1909-10.] The Significance of the Correlation Coefficient, etc. 493 
and if a and b be gathered against c, allowing for dominance, the correla- 
tion coefficient rises to a value of r—’5 1, and when the mean contingency 
is used to r = - 56. 
Thirdly — 
35. If b and c are both dominant over a and the hybrid (b, c) is 
distinct, the correlation becomes *460. 
Thus in all cases we have a higher figure than in the case where only 
two types intermingle. As Professor Pearson has shown, the figures in 
the latter case are quite independent of the number of zygotes, and the 
like will probably hold here. 
Table showing the Correlation between Parent and Offspring in two 
and three Paces. 
Two Races. 
Three Races. 
Correlation. 
Contingency. 
Contingency. 
Fourfold 
Division. 
Hybrid distinct 
•500 
*487 
•597 
Hybrid included in Dominant 
•333 
•316 
•425 
•51 
The same effects will also be produced in this case by assortive mating 
and parental selection as in the previous cases. 
Fraternal Correlation. 
36. The question of fraternal correlation remains to be considered. 
As we have seen, uni-parental selection does not in general affect seriously 
the values of the correlation coefficients. Assortive mating is more powerful. 
The effect of the latter on fraternal correlation can be estimated as follows. 
Consider a parentage of the following arrangement : — 
Husbands. 
Wives. 
(a, a). 
(a, b). 
(b, b). 
(a, a) . 
3 
4 
1 
(a, b) . 
4 
8 
4 
(b, b) . 
1 
4 
3 
This gives a correlation of ’25 between husbands and wives. With 
Professor Pearson let the average families be 4 n, and we get a family 
grouping as follows : — 
