David Hbiion 
111 
These results are very striking. We see that Mr Yule's " theoretical value 
of r" gives values which are roughly about a quarter of those given by his 
Coefficient of Association. It is difficult to see what sound conclusions can be 
based on such coefficients. 
One further example must be given. Mr Yule has devoted much attention to, 
and has given tables and diagrams in illustration of the decrease in the intensity 
of association with advancing age between blindness and mental derangement*. 
I have calculated on the same material for males only his "theoretical value of r" 
and the results are as follows : 
TABLE II. 
The Relationship between Blindness and Mental Derangement 
for different Age Groups. 
Age 
Group 
Coefficient of 
Association 
" Theoretical 
Value of r" 
5— 
•921 + -013 
•on 
15— 
■753+ -034 
•006 
25— 
•607 + -049 
•005 
35— 
•572+ -041 
•006 
45- 
•459+ -048 
•005 
55— 
•412+ -049 
■006 
65— 
•198+ -070 
•003 
75— 
- -126+ -111 
- "003 
We see therefore that while the Coefficient of Association decreases steadily 
from - 921 to — "126, the "theoretical value of r" ranges between - 011 and — "003. 
I have expressed those results graphically in Fig. 1 and it will be noticed that the 
line of the " theoretical value of r " can hardly be distinguished from the zero line. 
It will at once be admitted that these results justify a detailed examination of 
Mr Yule's methods. It is quite clear that he is unaware of the limitations of the 
processes which he recommends and that he has failed to apply the most obvious 
test of their validity, i.e. to compare the results obtained by the two methods when 
applied to the same data. 
I shall deal first of all with the Coefficient of Association. This expressed in 
the more usual notation is 
n _ad — be 
ad + be' 
where a, b, c, d are the frequencies in the four quadrants of a four-fold table. 
Mr Yule has given in his original paper a table showing the relative values of the 
Coefficient of Association and the actual correlation (not his "theoretical value 
of r ") for the special case in which the divisions are taken through the means, i.e. 
a-\-b = c + d and a + c = b + d. He found that " Q is always slightly in excess of r, 
the greatest difference being rather more than - 1 for Q = "7." Now this is a fairlv 
* This case is also given as an example in his Text-Book, p. 41. 
