SHOETER ARTICLES AND DISCUSSION 



A SIMPLE TEST OF THE GOODNESS OF FIT OF 

 MENDELIAN RATIOS 



In actual experimentation the so-called Mendelian ratios, 

 3 : 1, 9 : 3 : 3 : 1, 9 : 3 : 4, 9 : 7, 15 : 1, 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1, etc., are 

 never exactly realized because of the errors of sampling inherent 

 in all statistical work. Notwithstanding this fact, the best the- 

 oretical formulas must be selected on the basis of these mislead- 

 ing experimental results. 



Now the test of the validity of any Mendelian formula is two- 

 fold: the number of individuals found should agree with the 

 number expected within the limits of experimental error, 1 the 

 assumed germinal composition of the several groups of individ- 

 uals should be capable of substantiation from a study of the 

 soma of their offspring. 



For the most part, Mendelians have been satisfied to judge 

 the goodness of fit of the theoretical frequency to the empirical 

 by inspection merely. More recently, however, attempts have 

 been made to apply scientific tests to this problem. The first 

 was that of Weldon, 2 but Professor Johannsen doubtless de- 

 serves the credit of having interested the few Mendelian workers 

 who have taken the pains to calculate probable errors in this 

 indispensable part of their work. 



The test used by Professor "Weldon and recommended in a 

 much extended form by Professor Johannsen 3 is essentially the 

 determination of the probable error of the number of individ- 

 uals in one of the subgroups by the formula 



S.D. = \/nXpXq, 

 where p is the chance of occurrence of an individual of any 

 class, q = l — p, and n is the number of individuals. Thus the 



1 In some eases, valid reasons for discrepancy between calculated and 

 observed frequencies may be shown. These factors should then be taken 

 into account in calculating the theoretical numbers. 



3 Weldon, W. F. R, "Mendel's Laws of Alternative Inheritance in Peas," 

 Biometrika, 1: 228-254, 1902, especially pp. 233-234. 



8 Johannsen, W., "Elemente der Exakten Erblichkeitslehre, " pp. 402- 

 410, 1909. 



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