KiRSTiNE Smith 
7 
The fraternal correlation coefficient p for the present sample is, when all the 
^q{q — 1) pairs of siblings are used for the calculation, defined by 
where 
n 
.(13). 
nq (q-l)' 
To determine the s.D. of p one requires in addition to cr'v, the s.D. of IT and the 
product moment for 11 and crl 
(d) Mean Value and Standard Deviation of the Product Moment TT. 
Taking mean value of (13) for a great number of samples we find as 
2 iyiyd = inq (q - l)rs^ and (if) = af, 
1 
U^sUr [l + (,y_l)r] (14). 
[ nq ) 
For calculating the mean value of Tl- (13) may be written 
nY' (g _ 1) n = - (g - 1) S (yr) + 2 (nq - ? + 1) S (y,.V=) - 2 (g - 1) S (y,y.^ . . .(15), 
from which follows 
nY (q - ly = iq - 1)^2 (y^^)}' + 4 (nq - q + 1)= (S (y^y,))' + 
- 4 (g - 1) (nq - ry + 1) S (y-') 1 (y,y,) + 4 (g - \r(8(y,y,)r, 
the mean values of the two products being 0 according to (11). Substituting the 
rest of the values from (11) we find 
(q - l)n''q-n- = {2nq -(q-l) + 2r [nq (q - 8) - (q - If] 
+ r^ [hV/ (q-D- 2nq (q-2)- (q - l^']) (IG), 
and by squaring (14) is found 
(q - 1) 7iY iW = {q-l- 2r [nq (q-l)-(q- If] 
+ r"'[nhf(q-l)- 2nq(q - lY + (q - 1>'']|. 
By subtraction of this equation from (16) we arrive at 
2s' 
nq(q-l) { nq 
9. - 
iq-n- 
vq 
+ r- 
or arranged according to nq 
2s' 
cf - 32 + 3 - 
(q-iy 
nq 
which may also be written 
1 + 2r (q-2) + r"- (f/ - ^ + 3) 
9-1 
nq 
[l+r(2-l)]4, 
