332 Maine; agricultural e;xp]5rimlnt station. 1912. 



Further discussion of various points brouglit out by these 

 tables is deferred to a later section of the paper. 



Matings of Barred Plymouth Rock males of class ^. 



Males of class 4 have a gametic constitution fLJ.u fLL 

 Ihat is, they are heterozygous with respect to both fecundity 

 factors. Among the progeny are to be expected high, low and 

 zero winter layers. Four male birds of this genot3^pic constitu- 

 tion have been used in the breeding experim.ents. Their records 

 follow. 



B.P.R. $ 5(5p. Indicated constitution = fLJ,i. flJ?. 



This male was hatched in 1909, and bred the following year. 

 His breeding history was as follows : 



Maiings: A. With i $ indicated to be of class 2 = fLjLz- PL-^k. 



2 Progeny 



Winter Production: Over 30 Under 30 Zero 



Observed 2 o o 



Expected.... I I o 



Mean winter &gg production of 



$ ? indicated class 67.00 eggs 



B. With 4 ?? indicated to be of class 6 = //,!,.. F/1/2. 



2 Progeny 



Winter Production: Over 30 Under .30 Zero 



Observed 2 6 3 



Expected 2."/^ 5-5 ^-75 



Mean winter production of 2 2 



in indicated class 75.00 eggs 7.33 eggs eggs 



(loc. cit., p. 164, footnote) had indeed himself noted what is essentially 

 this same difficulty in using the test on ordinary frequency distributions. 

 The point noted obviously limits greatly the applicability of Pearson's 

 test, and in a most unfortunate direction. Tests of goodness of fit are 

 much needed in Mendelian work. But it is just here that classes where 

 the theoretical frequency is zero often occur. To determine the proba- 

 ble error of the individual frequency in measuring the goodness of fit 

 of Mendelian observation and theory, as was first practised by Weldon 

 (52) and later by Johannsen (21) and by Mendelian workers generally, 

 does not appear to the writer to be an altogether sound procedure. It 

 fails to take account of the correlations in errors am^ongst the several 

 frequencies. Yet these are just as important and just as certainly ex- 

 istent in a Mendelian 'category' type of distribution as m the ordinary 

 variation polygon of a continuously variable character. This point I' 

 have alluded to elsewhere recently (Pearl, 32). Pearson's test covers 

 this point, and were it not for the other difficulty noted above would be 

 be much more widely useful in Mendelian work than is actually the case. 



