294 On the Prohahle Error of Biserial rj 
But = (l - ^) , = (l - I) , 
Mean (S/fj^S/i,) = Mean {Bn^.Sii.^,^ + Mean (8n^,f 
+ >hs ( 1 
n) 
2) 
x). 
Thus -%.= '^S (viii)- 
It will be seen that (viii) is of the same form as (iv), although the value of ris 
is variable, while that of N is constant. 
Now multiply (vii) by and sum and we have 
Thus Mean (Sy,S«,) = 0 (ix). 
Returning to (vi), s(|uaring and summing, we find 
J«>\-p{r.-.(i-|) + 4«,v:j5l}. 
Again returning to (vi), multiplying it by the corresponding values of 2/<:s'8ks 
and summing, we reach 
iK^K,' Mean {8K,bK, ) = - yj^y/ + i y,y,- Mean (8y,8y,0 
+ 2 1| y,y/ Mean (S«,,.Sy,) + 2 y,y,^ Mean (8»,8y.,) . 
But 
Mean (8y,8y.) = -L L ^ - ^ + ^ + ^ 0. 
Further multiplying (vii) by 8«.y' we find 
Mean,K8y.J = -i(-'i5-+"jJ-;^ 
Accordingly k,Ks' Mean (8k,S/<:,.) = - - y/y/ (xi). 
Returning to (v) we can now evaluate it by aid of (x) and (xi) ; thus we have 
- |. {is[y.'n. (l - I)} + S f-s^'(l)] - JS (,.n..y.V/)} (xi.). 
