60 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



variables a constant, v, called the correlation ratio, and defined by the 

 expression 



V 



In other words, the correlation ratio is the ratio of the variability of 

 the means of the arrays of one correlated character to the total vari- 

 ability of that character, as exhibited by the sample as a whole. The 

 constant v has the same value as the coefficient of correlation r only 

 when the regression is perfectly linear. If the regression is not linear 

 r] will be greater than r. Then evidently -7 ~ r is a measure of the 

 approach of the regression to linearity. Recently Blakeman ( :05) has 

 given methods of obtaining the probable error of various functions of 

 7/ ~ r. 



Table SI.— Correlation between leaf-number and position. Whorls on all branches. 



Table 32. — Correlation between leaf-nutnber and position. Whorls on primary 

 branches. Series I, II, and III combined. 



In table 33 are given the values of r and rj with their probable errors 

 deduced from the data given in tables 30 to 32. The probable errors 

 of r tabulated were computed from the formula 



(1-^0 



Vn 



Probable error of >/ — ±0.67449 



