1909-10.] The Significance of the Correlation Coefficient, etc. 483 
which has a higher standard deviation than the parentage, being equal 
in the latter case to *5 and in the former to 
5n 2a , Qr ^ •£ a = i n , to *5625. 
on 
This latter value is not, however, constant with such mating, but increases 
gradually up to a limit. 
16. In addition to the correlation coefficients the contingency coefficients 
have also been calculated in some instances to show the degree of correspond- 
ence of the two. It is seen that for the parental correlations they fall short 
of the former, but approach them closely when they arrive at great-grand- 
parental correlations. Three sets of figures have been calculated for each case. 
Case 1. That when there is no assortive mating. 
© 
Case 2. That when there is assortive mating with equal fertility and 
population not immediately stable. 
Case 3. That when there is assortive mating with equal fertility and an 
immediately stable population. 
17. Tables of Parental, etc., Correlations based on Different 
Hypotheses. 
i. The hybrid separate : — 
No Assortive 
Mating. 
Assortive Mating. 
r= *25. 
Assortive Mating : 
Immediately 
Stable Population. 
r= 125. r=' 25. 
Product 
Contingency 
Product 
Contingency 
Product 
Product 
Method. 
Method. 
Method. 
Method. 
Method, i 
» 
Method. 
Parental 
•5 
•487 
•589 
•576 
•563 
•625 
Grandparental 
•25 
•242 
•366 
•343 
•316 
•391 
Great-grandparental 
•125 
T24 
•234 
•223 
T78 
•244 
Grt.-grt. -grandparental . 
*0625 
•0624 
•143 
•142 
•100 
•153 
ii. The dominant including the hybrid : — 
No Assortive 
Mating. 
Assortive Mating. 
r=\ 25. 
Assortive Mating : 
Immediately 
Stable Population. 
r=- 1875. 
Parental 
•3333 
•495 
•548 
Grandparental 
•1667 
•307 
•351 
Great-grandparental 
•0833 
•203 
•236 
Grt.-grt. -grandparental . 
•0417 
•141 
•161 
