ON A NOVEL METHOD OF REGARDING ASSOCIATION 



23 



(iv) The coefficient of association comes out badly from these tables — it gives 

 a difference of mean square = -109 against that of Vp = -036. But its value here is by 

 no means as bad as it can be. Its chief evil is that it gives wildly different values 

 according to the position of the dividing lines, and when for Gaussian material r = 0, 

 Q^ may take any value from to 1 according to the position of the dividing lines, 

 i.e. the percentages of the two variates in their sub-categories. When we know this 

 is so, for material the distribution of which we can measure, what confidence can we 

 have that the result has any significance when we know nothing at all of the 

 frequency distribution ? This may be exemplified as follows : 



Illustration X. 



Here 



which give 

 and thus 



X'= -14225 and P=-986*, 



1(1+ a,) = -977, i(l + a,) = -994, 



X,^ = 2-7377,, Xa, = 4-5419, 



oO-r = -r^xXa XXa ='3932, 

 VlOOO ^ ' ' 



and this gives r for equal probability = "008, i.e. sensibly zero. Actually the table 

 was obtained from material having zero correlation. The same material divided at 

 the mean gave 



for which the correlation is absolutely zero. In the above table, however, the 

 association coefficient of Mr Yule is unity, in this second table it is zero ! — Clearly 

 such a coefficient when it is liable to swing over from zero to unity can be of no real 

 service for accurate work, such as the determination of the relationships between 



* Calculated from 



-yif'-'^^v! 



e ^'^\: 



see Pearson, Phil. Mag. Vol. l. pp. 157 — 75, or Biometrika, Vol. i. p. 156. 



