EFFECTS OF INBREEDING AND CROSSBREEDING. 13 



There are certain interrelations among the characters, such as be- 

 tween percentage born ahve and percentage of those raised, and be- 

 tween frequency and size of litter, of which account will be taken later 

 in interpreting the results. 



SIGNIFICANCE OF DIFFERENCES. 



The records of the various experiments have now been corrected 

 for the effects of size of litter and seasonal conditions, and it has been 

 shown that no other important corrections need be made. It remains 

 to be shown that the resulting differences (Table 30) are statistically 

 significant. 



The general significance of the differentiation among the inbred 

 families has already been shown (Part II, Bulletin 1090) through the 

 existence of high correlations between the records of the families in 

 1916-1919, and their records in 1911-1915 and 1906-1910. The 

 considerably greater differences among the experiments relative to 

 the system of mating fall into a consistent scheme which of itself 

 leaves little doubt as to the general significance. 



As to particular cases, the probable error of size of litter has been 



calculated by the usual formula, PE = . 6745 ,■= where <t is the stand- 



■yln 



ard deviation, which may be calculated from the data in Table 14 

 and n is the number of litters. 



The same type of formula has been used in the cases of litters per 

 year, young per year, and young raised per year. If n is the num- 

 ber of mating years, <t is the standard deviation of number of litters, 

 number of young, or number of young raised, respectively, during a 

 year. An estimate of these standard deviations was made by 

 tabulating the records for the first year after maturity for all matings 

 which lasted at least 12 months. The records for the second and 

 third full years were also used where available. The means and 

 standard deviations were calculated for each group (Families 2, 13, 

 etc., Experiments CO, CA, AC, etc.). As the standard deviations of 

 these individual groups were rather irregular, owing to small numbers, 

 it seemed best to use the average standard deviations in calculating 

 the probable errors, making allowance for the correlation between 

 mean and standard deviation, a correlation which is very important 

 in the case of litters per 3^ear. Combining all of the above data, there 

 was an average of 3.77 litters per year, 9.27 young per year, and 6.56 

 young raised per year. Letting X, X', and X" represent the 

 departures from these averages in any particular case, the standard 

 deviations can be fitted reasonably well by the formulae, 0.93 — 0.50-X' 

 for litters per year, 3.19 + . 13-X'' for 3'oung per year, and 2.57 + . QbX" 

 for young raised per 3^ear. The probable errors in Table 31 were 



calculated from the formulae P£'= 0.6745 ,— where n is the number 



■yjn 



