Alice Lee 
539 
the time-factor by correlating the differences of these variates, then we shall free 
ourselves from the influence of the time-variate, and in doing this we shall also 
free ourselves practically from the influence of change of population, which is a 
time change. 
The following table resulted from this investigation. 
TABLE II. 
Coi'relation of Crude Phthisis Deaths (</>) mid Indoor Puiqyers (2)1). 
Variates 
England with Wales 
Scotland 
Ireland 
Crude 
-•934+ -014 
-•718+^053 
+ ^457 + '086 
Ai 
-•376 + -116 
-•206 + ^1.30 
-•092 + -134 
A3 
-•302 ±-141 
-•219 + •US 
-•103 + ^154 
A3 
-•213 + -164 
-•180+ •166 
- 143+ -168 
A4 
-•100+ -183 
-•157+-181 
-•147 + ^181 
A5 
-•016 + •IDS 
-•158 + •193 
- -140+ ^194 
It will be seen that for all three countries, whether we start with the positive 
correlation of the Irish or the negative correlation of the English and Scottish 
I'eturns, there is no remaining significant correlation after annulment of the time- 
factor between indoor pauperism and phthisis. 
A second method of verifying our conclusions is to find the partial correlation 
between indoor pauperism and phthisis deaths for a constant value of the total 
population and a constant value of total pauperism. We thus ask the question 
whether with a constant population and a constant amount of total pauperism, 
an increase of indoor pauperism would organically affect the number of deaths 
from phthisis. By making the population and the total pauperism constant we 
are largelj' producing an annulment of the time-factor and ascertaining whether 
a change in the number of indoor paupers due to causes other than temporal 
influences the number of deaths from phthisis. 
The system of correlation coefficients given in Table III, p. 540, was determined : 
Here the values of pp^rp,^ for England with Wales and for Scotland confirm 
the conclusions we have reached by other methods, i.e. there is no significant 
relationship at all between phthisis and indoor pauperism. The value for Ireland 
is, perhaps, significant, but having regard to its smallness (— '3 + "1) and the size 
of its probable error, no one can lay real stress on it, in opposition to the results 
of the other two countries. In general the coefficients for the Irish data appear 
very anomalous, and certainly divergent from those for Great Britain. 
Thus our investigation of the relation between indoor pauperism and phthisis 
appears to be entirely opposed to Dr Newsholme's conclusions. We find the 
segregation of paupers to have no substantial influence on deaths from phthisis. 
The one outstanding point at present, the relation between pr/P and (pjP after 
Biometrika x 69 
