34 EMPIRICAL STUDIES OF MEASUREMENT 



, TT 1 labcdN 



I. r = sin - where F = -, j-^ 



1 H 



cases being so chosen that ad > &c. 



III. r = sin * -^L -z^. 

 + l/6c 



t 2 - 3), etc. 

 Since 



and 



(a + &) (c + d) 



-IT" 



7i and A; are found from tables of the probability integral, a, &, c 

 and eZ being known. 



H is taken as -4= e~ y ^ 



H and K are thus found from tables. 



Of these^formulas IV. is for 'normal' correlation the most ac- 

 curate. It presupposes 'normal' correlation: I., TT anH TTT Hn not 



When the facts to be related are measured on a fine scale but in 

 terms of relative position only, not of amount, the relationship may 

 be measured, as Spearman has shown, by the degree of conformity 

 of the second member's position to that of the first member. 1 This 

 method suffers from the disadvantage of giving results only with 

 much difficulty comparable with other methods and of taking much 

 more time without being much more reliable than the cosine irU 

 method. 



From the reduction in variability of an array of y related to a 

 given value of x below the variability of the total series of y, the 

 correlation may be inferred on the supposition that the correlation is 

 'normal' and that the variabilities of all arrays of y are equal. 



The infrequency of 'normal' correlation and the fact that, as 



1 See American Journal of Psychology, Vol. XV., p. 86 ff. 



