Alice Lee 
531 
of bananas per head of the population and the fall in the birthrate — will exhibit 
high correlation and will show graphically very high association, if plotted to 
appropriate scales and on a common time basis. Until the time factor has 
been removed, either by partial correlation or otherwise, it would be most un- 
wise to interpret such cases as providing any causal relationship. 
It seemed accordingly worth while to reinvestigate Dr Newsholme's problems 
with the aid of a rather more adequate statistical apparatus. 
(2) We must frankly confess at the outset that we have had great difficulty 
in following Dr Newsholme's description of the methods he has adopted to 
measure the amount of segregation. His charts do not seem always in ac- 
cordance with his tables, and both are occasionally out of agreement with his 
definitions. As he does not give the raw data on which his correlations are 
based, but only condensed versions of them in his tables and graphs, it is 
impossible to test his conclusions without returning to the original sources, 
which are not always stated, and when we have found them and our results 
differ, we are unable to say whether the difference is due to failure in his or 
in our arithmetic, or to divergences between his and our records. 
Dr Newsholme uses in all some six measures of the segregation ratio, four 
intentionally and two apparently by inadvertence. 
Let P = total population of a given area, <^ = the total number of annual deaths 
from phthisis. Then 0/P multiplied by 10,000 or 100,000, as the case may be, gives 
the crude deathrate from phthisis. Let Di be the deaths from all causes which 
occur in institutions and D the total deaths in the same area, then lOODi/D is 
Dr Newsholme's first approximation to the segregation ratio*. On p. 270 he 
gives two tables which show in (a) England and Wales as a whole, (6) in London, 
that, while in the course of forty years 1000^/P has practically halved, lOODi/D 
has practically doubled. The data, Dr Newsholme tells us, show " not only a 
very close correspondence between the increase of total institutional segregation 
measured by the ratio in question and the decrease of phthisis, but an even more 
striking similarity in the ratio at which these changes have occurred" (p. 271). 
This is illustrated by a graph on p. 271, in which the logarithms of the phthisis 
deathrate are plotted to time against the logarithms of the indices of institutional 
deaths to all deathsf. We do not know why Dr Newsholme has chosen this 
method of representation ; it certainly, with his choice of scales, makes the two 
curves roughly parallel, but this does not demonstrate the "similarity in the ratios 
at which these changes have occurred." For, if the actual values be plotted to 
the time, the curve of phthisis deathrate is convex and the institutional death- 
rate concave to the time axis, in other words while the rate of one is increasing-, 
* The assumption made appears to be that for the period iu question is proportional to the 
institutional deaths from phthisis, — a very big assumption. 
t The logarithms of the ratios of institutional deaths to all deaths appear to be either wrongly 
plotted or wrongly calculated. 
Biometrika x r 68 
