348 Distribution of Correlation Coefficient in Small Samples 
Remembering that 
e. '^0--Po'^ z^'dz = V277 ^ / ^ -P^ (2s - 1) (2s - 3) ... 1 X ^- — 
we find 
dz 
lo(coshz-poT 2(1 -poT^ w 
+ 
n ' 128 
1024^3 
3675po« + 4200po6 - 2520po^ - SSQOpo^ - 336 
32768n4 
w - 1 n - 4 
+ etc 
,) ...(xlix). 
But y. 
and thus we have 
1 n-2 
a/277 v«r^i 
(1-p¥xo(p,0 
4 
(1 _p2)-ir (i_,.2) 2- 
(w-l) (w-l)2 (w-l)3 ' (n-1)* 
?i - 4 ?( - 4 
n _ „2 
where Xo ' ) 
is symmetrical in p and r and 
rp + 2 
...) ...0), 
01 (p'"] 
03 
04 (/"•) = 
02 ipr) 
(1 - pr)"-^ 
(3fp + 2)2 
128 
5 {15 (rp)^ + 18 (rp)^ - 4 (rp) - 8} 
1024 ' 
3675 (rp)" + 4200 (rp)^ - 2520 (rp)^ - 3360 (rp) - 336 
I ...(li), 
32768 
thus depend only on the product of p and r. 
We may write 
Vn = 
where 
and 
7i — 2 
Vn- 1 
{I -p^-yixip, >■)]! + 
0i(p''") , 02 , 03(P'") , 04 
T, + 
+ 
(n-l) {n-iy ' (n-l)3 ' {n - 1) 
log X (p. ■'■) = - {n- 1) log xi - log X2, 
1 — pr 
+ 
.(Hi), 
Xi = 
X2 
{(l-p2)(l-r2)}r 
\/2^{(l-p2)(l-r2)}^ 
botli being symmetrical in r and p 
(1-pr)^ 
