286 



Ml I. <*. UDNY YULE ON THE ASSOCIATION 



In the case of equality of contraries we may express the standard error of Q as a 

 function of Q only (vide equation 9, p. 275), viz., 



1 - Q- I + 



(12). 



The standard error of the correlation coefficient is simply (1 r z )/ v /N, so the S.D. 

 of Q is the greater (for equal numerical values of Q and r) by the fraction on the 

 right. The value of this fraction is given below : 



Ratio of Standard Error of Q to Standard Error of r 

 (for equal numerical values o/Q and r). 



For corresponding values of Q and r, however, the probable error of Q is less, not 

 greater, than that of r, i.e., if we form Q and r for the same material the prob- 

 able error of the former constant is the smallest. The table on p. 276, 26, gives 

 corresponding values of the two coefficients, and these are repeated below with their 

 probable errors : * 



In determining the value of the probable error of Q we have, however, implicitly 

 assumed that the dividing points between A and a, &c., were fixed and not liable to 



* In both these tables the value used for the probable error of r corresponds to the determination of r 

 by the product-sum method. By any other method, e.ij., Mr. W. F. SHKPPARD'S, the probable error is 

 greater, and this would increase the divergence between Q and ;, as regards reliability, in the last table. 



