1908.] PUBLIC DOCUMENT — No. 33. 69 



Studies in Correlation. 



These questions bring us immediately to the study of corre- 

 lation in variation, — one of the most im})ortant fields of plant 

 study. In no field, moreover, is the value of the statistical 

 method more conspicuous than in this. 



There are two algebraic methods of answering the questions 

 just asked, the first known as Yule's method,^ and the second 

 may be called Pearson's method ^ or the method of compound 

 series. In applying the former method it is necessary to sepa- 

 rate the plants into four groups, according to the two characters 

 to be compared. 



If we select those vines which bear 8 pods each or more, 

 putting them in one class, with those bearing 7 pods or less in 

 another class, and if we then sul)divide each of these classes 

 according to the average number of peas per pod on each vine, 

 we shall have the following groups and figures : — 



From which the following computation is made according to 

 Yule's formula : — 



(GGX10)-(9X85) _489_ 



(66 X 19)+(9X85) — 2019 — ^ ^•^*^" 



Showing a correlation of character in these groups of over 

 24 per cent. 



Now, if the arbitrary division is made between vines bearing 

 7 pods or over and those bearing 6 pods or less, the rest of the 

 computation following as before, we find the coefBcient of cor- 

 relation reduced to — 0.067 ; or with the division made between 

 vines bearing 5 pods and those bearing 4, the coefficient of cor- 

 relation becomes — 0.0126, showing a very little or slightly 

 negative correlation in these groupings. 



1 See E. Davenport, "Principles of Breeding." 



2 See C. B. Davenport, p. 456, 1907, " Statistical Methods." 



