21 



ability without fertility; but there may be one hundred per cent fertility and zero 

 hatchability, or there may be only five per cent fertility and one hundred per cent 

 hatchability. 



The above facts show that the coefficient of correlation between fertility and 

 hatchability could neither be zero nor negative. Pearl ('09) found a correlation of 

 — .127±.071 between the percentage of infertile eggs and the percentage of fertile 

 eggs hatched from pullets. Such a factor, in view of the large probable error, in- 

 dicates no sensible correlation between the degree of fertility and the percentage 

 of fertile eggs hatched. 



In table 1 presented below, the percentage of fertile eggs from 758 pullets is 

 correlated with the percentage of fertile eggs hatched. These percentages represent 

 each pullet's average fertility record and her average hatching record for the season. 

 The records were obtained in eleven breeding seasons. The table includes all 

 pullets used as breeders during the period covered, except those showing zero 

 fertility. The zero-fertilitj^ class had to be omitted because zero fertilitj'^ always 

 means zero hatchability, and if the fifty-three pullets that laid no fertile eggs were 

 included, a spurious correlation would arise and not the true correlation coefficient. 



Constants calculated from Table 1. 



Mean fertility 688272 ± .005466 



Fertility standard deviation 2231 ±.003865 



Mean hatchability 637875± .007119 



Hatchabilitv standard deviation 2906zb. 005034 



Coefficient of correlation 0672± .024,390 



Table 1 gives a positive correlation coefficient of .0672±. 02439 which must be 

 interpreted in the light of a probable error of more than one-third as signifying 



