EFFECTS OF INBREEDING AND CROSSBREEDING. 13 
There are certain interrelations among the characters, such as be- 
tween percentage born alive 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 A where a is the stand- 
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 nis the num- 
ber of mating years, oc 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 year. 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 formule, 0.93 —0.50X 
for litters per year, 3.19+. 13X’ for young per year, and 2.57+.05X"" 
for young raised per year. The probable errors in Table 31 were 
calculated from the formule PE=0.6745 p= where n is the number 
