No. 536] COEFFICIENT OF INDIVIDUAL PREPOTENCY 477 



of a family from the population with respect to the dis- 

 tribution of a character. At present the second of these 

 methods seems of little practical importance for our 

 purpose because of the relatively small numbers of indi- 

 viduals available in breeding experiments, even with 

 plants, and because of the arithmetical routine. 



Consider the first method. Let N be the number of 

 individuals in a population due to P parents. Let X be a 

 character common to all but appearing in different inten- 

 sities (say from development to the greatest possible 

 intensity) in the several individuals, not measurable but 

 capable of division into m classes. Let s x ,s 2 ,s i ---Sm be the 

 classes and ?/,,.,, y H - ■ >y lm be the frequencies in the popu- 

 lation as a whole. Now if a single family of n members 

 be observed the probability of an individual belonging to 

 any class, say s 2 , is y H /N = p, while the probability of its 

 not belonging to that class is (1 — p)—q. The actual 

 number of individuals with character s 2 in the family 

 should be np = y,[ , while the frequency for the m — 1 

 remaining classes within the family will be given by 

 Vh* V>'z • ■ • .'/.<„' providing (a) that the family is not 

 differentiated from the population, e. g., that there is no 

 individual prepotency in the sense that we have used the 

 term, and (b) that n is so large that the probable errors 

 of random sampling are negligible. In actual work (b) 

 can never, or almost never, be realized. Our problem is 

 to determine whether differences between the theoretical 

 class frequencies, yf, and the actually observed class 

 frequencies, y s ", in the family are to be regarded as due 

 to chance merely or whether they are so large that they 

 can reasonably be considered as indicating a differentia- 

 tion of the family from the population to which it belongs. 

 In short, our problem is to test (r^ — J',',) against its 

 probable error. 

 Pearson has shown that the standard deviation of 



