POSTNATAL GROWTH IN THE ALBINO RAT 17 



di, . . . . dr, the standard deviation a of the whole series 

 is given (using m to denote any subscript) by the equation: 

 N.a'- = Z (.Vn,. (fj) + 2 (iVn,. rfn,2)." If We let dm represent the 

 mean standard deviation of the component series (which may 

 be assumed to be fairly constant) then 



3 (iV„ a J) 



becomes 



and 



N<7'-i:(Nr.dj) 



(Tm'- = 



N 



whence the value of am is obtained.^ In applying this method 

 to the rat data A^ represents the total number of rats at a given 

 age; o-, the standard deviation of the body weight of all the rats; 

 dm, the deviation of any litter mean from the total mean, Nm, 

 the number of individuals in the corresponding litter;' and cm, the 

 average standard deviation within a litter. The sexes are con- 

 sidered separately. The results, as shown by the preceding table, 

 do not differ materially from those by the first and third methods. 

 In the third method^ of determining fraternal variation, all the 

 litters at each age (sexes separately) are reduced to a common 

 litter basis. This is accomplished by multiplying the body weight 

 of each member of a given litter by the factor 



Mean of total population (at given age) 

 Mean of given litter 



^ Since the formula may be written in the form: 

 crm=a- . 



and since ^ "^ — is necessarily a positive quantity, it is evident that accord- 

 ing to this formula the standard deviation of the individual fraternity is 

 usually (and on the average necessarily) less than that of the total population. 

 The formula gives no indication as to the magnitude of the difference, however. 

 * For this method, and for aid otherwise, I am indebted to my colleague Prof. 

 O. D. Kellogg, of the Department of Mathematics. He adds the caution that 

 under some circumstances the method might tend to give a spurious reduction 

 in the standard deviation and coefficient of variation, but this does not appear 

 to be the case with the present data. 



THE AMERICAN JOURNAL OF ANATOMY, VOL. 15, NO. 1 



