204 PHYSIOLOGIC GENETICS 



Table 45 



Some weighting factors to be applied to the means of full-sib families of different 

 sizes, in regressions of offspring on the mean of both parents 



Listed according to the phenotypic correlation (t) between full sibs, and the heritability 



(h 2 ) of the character 



Some examples of weighting factors are given in table 45, the value of T under which 

 the weights are listed being appropriate to the heritabilities shown at the heads of the 

 columns when the regression is to be made on the mean of both parents. The meaning 

 of the weighting factor, w n , is that the mean of each family of size n, and the correspond- 

 ing parental value, are to be counted w n times in the computation of the sums of squares 

 and products. [It should be pointed out that the weighting factor given above 

 differs slightly from that of Kempthorne and Tandon in that it gives unit weight to 

 families of n — 1, which theirs does not do. The weight given here is equal to theirs 

 divided by 1/(1 -f T), which is their weight for n = 1 .] 



The computation of the regression coefficient, b, may be summarized as follows. 

 Let X be any parental value, Y the mean value of the corresponding family of offspring, 

 and w the weighting factor appropriate to the number in that family. Then the 

 regression of offspring on parents is computed thus, 2 indicating that the quantities 

 are to be summed over all families: 



where 



and 



b = 1 (wxy) 



> w 



z w 



Also needed will be 



2 (<V) = I (wY 2 ) - H^Dl 

 > w 



