476 



THE AMERICAN NATURALIST 



[Vol. XLV 



individual family from the mean of the population to 

 which it belongs. 



Suppose a population composed of N individuals with 

 a mean of M and a variability of 2 is due to P parents. 

 Now if this population be divided into two random 

 samples of n and N' individuals, m and M' means, and 

 a and 2' variabilities the differences in their means 

 will be 



But Pearson has shown that the difference between the 

 mean of a sub-sample m which in our case may represent 

 the offspring of a single parent (or pair of parents) and 

 the population mean M is not given by the preceding 

 formula since n is included in N. The formula for such a 

 case as this he has shown to be 



This is the formula which we are seeking, the probable 

 error of the difference between the mean for any family 

 and that for the whole population. By calculating 

 (m — M)/E (m _ M > for every family we should have a 

 criterion of its superiority or inferiority — the individual 

 prepotency of the parent in question— relative to the 

 average condition in the series to which it belongs. 



Tocher has pointed out advantages in using 

 {m — M)/<r {m _^ instead of (m — M)/E (m _ M) , but this is 

 merely a matter of convenience. The significance of the 

 ratios can be tested by tables of the normal curve. 



(b) Case of Characters not Measurable on a 



For characters not quantitatively measurable two 

 methods of treatment are available. The first consists in 

 testing the divergence of a family from the general popu- 

 lation on the basis of the relative frequency of a given 

 character. The second consists in testing the deviation 



(m -J/) ±.67449 



Quantitative Scale 



