No. 552] SHORTER ARTICLES AND DISCUSSION 



743 



the deviations from the theoretical frequencies may be reason- 

 ably supposed to be due to the errors of sampling, may be cal- 

 culated from x 2 by formulae which need not concern us here, 

 since its values for systems of frequency of 3-30 classes have 

 been tabled. 7 Hence the Mendelian has only the simple task of 

 calculating x 2 and looking up the value of P in Elderton's tables. 

 Illustrations will make method of computation and usefulness 



Whence, from the tables in BiometriJca, and by interpolation, 



n' = 3, x 2 = 3, P = . 223130 



n'=3, x 2 = 4, P = . 135335 

 Diff. = .087795 



P = .223130 — .087795 X .402 = .1878. 

 Thus only in about one case in five would the errors of sampling 

 lead to divergences from theory as bad as this. The theory is, 

 as far as this evidence goes, possible, but certainly not demon- 

 strated. 



Round, Yellow. 

 Wrinkled. Yelloi 

 Round, Green. . 



x 2 = 8.4476, P = .0384. Thus taking the data as they stand, 

 it is impossible to regard the 9:3:3:1 ratio as satisfactorily 



is given by W. Palin Elderton, "Tables for Testing the Goodness of Fit of 

 Theory to Observation," BiometriJca, 1: 155-163, 1901. 



8 These are not the calculated frequencies given by Bateson and Killby, 

 but have been recalculated as closely as possible on the 9:3:3:1 ratio. 

 Theirs are nine seeds short. 



