196 
On Theories of Association 
might be thought, give small values except in immediate proximity to the 
boundaries, it rises to quite substantial values when the percentage in any quad- 
rant takes a value which Mr Yule has not hesitated to use when criticising 
other methods of approaching the problem of association, and — according to 
Mr Yule — as it approaches these values the reliability of his coefficient increases ! 
Diagram II. Frequency surface of zero correlation exhibiting every possible variation of 
Q with different dichotomic lines. 
o'o 
+ I O O'O — I 'O 
oo 
(3) Let us now take a cylinder on circular base. Here again the correlation 
coefficient is zero, but Mr Yule's coefficient runs through its whole range from — 1 
to + 1, being negative in two quadrants and positive in the other pair. 
The above cases illustrate, we think effectively, the point that the coefficient of 
association tells us absolutely nothing, unless we make some assumption as to the 
