56 STATISTICAL METHODS. 



nity will be 



where 7^= average abmodality of fraternity; 



h 2 = average abmodality of male parent; 



h 3 = average abmodality of female parent; 



r 2 = correlation coefficient between fraternity and 



female parent; 

 r 3 = correlation coefficient between fraternity and male 



parent; 



o 1 = standard deviation of fraternity; 

 o 2 = standard deviation of male parent; 

 <7 3 = standard deviation of female parent. 

 When assortative mating occurs, as is usually the case, the 

 abmodality of a fraternity is given by 



where r x = correlation between male and female parents. 

 The other letters have the same signification as before. 



The strength of heredity in assortative mating is measured 

 by the formula 



To find the coefficient of correlation between 

 brethren from the means of the arrays. 



This is given by the formula 



where rij is the number of the brethren in an array [and there- 

 fore JrijCnj 1) is the number of possible pairs of brothers in 

 that array]; A l is the mean value of the array; a is the 

 standard deviation of the character in the brethren taken 

 all together, n is the total number of variates, and A 2 is the 

 average of the brethren. This method will be found useful 

 where to take all possible pairs of brethren would be found 

 a work of too great magnitude (Pearson, Lee, etc.,'99, p. 271). 



