18 Fraternal and Parental Correlation Coefficients 
(g) Nu merical Evaluation of the Formula for the s.D. of a Parental 
Correlation Coefficient. 
We shall first examine how valuable a material consisting of n groups of q 
siblings with corresponding parental values is compared with 7}q pairs of values from 
different families. Denoting the s.D.'s of pp calculated from the two materials by 
a-^p^ and a^p^^ we find by applying (36) 
< = = g_Li£)_ _ ^37). 
q (1 - r/)^ - _ 1) (1 _ |l - } 
This ratio indicates the value of an observed pair, when the parental value also 
occurs combined with {q — 1) other offspring values, in proportion to the value of an 
observed pair when the parental value only occurs once in the calculation. 
The numerical values of (37) are, for values of rp and r, fairly well representative 
of the values met with in investigations of inheritance given in Table IV. 
TABLE IV. 
^'1 ='^\pp '■ ^%Pv 
1 
rp=-3 
>-,= ^4 
r=-4 
r=-5 
r=-6 
1 
1-000 
rooo 
rooo 
2 
•735 
•698 
•666 
3 
•581 
•536 
•499 
4 
•481 
•4.35 
•399 
5 
•410 
•366 
•332 
6 
•357 
•316 
•285 
7 
•316 
•278 
•249 
8 
•284 
•248 
•221 
9 
•258 
•224 
•199 
10 
•236 
•204 
•181 
It appears that entering into the same parental correlation table families with 
numbers of offspring varying from, for example, 1 to 5 the same weight is given 
to pairs of observations which according to Table IV ought to vary in weight from 
Ito 1 
It is therefore a more rational proceeding to sort the families according to the 
number of offspring and deal with each group separately. The work may then be 
shortened by calculating the correlation coefficient between the parental value 
and the mean for the offspring from which the pai'ental correlation for individuals is 
obtained by multiplying with — , Oq being as above (see ^{g)) the s.D. for means 
of fraternities of q individuals. It is then possible to calculate the correlation 
coefficient with s.D. for each group of families and finally calculate a mean value 
for the correlation coefficient. 
