OF ATTRIBUTES IN STATISTICS. 



285 



j. 4. *! 4. * 



V' h V h <i h 9f 



<r * I<r * 1 



(9)- 



We may write the above 



* 3 " 



-8 - 



+ ^1 



4 + 



Hence, if fa or <j> 3 is zero, Q = 1, K = o> , and o- = oo ; if tf> 2 or fa is zero, 

 Q = 1, K = 0, and <r f = 0. 



40. To take Q next, the standard error of which can be derived at once from that 

 of K, 



8Q= - 



1 + 1 + ic 

 2 



(! + *) 

 4 



Transform by substituting Q for K 



- 



Q ~ 



9i 



+ J 



s 94 



(10). 



(11). 



This again becomes apparently infinite if one of the <j>'s vanishes, but 



whichever of the <j>'a is zero. So that the probable error of the association coefficient, 

 like that of the coefficient of correlation, vanishes at the limiting values 1. 



