SHOETER ARTICLES AND DISCUSSION 



THE APPLICATION OF CORRELATION FORMULA TO 

 THE PROBLEM OF VARIETAL DIFFERENCES IN 

 DISEASE RESISTANCE: DATA FROM THE 

 VERMONT EXPERIMENTS WITH 

 POTATOES 



The ultimate practical object of any study of disease resistance 

 in a series of varieties is the selection for future cultivation of 

 the few which are least susceptible. In practise a relatively large 

 series of varieties or strains is taken into cultivation for pre- 

 liminary study. The size of the cultures of the individual strains 

 must, on a given area, be inversely proportional to their number. 

 Since the individual cultures are necessarily small, it is impos- 

 sible to assert from the results of a single test that the observed 

 differences between the strains really represent varietal differ- 

 ences in disease resistance. They may be due merely to inade- 

 quately large cultures or to imperfectly controlled experimental 

 conditions. It is therefore necessary to repeat the experiment 

 another year or in a different locality in order to determine 

 whether the observed differences are really persistent, and so 

 characteristic of the strain, or whether they are due to transient 

 conditions only. The problem is then purely and simply one of 

 correlation. This is obviously true whether one chooses to avail 

 himself of the advantages of the statistical formulfe or not. If 

 the correlation between disease incidence in cultures of the series 

 of varieties grown in different years, or places, be zero, the vari- 

 eties show no permanent differentiation in disease resistance. If 

 the correlation has a significant positive value it indicates at once 

 that there are really inherent varietal differences in disease re- 

 sistance. The numerical magnitude of the correlation indicates 

 something of the extent of this differentiation. If the correla- 

 tion be low, the prospect of isolating varieties sensibly more re- 

 sistant that the average will be slight. If the correlation be high, 

 it should be relatively easy to secure highly resistant strains. 



Since the correlation method seems to have considerable value 

 in the analysis of data of this kind, I have thought it might be of 

 service to geneticists and plant pathologists to illustrate it by the 

 constants which I luivo found it necessary to deduce for another 

 purpo'io froni the [nil'l isli. , 1 ivrords of the series of experiments 

 on di^onso rc'^i^l m ■.• m v;i fid it s of potatoes carried on during 



1 Stuart, W., "Disease Hesistaiiee m Potatoes." Bull. Vt. Agr. Exp. Sta., 

 179, 1914. 



238 



