102 



GENKV1CS /# DELATION TO AGRICULTURE 



A better method of testing goodness of fit has been suggested by 

 Harris. The formula employed is 



x, (o - c) 2 



In this formula o = the observed frequency of any class; c, the cal- 

 culated frequency of that class; and S indicates that all values of the 



type 



A 



are added together. When this formula is applied to the 



, 



case treated above the values obtained are as given in Table XVIII. The 

 value of X 2 is 8. 14. The number of phenotypic classes is four. To deter- 

 mine the significance of this value it is necessary to refer to Elderton's 

 tables for calculating goodness of fit. The value for P, the probability, 

 for this case derived from such a table is 0.0437. The chances that the 

 deviations shown in this ratio are merely due to random sampling are 

 about one in twenty-three, again confirming our previous statement 

 that some unknown slightly disturbing forces may be operating in this 

 case. The deviation, however, is not enough to establish this certainly, 

 for such a deviation might be expected to occur in about 4 per cent, of 

 cases. 



TABLE XVIII. GOODNESS OF FIT IN A MENDELIAN EXPERIMENT 



Mathematically the method suggested by Harris is preferable. It 

 has also the advantage that it gives a measure of the goodness of fit of the 



ratio as a whole; which particular terms are most seriously at variance 



( o _ c )2 

 may be determined by simple inspection of the values of - . For 



C 



determining the significance of X 2 , it is necessary to have available 

 Elderton's table for test of goodness of fit. These are given in Pearson's 

 tables for statisticians and biometricians. It must ever be held in 

 mind that forces which tend to disturb Mendelian ratios may not neces- 

 sarily be of significance as bearing upon the essential feature of the analy- 

 sis, namely, that a given number of independent factors are concerned 



