F. M. Turner 
501 
In the numerical example worked out above 
r = -4016 + -010, 
from the tables, h = - 023 398, 
p = + -899 0257, 
whence ?•' = "2570. 
This agrees closely enough with the value '2446 obtained by direct calculation 
considering the probable error of r. 
In a curtailed normal distribution the use of fourfold tables and formulae is 
not strictly applicable, i.e. the result obtained from them is not the true correlation 
of the figure, for the formulae only apply to truly normal figures. Since, however, 
the formulae give a numerical result to whatever fourfold table they are applied, 
it is useful to discover the relation between the value so obtained, and the correla- 
tion coefficient of the whole figure. 
I have not succeeded in finding a solution of the general problem. I have, 
however, calculated a fair number of curtailed normal tables by the fourfold 
formulae either chosen from the tables in MacdonelTs paper on " Criminal 
Anthropometry," or formed by first using the fourfold formulae to get the 
frequency of a normal table with the value of r = 5 at various points of division ; 
and then using these frequencies to form curtailed tables and calculating r'. It 
is rash to generalise from a few instances, but I think the following statements 
are true. 
(1) The apparent correlation is always less than the true correlation r. 
The difference increases as the unobserved portion g increases, or as h decreases. 
(2) In the same distribution, when r and h are constant, ?•' varies with the 
point of division. If this is close to the bounding line r' becomes very small. 
An interesting problem, which may prove of practical application, is to solve a 
table of the form of Table C, when a and d are unknown, but g — a + d is 
known. This may be done by the tedious process of trial and error. Give any 
value to a and fi'om the sixfold tables deduce two fourfold tables. If the normal 
distribution holds good, the values of r obtained from the two tables will be 
identical. 
As an example let us suppose that the number of persons exposed to infection 
in London was double the number who developed the disease. From this we get 
the foUowinsf sixfold table. 
