to 
Fraternal and Parental Correlation Coefficients 
We notice that for values of r somewhat greater than 0"5, such as are usually 
found for mammals, has already decreased to about ^ and to about \ . By 
giving the same weight to each pair of siblings when forming fraternal correlation 
tables from a material consisting of fraternities of different size, we therefore fail 
very largely to pay due regard to the observations. With material under conside- 
ration, as for example anthropometric data, which according to its nature consists of 
small groups of siblings of varying number, and which is not so numerous that we 
can afford to omit observations from the calculation to make q constant for all 
fraternities, the rational proceeding must be to sort the material according to the 
number of siblings and calculate the correlation coefficient of each group separately. 
It is then possible to effect considerable saving of time and labour in the 
investigation of correlation by avoiding the forming of fraternal correlation tables 
and using instead the formula 
where aq is the directly calculated S.D. for mean v^alues of fraternities. The results 
found by the formula are identical with those of the defining formula, so that the 
only objection to this method of calculation is the lack of opportunity to examine 
the shape of the regression curve. 
From the correlation coefficients found for different values of gf, it is finally 
possible with knowledge of their S.D.'s to calculate a mean value of the fraternal 
correlation coefficient and its S.D. 
In investigations of inheritance with animals with numerous offspring, where a 
great number of siblings are available, we have to face the problem of deciding 
what number of siblings it is profitable to employ for the investigation. 
We shall state provisionally the problem as follows : with which value of q do 
we, provided the number of examined offspring individuals {nq) be fixed, obtain the 
most accurately determined fraternal correlation coefficient ? Or in other words for 
which value of q 'l?, 
(1 + ?' — 1)}- a minimum ? 
q-l 
* Vide K. Smith, Comptes-Rendus cles Trav. dit Lab. Carhlt. Vol. xiv. No. 11, 1921, p. 8, where the 
formula is deduced for the special case q = 10. 
t In the memoir quoted it is shewn (p. 29) that the above formula may also be written 
'•=1- 
q-l CT^ 
ay,q being the squared s.d. inside fraternities of q siblings and being calculated as a mean of such 
values obtained from each of the n fraternities. We may here instead of o-/,, introduce the pre- 
sumptive S.D. inside a fraternity pcrf that is the s.d. we expect to find in fraternities consisting of 
a great number of siblings. The relation is 
1 2 
'^"^■/"^^l ''•9' 
• SO that we find r = 1 - ^'"^'x- , 
which shews that the value of r arrived at must be expected to be independent of (7. 
