144 Ai)his rumicis on Varieties o/ Vicia faba 



for, if the standard deviations have been correctly calculated, this must 

 be distributed as in x" when n'= 5 in Elderton's table of Goodness of Fit. 

 For the 17 values we have the following comparison. 



Expected 



a;2 = 2-22 



Since we have introduced one empirical value we must take w'= 3, 

 and obtain P = -336. Thus in 33 cases out of 100 we should expect a 

 worse fit to occur by chance, and this shows that the totality of the 

 observations shows no significant deviation from the set of standard 

 deviations which we have assigned to them. 



With a knowledge of the probable errors of the infestation numbers 

 it is possible to test to what extent the several varieties may be grouped 

 together as possibly identical in respect of aphid infestation. From the 

 genetic standpoint it is of the highest importance to determine the con- 

 tinuity or discontinuity of susceptibility; and it is only too frequently 

 that statisticians infer the continuity of a variable quantity without 

 testing to what extent the apparent continuity is due to genuine con- 

 tinuity, due to a multitude of underlying genetic factors, and to what 

 extent a real discontinuity has been obscured by chance variation. In 

 the present case the homogeneity of certain groups is suggested by the 

 mean values. Without being able to test this delicate point with rigour, 

 it is worth while to note that the numbers obtained from certain groups 

 are consistent with the supposition of identical susceptibility. 



The group of three varieties (Nos. I, II, XIX) giving mean infestation 

 numbers 1007 to 1037, may be regarded as samples from a single group 

 with mean infestation number at 1020. The standard deviation of the 

 individual plants from this value is 167, and that calculated as explained 

 above is 171. 



The variety No. Ill with infestation number 737 appears to be 

 isolated. 



The four varieties (Nos. IV, V, VI, VII) with infestation values 513 

 to 616 are distributed consistently with the supposition that they are 



