Karl Pearson and J. F. Tocher 
177 
If we consider the order of the significance deduced from the two standard 
populations we have : 
Q 
Pair 
{M'-M)l<rjf^j[._j^ 
1309 
London and Rural Districts ... 
11-53 
12-25 
County Boroughs and Rural Districts 
9-61 
8-95 
London and Urban Districts ... 
7-74 
7-39 
County Boroughs and Urban Districts 
4-89 
6-96 
London and County Boroughs 
3-93 
6-76 
Urban Districts and Rural Districts 
5-32 
The Q order shows that London and the County Boroughs are markedly 
differentiated from the Rural and Urban Districts — in the higher degree from the 
former. Thus the city districts tend most to a high cancer rate. London is 
differentiated from the County Boroughs, and the Urban from the Rural Districts, 
but to a less extent than in the previous cases. The (M' — M)jaj^i-^ja test confirms 
this order except in the case of Urban and Rural Districts which are now more 
highly differentiated than County Boroughs and Urban Districts. Thus we note 
that a particular standard population may not only influence the significances of 
the differentiated deathrates, but also the order of these significances. This result 
will be confirmed in the case of diabetes. 
The following are the values of Q'^ and '• 
Pair 
London and County Boroughs 
London and LTrban Districts ... 
London and Rural Districts ... 
County Boroughs and Urban Districts 
County Boroughs and Rural Districts 
Urban Districts and Rural Districts . . . 
48-4.567 
80-0869 
171-3498 
54-5901 
149-9172 
45-6922 
49-2414 
80-6986 
164-2686 
54-3279 
151-0230 
46-5109 
It will be seen that the only considerable difference between Q"^ and X(? arises 
in the case of the London and Rural Districts pair, and more than half this 
difference is due to the very heavy deathrate in London from cancer of persons 
between 65 and 75. 
Before we discuss the inferences to be drawn from these results, we will place 
. . 1 
on record the ratio of m to its standard deviation The easiest way to 
calculate this ratio is from the components 
Q 
d, + d's 
a's 
Biometrika xi 12 
{d. + d',)!!-"^' 
