282 MR. G. UDNY YULE ON THE ASSOCIATION 



1 + i _ ft <1_ - P> (l ~ P*W + s "IL (1 -_?i) / 1 6 \ 



' 



Sj, 2 . s s being the surplus ratios for A, B, and C. Hence if s 3 = s 3 the right-hand 

 side is certainly less than unity, and 



f i < *s 

 or Qi > Q 2 



That is to say, if the surplus ratios ofB and C are the same, Q, > Q, when p l > p. 2 ; 

 but if they are not, this result does not follow. We can, then, only refer to 

 equation (16). QITETELET'-S function is for this purpose the same, in effect ; as he only 

 divides the difference of the chances by (A)/(U). We may write his function in the form 



- 



34. Now it seems to me that association coefficients and QUETELET' s functions, or 

 chances like (AB)/(B), &c., roughly correspond in their uses to correlation coefficients 

 and regressions. The correlation coefficient is a symmetrical function of the variables, 

 ranging between 1, and is zero when the variables are independent. The associa- 

 tion coefficient is a symmetrical function of the attributes, ranging between 1 , and 

 is zero when the attributes are unassociated. The regressions are zero when the 

 correlation coefficient is zero, but are not symmetrical functions of the variables ; they 

 depend on the values of the standard deviations as well as the correlation ; and 

 even if the regression of x on y be greater than the regression of x on z, it does 

 not follow that r fy > r i: unless <r y = ar : . The QUETELET functions (or simply 

 differences of the chances (AB)/(B) (A)/(U)) are zero when the association coefficient 

 is zero, but are not symmetrical functions of the variables ; they depend on the 

 values of the surplus ratios as well as the association ; and even if < for AB be 



greater than d> for AC or 



(AB)/(B) > (AC)/(C), 



it does .not follow that | AB | > | AC | unless s c = S B . Finally the regressions of 

 x on y, z, &c., may be said to measure the " relative degrees of influence " of unit 

 alterations in y t z, &c., on x, just as QUETELET takes his function to measure the 

 " relative degrees of influence " of B, C, &c., on A. Thus, referring to the table given 

 (p. 281), he remarks, "on voit par Ik qu'une instruction sup^rieure exerce une influence 

 cinq fois plus grande que 1'avantage d'etre femme," since '348 is some five or more 

 times '062. 



I confess I do not altogether like QUETELET'S function, as there does not seem to me 

 any point in this sort of case in dividing by (A)/(U), or p in our previous notation. 

 If p was in one case "9 and in another "45, it seems absurd to count an attribute 

 that raises p by '05 in either case, half as effective in the former case as the latter ; 

 one would rather consider it more effective in the former case, 



