204 RAYMOND PEARL 



Further discussion of various points brought out by these 

 tables is deferred to a later section of the paper. 



Mating s of Barred Plymouth Rock males of class 4- 



Males of class 4 have a gametic constitution fLiLo . fhk. 

 That 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 genotypic constitu- 

 tion have been used in the breeding experiments. Their records 

 follow, 



B.P.R. d' 569. Indicated constitution = fLiLo . fhU. 



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

 His breeding history was as follows : 



Matings: A. With 1 9 indicated to be of class 2 = /L1L2 . FLih. 



9 Progeny 



Winter Production: Over 30 Under 30 Zero 



Observed 2 



Expected / 1 



Mean winter egg production of 



9 9 indicated class 67.00 eggs 



Yet, because the theoretical frequency on class 4 is zero, the probability by Pear- 

 son's test is literally infinite against the observed distribution being regarded as 

 a random sample of a population distributed in accordance with the theoretical 

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

 essentially this same difficulty in using the test on ordinary frequency distribu- 

 tions. 



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 probable 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 amongst the several frequencies. 

 Yet these are just as important and just as certainly existent in a Mendelian 'cate- 

 gory' type of distribution as in 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 much more widely useful in Mendelian work than is actually the case. 



