No. 603] MENDELIAN CLASS FREQUENCY 145 



tical Mendelian work), and (2) the fact that the test takes 

 into account only the magnitude of the error and not its 

 direction {i. e., whether in excess or defect) in any par- 

 ticular case. (3) It gives a result not particularly well 

 adapted to the actual needs of Mendelian research. The 

 test gives a measure of the goodness of fit of the 

 whole distribution, and only that. Now besides being in- 

 terested in that point the Mendelian worker quite as often 

 wants to know, in addition, something about the prob- 

 ability that particular classes observed are significantly 

 different from the expected. To that sort of knowledge 

 the test helps him not at all. It is an "all or none" 

 sort of method.^ 



2. It has seemed to the writer that it would be useful 

 to discuss methods of determining the true probable error 

 of each class frequency in Mendelian distributions as a 

 supplement to the x^ test, and for use in cases where it is 

 not applicable. The fundamental theorems have all been 

 given by Pearson^ in a very important paper, which is 

 apparently almost entirely unknown to biologists. The 

 purpose of the present paper is first to show the appli- 

 cability of these theorems to the problem in hand, and 

 second to point out some matters regarding the practical 

 use of the method likely to be helpful to biologists with 

 but little mathematical training who mav attomi)t to 

 use it. 



3. In the paper referred to, Pearson, stai'ting from 

 Bayes' theorem, shows that the distribution of chances 

 of an event occurring in a particular way in a second 



yields a small frequency on classes where the expectation is zero, and need 

 not further discuss them here. I have never thought it necessary to make 



nor do I yet. The test leads to this absurdity: if I perfonn a Men- 

 delian experiment in which I get ten thousand million offspring agreeing 

 perfectly with expectation save for one lone individual (perhaps a mutation, 



pected, then Pearson and the x- test agree that the [)rohability is infinitely 



• Pearson, K., loc. cit. 



