THE INFLUENCE OF ISOLATION ON THE 
DIPHTHEKIA ATTACK- AND DEATH-RATES. 
By ETHEL M. ELDERTON, Gallon Research Fellow 
AND KARL PEARSON, F.R.S. 
(1) Introductory. The problem of the advantages of isolation, not only in the 
case of diphtheria but of other diseases of an infectious character, is likely, owing 
to modern views as to " carriers " and other sources of transmission, to be much 
discussed in the near future. It is therefore well to consider what may be learnt 
from the statistics available. The questions which naturally arise are of the 
following kind : 
(i) In districts with a maximum of isolation is there a minimum of incidence? 
(ii) In districts with a maximum of isolation is there a minimum deathrate 
from the disease isolated ? 
There cannot be the slightest doubt that, if these two questions were answered in 
the affirmative and we could show that the incidence was markedly less and the 
deathrate significantly smaller in districts where isolation was most stringently 
carried out, then these results would be advanced as a strong argument in favour 
of isolation. 
To the trained statistician, however, no conclusion based upon such results 
without much further analysis would have any validity. To illustrate this point, 
let us consider the hypothetical case that medical or popular opinion in a given 
town has been persistently in favour of increasing the isolation-rate, and further 
suppose that in this district improved economic conditions have increased the 
immunity, or bettered sanitation lowered the incidence, while at the same time 
new methods of treatment have lowered the deathrate of the disease ; it will be 
clear that in considering the statistical results over a course of years we should 
find a high isolation-rate negatively correlated with both the incidence- and the 
death-rates. Thus if we considered this correlational as a causal nexus, we 
should be raising an apparently strong argument in favour of a maximum of 
isolation, which would be based on the statistical fallacy, that when two quantities 
are both changing continuously with the time, this must of itself denote a causal 
relation. 
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