206 
On Theories of Association 
Mr Yule would no doubt tell us that he has distinctly stated that he distin- 
guishes between correlation and association and that he knows they may lead 
to diverse results. We reply that, wherever there is any real continuity, the 
assumption of a discrete " attribute " disguises its existence and will lead to 
erroneous conclusions. Further he directly states* that : " The methods applicable 
to the former kind of observations, which may be termed statistics of attri- 
butes, are also applicable to the latter statistics of variables. A record 
of statures of men for example may be treated by simply counting all measure- 
ments as tall that exceed a certain limit, neglecting the magnitude of excess or 
defect, and stating the numbers of tall and short (or more strictly not-tall) on 
the basis of this classification. Similarly, the methods that are specially adapted 
to the treatment of statistics of valuables, making use of each value recorded, are 
available to a greater extent than might at first sight seem possible for dealing 
with statistics of attributes. For example, we may treat the presence or absence 
of the attribute as corresponding to the changes of a variable which can only 
possess two values, say 0 and 1." 
Here Mr Yule directly claims that his methods can be applied to stature, and 
in the next sentence suggests that it is reasonable to treat the difference between 
any tall man and any short man as unity because they have been placed under two 
class-indices " tall " and " short " ! He started his statistical work from the stand- 
point of the pure logician, and he does not perceive that he is applying his 
reasoning to the class-names of things and not to the things themselves behind 
these names. Let us take head length and head breadth with a correlation, 
say, of '50, and lengths of femur and humerus with a correlation, say, of '60, then 
it is perfectly easy by selecting your head length and breadth division and your 
femur length and humerus length divisions, to make the association between head 
length and breadth either greater or less than that between femur length and 
humerus length. What is the value of the coefficient of association as a measure 
of relationship if this be the case ? Every new division gives a different ratio 
of association for the two sets of attributes. The application of such methods 
in practice can only tend to the detriment of modern statistical theory. 
(H) On the Application of Mr Yule's Coefficients to Discrete 
Variates. Mevdelism. 
May we not, however, accept Mr Yule's claims for his coefficients of association 
when the classes differ by a real discrete unit- — not a unit arbitrarily introduced 
by calling a "short" man 0 and a "tall" man 1 ? Well, the difficulty is to find 
such cases. However, supposing them to exist, then there is no question that the 
coefficients of association and colligation are not the right methods of approaching 
the problem, but that the ordinary product-moment correlation coefficient is the 
* Theory of Statistics, pp. 7—8. 
