It was the same in the case of cancer 
because Q"^ was always greater than 2m. Positive or negative values of {^Q^ -u) only signify that the 
mean of the squares oi deviations exceed or fall short of the theoretical value respectively. 
