EFFECTS OF INBREEDING AND CROSSBREEDING. 43 



A certain amount of difference between families from 1911 to 1915 

 would be expected to occur simply by chance, owin<* to the limited 

 number of observations. It is important to determine whether the 

 actual differences are greater than those expected by chance. The 

 actual differences can best be measured by considering the families 

 as units and finding the standard deviation in the group of family 

 means, with respect to each character. The reliability of each 

 family mean can be estimated by calculating its standard deviation 

 (<r m ). The average of these standard deviations gives the standard 

 deviation in the group of family means which might be expected by 

 chance, and may be compared with the figures actually found. 



The expected standard deviation in each family in the cases of the 

 percentage born alive, the percentage raised of those born alive, 

 and the total percentage raised, can be calculated by the formula 



°"ioop = 100-*/-^ 2z where 100 p is the percentage in question and n 



is the number of cases. In the case of the size of litter, the formula 



for the standard deviation of the mean is _^L wnere a j s the standard 



■yjn 



deviation within a family (about 1.14) and n is the number of litters. 

 In the cases of the weights the same formula applies, but the use of in- 

 dexes somewhat complicates the matter. The indexes for the standard 

 deviations of the weight at birth of the young raised to 33 days, the 

 gain, and the weight at 33 days are approximately 11.0, 34.0, and 

 39.4 grams. These figures were derived from the total inbred fami- 

 lies in 1916 and 1917. The figures within a single family would be 

 slightly smaller, but these results are sufficiently accurate for the 

 present purpose. For the reasons given in the discussion of the in- 

 dexes in Part I of this bulletin this should be a compromise between 

 the number of litters of 1 to 4 and the number of individuals in these 

 fitters. A standard deviation of means based on litters is about 

 60 per cent larger than one based on individuals. A reduction of 

 23 per cent from the figure based on a number of litters is in accordance 

 with the assumptions involved in the indexes and is used here. In 

 the cases of the number of litters and number of young produced 

 per year the writer has not attempted to calculate the standard 

 deviation to be expected by chance, and the reality of the differen- 

 tiation among the families must be established by other means. 



Having found the standard deviation of the mean in each family, 

 the unweighted average in the 22 families has been used to measure 

 the standard deviation to be expected by chance in the population 

 of family means. Table 2 gives the comparison of these expected 

 figures with the standard deviations actually found. It will be seen 

 that in every case the actual variation is much the greater. The 



