534 WRIGHT! CORRELATION IN SUBGROUPS OF POPULATION 



The correlation within a subgroup is 



' xy (g) 



n (g) °"x (g) °V (g) 



2 -^(g) ^(g) = r xy (g) °"x (g) 0-y (g) W (g) 



The correlation and standard deviations within a subgroup 

 are assumed constant. Hence n (g) is the only variable in the 

 expression above. 



Combining all subgroups: 



„ _ S n ( g) X (m) F (m) + r xy (g) o- x (g) cr y (g) Z n (g) 

 ' xy (t) 



°"x (t) °"y (t) ^ "'(g) 

 _ r xy (m) °"x (m) °~y (m) + r xy (g) Q~x (g) °> (g) 

 0"x (t) 0"y (t) 



Thus the relation between the correlations and standard 

 deviations of the total population, of the weighted means of sub- 

 groups, and of the individuals within an average subgroup are 

 expressed by the following formula: 



^xy(t) 0"x(t) 0>(t) = ^xy(m) 0"x(m) 0"y(m) + ^xy(g) 0"x(g) 0" y ( g ) 



The following example deals with correlation between weight 

 at birth and weight at the age of a year in male guinea-pigs born 

 in litters of three in an inbreeding experiment carried on by the 

 Animal Husbandry Division. In this experiment, 24 families 

 have been developed by exclusively brother-sister matings from 

 24 original pairs. These 24 families have become strongly 

 differentiated in various respects which can not be ascribed 

 merely to variation in vigor. The present data involve records 

 collected up to a certain date and include animals from the first 

 to the 15th generation of inbreeding. There were 560 guinea- 

 pigs in all families combined. This mixed population gives a 

 correlation of + 0.375 ± 0.024. The correlations of the means 

 of the 24 families, each weighted by the number of individuals, 

 gives + 0.630 ± 0.083. In order to discover the average cor- 

 relation within the families apart from the differentiation be- 

 tween families, correlations were calculated separately for the 8 



