14 BULLETIN 1121, U. S. DEPARTMENT OF AGRICULTUEE. 



of mating years (Table 14) and a is calculated from the above formu- 

 lae, using the means in Table 14. 



The formula for the probable error of a percentage (p) is 0.6745 



V7? (i — v) 

 j^ ' Ii^ applying this to percentage born alive, the question 



arises as to whether n should be the number of individuals (m litters 

 of 1 to 4) or the number of litters. In the former case -yjn is about 

 50 per cent larger than in the latter. A compromise is in line with 

 the system of indices which has been used. Accordingly, n has been 

 taken as the number of individuals born in litters of 1 to 4, but the 

 resulting estimate of the probable error has been increased by 25 per 



cent, i. e., PE= 1.25 X 0.6745 JvJkzH . 



\ n 



The percentage raised of the young born alive has been dealt with 

 similarly, n being the number born alive in litters of 1 to 4. In the 

 case of the percentage raised of all young, n is again the total number 

 born in such litters. 



Similar considerations apply in the case of the weights. The 



formula P^= 1.25x0.6745 ,= has been used in each case, n being 



■yjn 



the total number born in litters of 1 to 4 in the case of the birth weight 

 of all young, and mereh^ the number raised in such litters in the other 

 cases. The standard deviations for a given size of litter have been 

 taken as 14.76 grams for birth weight of all young, 13.62 grams for 

 birth weight of young raised, 1.285 grams per day for gain, and 49.53 

 grams for 33 days' weight. These figures apply to litter means and 

 follow from the following determinations based on an analysis of 

 3,009 litters of inbreds and controls : 

 Birth weight (total) o-b' = 19.49 grams. 



rBL= - 0.6580 ±0.066. 



lo-b' = 14.76 grams. 

 Birth weight (raised) 0-6= 18.09 grams. 



r*BL= -0.6580 ±0.066. 



lo-b= 13.62 grams. 

 Gain o-g = 45.87 grams (33 days) . 



r^^= -0.3807 ±0.0105. 



l(7g = 42.42 grams = 1.285 grams per day. 

 Weight at 33 days 0-33 = 57.58 grams. 



rBG= +0.5326. 



1,0-33 = 49.53 grams. 

 The formula for standard deviation for a given size of litter (L) 

 is of the type 



lO'b = cb ■yji — i^-BL' 

 The formula for 1,0-33 is derived from the equation 



iS^iZ ~ l'^^ + iP^o, + 2i,o-b-lO'g'l^bg- 



