Karl Pearson and David Heron 
291 
(c) Fallacies involved in the use of Percentages. Coefficient of Colligation. 
Mr Yule has endeavoured to give his Q a physical meaning by deducing from 
it for the " equivalent symmetrical table " his coefficient of colligation u>. For 
such a table 
A 
Not-4 
B 
J ad 
Jbc 
Not-5... 
Jbc 
J ad 
Totals 
ijad+ Jbc 
Jad+ Jbc 
_ J ad — Jbc 1 [/percentage of A 's\ /percentage of not-vl's> 
Jad+Jbc 100 (V which are B's ) V which are B's 
We have given grave reasons for doubting the process by which Mr Yule deduces 
this table from his original data. But this very method of percentages itself 
is liable to gross misinterpretation, and illustrations of this occur throughout 
Mr Yule's text-book*. 
Given a fourfold table : 
A 
Not-A 
B 
a 
b 
a+b 
Not-5 ... 
c 
d 
c + d 
a + c 
b + d 
N 
the percentage difference is q v = 100 ( 
^=100 
for the vertical treatment and 
\a + c b + dj 
. , , for the horizontal treatment. Which is to be taken as a 
\a + b c + dl 
real measure of the relationship ? Mr Yule in his text-book uses either and 
apparently has some personal scale of values. He gives no probable errors which 
alone could give any soundness to his discussions. Actually we find 
P.E. of q 0 =67-ll!J 
ac 
bd 
(a + cf (b + d) 3 ' 
cd 
(a + b) 3 (c + dy 
* Theory of Statistics, 1911. 
