I] Introduction 



Now r* Vi c = S J% ( &t* ) L . \\ T e fi n( j this as follows : 

 (" V ' J 



xxvii 



Thus the class-index correlation r tf(Cy = -9192. 

 Corrected correlation r = r'/r 2 ^ Cy = '2871. 



It is known that ^ = 8 fe (^'i - (^\ . 



Now to determine rf we may use (e) or (/) and we shall get two values, rji* 

 and rjz'*, which will differ as we have used the unadjusted mean of arrays; or we 

 may use the adjusted means which should give results in fair agreement with 

 each other. In the former case we take the mean of yi and 773' to represent 17'. 

 the value of the correlation ratio before correction for the broad categories of y. 



Mean value of rji and 7? 2 ' = V = '2845. 



This must be corrected for broad categories of the y's and we have (see 

 Biometrika, Vol. ix. p. 118) 



Vx. y = n'/r y . Cy = '2845/-9192 = -3095. 



We may now proceed in precisely the same way, using, however, the corrected 

 means ie/a- x = T3799, and xj<r x '6606, or, subtracting from the sums of (p) x (w) 

 and (p) x (x), 1'904-,124 and -436,392 respectively. 



* The z's were determined from (p) or () with greater accuracy than in () and thus (t) is more 

 accurate than (u). 



