16 



C. M. JACKSON 



3. Fraternal variability 



It is a matter of common knowledge that yariation within 

 fraternities is always less than that of the general population. 

 In the various litters of rats used for the present study, it is 

 in most cases evident from mere inspection that variation in the 

 body weights within the litter is much less than the variation in 

 the total population of the same age. To measure the variation 

 within the litter, three methods were used and the results are 

 summarized in table E. 



TABLE E 



Coefficient of variation in body weight for total population by ordinary method, and 

 on litter basis {fraternal variation) estimated by various methods 



Total population (ordinary 

 method) 



Litter basis (average of lit-1 

 ters, calculated by ordinary > 

 method J 



Litter basis (calculated from 

 Yule's formula) 



Litter basis (from Kellogg's / 

 formula) \ 



18. 51 

 15.31 



7.4 

 10.4 



8.1 

 9.3 

 8.5 

 9.0 



1 For net body weight. 



2 For gross body weight, larger series. 



The first method of determining fraternal variation consists 

 simply in calculating the standard deviation and coefficient of 

 variation for each separate litter by the usual formula. The sexes 

 were calculated separately, only those litters with four or more 

 of either sex being used. The average coefficient for each sex at 

 each age is given in the preceding table. On account of the small 

 number of individuals in each litter, the results can of course be 

 considered only as grossly approximate. 



The second method of calculating the fraternal variability is 

 based upon a formula by Yule ('11) who demonstrates (p. 142) 

 that ''if a series 'of (N) observations consists of r component 

 series with standard deviations (Xi, a^, ■ ■ ■ • o"r, and means 

 diverging from the general mean of the whole series by di, 



