1909-10.] The Significance of the Correlation Coefficient, etc. 4 77 
Parent. 
Offspring. 
(a, a) + (a, b). 
(b, b). 
Totals. 
(a, a) + (a, b) 
5 
1 
6 
(b, b) . . 
1 
1 
2 
Totals 
6 
2 
8 
Here again the regression is linear, and as the result we have 
•333. 
So far all is clear. In the last case, however, the distribution is markedly 
skew, and while the product method is applicable it is only applicable 
because the regression is linear. 
7. It is therefore specially important to consider what happens when 
other methods of obtaining the correlation are employed. The chief of 
these is the fourfold division method. In a Mendelian instance such as 
this, the fourfold table seems specially applicable, but it assumes normality 
of distribution so that the fourfold table should give a higher correlation 
than r — - 3333. As a matter of fact it does. The equation for determining 
r is 
•62035 = r + ’22747r 2 + , 04951r 3 + -12279r 4 + *001898r 5 + . . . 
which gives 
r = *53, 
That is to say, the correlation is even higher than that obtained when the 
hybrid is distinguishable from the dominant, and in applying the fourfold 
method we have returned to or even gone beyond the uncondensed table. 
The higher coefficients are likewise increased and the series becomes 
Parental. 
Grand- 
Great- 
Great-great- 
parental. 
grandparental. 
grandparental. 
•53, 
•29, 
•15, 
and -073 
as against 
© 
•5, 
•25, 
T 26 , 
and -063. 
8. If the simple Mendelian table be again considered, and if for the 
moment the distinguishing character of the hybrid and the dominant be 
assumed somewhat indefinite, we can make several tentative divisions, 
either bisecting the hybrid or dividing it into such divisions that one- 
fourth resembles the recessive as follows : — 
