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108
1938]
Now it is possible to calculate the expected distribution of cases, supposing they
were to follow a chance distribution, using the formula :
MnCrprqn-', where M denotes the number of inhabited houses (45,000)
and n the number of cancer deaths (2,464), p= ^//Mand q = 1 — 1/M.
If r has the values 0, 1, 2, 3 in succession, the formula gives the number of houses in
which 0, 1, 2, 3 deaths, respectively, may be expected to occur.
This formula applied to the spread of cancer is at first sight open to the following
objections:—
1. The probability that a case will occur is not constant, but varies from
house to house according to the number of occupants who are of "cancer age."
2. Multiple cases cannot occur except in houses where two or more people
are of "cancer age."
3. When one death has occurred in a house the probability of a second case
in a house will in general be reduced owing to the reduction of the number of
persons at risk in the house.
Closer mathematical investigation, however, shows that when these three factors
are taken into account the formula still gives a very close approximation to the
distribution which is to be expected on the hypothesis of chance.
Comparison of Observed and Expected Results.

It must be admitted that these figures reveal a striking similarity, and leave no doubt
that the house-to-house distribution of cancer in Islington is of a chance nature.
It is interesting to compare the above figures with the results given by the
application of the same method to the deaths from cancer which occurred a few years
earlier in the two boroughs investigated by P. Stocks.