152 THE AMERICAN NATURALIST [Vol. LI 



problem which had arisen, in connection with his Men- 

 delian breeding experiments. A certain type of mating 

 gave the following class frequencies : 



6363 + 579 + 3638 + 1208 + 128 + 115 



+ 350 + 6 = 12387 . . . (a). 



Another group of matings gave a total of 9,017 off- 

 spring, of which 30 fell in the x class, this being the only 

 class in regard to which a comparison is to be made. On 

 certain theoretical grounds the percentage frequency in 

 this X class in the second sample would be expected to be 

 0.582 times the percentage frequency of this same class in 

 the first sample. The question is whether the actually ob- 

 served frequency of 30 in this second sample is such as 

 could reasonably be expected to occur if the theoretical 

 assumption actually were the fact. 



It will be seen at once that, owing to the very small ab- 

 solute frequency of this x class in both samples, ordinary 

 probable error methods will be of no avail. 



Approaching the problem by the method here proposed, 

 we have, as basic values for the computations, 

 = 12387 

 w = 9017 



p = 115, q = 12272 

 p = p/n = .009284. 

 q = q/n = . 990716. 



Whence we have for the mean in the second sample of 

 9017 by (i) 



Mean = 84.428137 



and by (iii) 



<T = 12.020652. 

 By (ii) the mode = S^, whence = 1.428137 



