102 GENETICS IN RELATION TO AGRICULTURE 
A better method of testing goodness of fit has been suggested by 
Harris. The formula employed is : 
X2 = 5 = 9)”, 
Cc 
In this formula o = the observed frequency of any class; c, the cal- 
culated frequency of that class; and = indicates that all values of the 
— 2 
type e— are added together. When this formula is applied to the 
case treated above the values obtained are as givenin Table XVIII. The 
value of X2is 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.—Goopness oF Fir In A MENDELIAN EXPERIMENT 
Phenotypes Observed | Calculated ero 
0 | c 
Purplerstarchy se cccce cic a stasis oe 1,861 | 1,822.5 0.81 
Purpleisweetiaesaccs scacscnesee es 614 607.5 0.07 
Wihitestanchyza. sense ae tole 548 607.5 5.83 
Wihite sweetivicwauce ce sain amie es 217 202.5 | 1.438 
3,240 | 3,240.0 | 8.14 =X? 
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 
(OCA ae 
determining the significance of X?, 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 
may be determined by simple inspection of the values of 
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