u 
Fraternal and Parental Correlation Coefficients 
€i, e.,, e-. and are sums, the means of which are 0. The product moments 
arc, as in the previous section, denoted by /3 and the indices concerning " w's " are 
placed in front of /3, for instance — S i^^y^) is denoted by .j/83. We thus find for 
the mean values of the sums occurring in (24) : 
2 {x;%y.;) = Inq {q-l) 
^ (a-i2/i'2/2) 1)1/3.1 
S {.x^y^y^yi) = Inq (q - 1) {q - 2) i/^j; 
S {a,\^x.,y^) 
s 
S (xi'yi") 
11 (n-l)qo^ 
d s 
n (n — l)q 2^2 
8{x,Hj,y2) =-\n{n-\)q{q-l).,fi,. 
d s 
S {x, y.x., yo) = I71 (n-l)q-, ,/3i 1* 
s s d s d 
S{oc^y^y.l) ^n{n -l)q\/3, ^ 
s s d 
.(25). 
S («i y,y2 y,)=^n{n - 1) q- (q -1)^/3,,, 
» s d A- j 
From Bergstrom's formulae (9) we find, when introducing r^„ r and 0 for the 
correlation coefficients and remembering that in his formulae « and s' are taken as 
units for y and x : 
,13, = Svps'-'s ^ 
,132 =(2r/+l)sV 
(27-/ + r) s'^s- 
./3n 
1/33 
1/8-31 
1^111 
.i/3i 
d s 
202 
d 
./81: 
d s 
R 
d s d. 
= Svp s's^ 
= + 2r) sV 
(26). 
1^1 2 = ''>sV 
! ^1 1 1 — TVpS 
n d s ) 
* In this single case the notation fails, as it ought to be indicated that the first x and the last y 
belong to the same class. 
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