THE DANGER OF CERTAIN FORMULAE SUGGESTED AS 
SUBSTITUTES FOR THE CORRELATION COEFFICIENT. 
By DAVID HERON, D.Sc. 
Statistical Theory has suffered much in the past from the illegitimate appli- 
cation of processes which, when applied to appropriate data, are perfectly sound ; 
but the introduction, without a single word of warning, of methods which in 
no circumstances can give correct results is much more dangerous. Especially 
is this the case when the methods claim to shorten the labour of the calculation 
of statistical constants, since they are invariably adopted by those who, unable or 
unwilling to examine critically their claims to validity, are dependent on any 
formula that is offered to them. 
A Text-Book of Statistical Theory should above all be free from such blunders 
and it is therefore much to be regretted that in Mr G. Udny Yule's recent text- 
book*, greater care has not been taken to ensure that the processes described there 
have a sound theoretical foundation. 
On the present occasion, attention will only be directed to a single point, the 
methods suggested by Mr Yule for the measurement of the degree of association 
between characters which are classified alternatively. 
Two distinct methods are given by Mr Yule to meet this case which arises so 
frequently in practical statistical work. The first is the Coefficient of Association -J- , 
which in Mr Yule's somewhat cumbersome notation is 
in which A and B are used to denote the number of objects or individuals with 
the qualities A, B, while the corresponding Greek letters are used to denote the 
number of objects or individuals who are "not A," "not B," and AB denotes the 
number of those who are both A and B, and so on. 
The second method suggested is to use a formula given by him in his 
text-book j, 
Q = 
(AB)( a /3)-(A(3)(aB) 
J(A)(a)(B)(0)' 
* An Introduction to the Theory of Statistics, Griffin and Co. Ltd., 1911. 
t Phil. Trans. A. Vol. 258, p. 272. % p. 213. 
V 
