Ktrstine Smith 
9 
from which is found 
nq(q-l) 
l^l+riq-2)-rHq-l)Y- 
and 
For q = 2 this formula coincides with the usual formula for the standard 
deviation of a correlation coefficient calculated from two series of values of two 
variables corresponding in pairs, the values of each series being mutually iincorre- 
lated. 
(g) Numerical Evaluation of the Formula for the s.D. of a Fraternal 
Correlation Coefficient. 
The number, N, of observed pairs of observations being equal to ^nq(q — I) the 
formula (19) may also be written 
7~N' 
a,= —^j{l-r){l + (q-l}r] 
Comparing materials of observations with different number of siblings q, we 
see that for the calculation of fraternal correlation information of each available 
pair of siblings has a value inversely proportional to {l+(q — l)r}\ The ratio 
= I ; — — ) serves as a measure for the value which must be attributed to 
^ \l + {q-l)rj ^ 
information of an observed pair among q siblings, supposed that all of the i^S'C'i"!) 
pair of siblings are used for the calculation, and supposed that the value of infor- 
mation of a pair of siblings for q = 2 is put equal to 1. On the other hand — 
indicates the ratio between the numbers of pairs of siblings which are required for 
obtaining the same accuracy in the correlation coefficient in the case of q and in 
the case of two siblings from each fomily. Table I gives the numerical values of v 
for different values of r and q. 
TABLE I. 
1 + 7- 
l + {q-l)rj ■ 
3 
r = 0-l 
0"2 
0-3 
0^4 
0-7 
0^8 
0-9 
2 
1-000 
rooo 
1 •ooo 
rooo 
rooo 
rooo 
1 -000 
1-000 
1-000 
3 
•840 
•735 
•660 
•605 
•563 
•529 
•502 
•479 
•460 
4 
•716 
•563 
•468 
•406 
•360 
•327 
•301 
-280 
•264 
5 
•617 
•444 
•349 
•290 
•250 
•221 
•200 
-184 
•171 
6 
•538 
•360 
•270 
•218 
•184 
•160 
•143 
•130 
•119 
7 
•473 
■298 
•216 
•170 
•141 
•121 
•107 
-096 
•088 
8 
•419 
•250 
•176 
•136 
•111 
•(J95 
•083 
•074 
•068 
9 
•373 
•213 
•146 
•111 
•090 
•076 
•066 
•059 
•054 
10 
•335 
•184 
•123 
•093 
•074 
•063 
•054 
•048 
•044 
