INDEPENDENT MEND'ELfA'N INHERITANCE 



101 



sents the sum of all the terms of such a ratio. This gives for the probable 

 error E n of a given term N of a Mendelian ratio the value 



E n = 0.6745 



In this formula n = the total number of individuals classified. 



The actual application of this formula may be illustrated by the use 

 of data from East and Hayes given in Table XI. The totals in this table 

 give observed frequencies as shown in Table XVII. 



TABLE XVII. GOODNESS OF FIT IN A MENDELIAN EXPERIMENT 



The results are expected to be in agreement with a 9:3:3:1 ratio; 

 therefore these observed results are first reduced to the form of a ratio 

 per 16 by dividing each term by }{Q of the total number of individuals, 



or by 1fi - = 202.5. By this method the observed ratio in Table 



XVII was calculated. 



To obtain the probable error for the purple starchy class values are 

 substituted in the above formula as follows : 



E 9 = + 0.6745 





~ 9) = 0.094 



The observed deviation 0.19 is approximately twice the value of the 

 probable error. For practical purposes a deviation less than three or four 

 times the probable error is not considered significant. A deviation of the 

 above magnitude in comparison to the probable error occurs about once 

 in four times. In Table XVII the values of the probable error have been 

 calculated for all four of the terms of this ratio. One term lies considerably 

 within the probable error and its probability has been put down as 1:1. 

 This is not strictly correct but serves the purposes of these calculations. 

 It will be noted that there is one serious deviation, that of the white 

 starchy class which could occur only once in 142 times. This deviation 

 is not serious enough, however, to lead us to reject the hypothesis of 

 two factor differences for this case, but it may indicate that other dis- 

 turbing forces are in operation in this experiment. 



