54 STATISTICAL METHODS. 



QUICK METHODS OF ROUGHLY DETERMINING THE COEFFI- 

 CIENT OF CORRELATION. 



The method just described may be used in lieu of the rela- 



2x y 

 tion r= 1 l whenever the distributions of frequencies of 



fUFjtfj 



the two correlated organs are normal. An exceedingly sim- 

 ple relation that is independent of the assumption of a normal 

 distribution has been given by Yule ('00 b ) as 



ad be 



and this may be used as a rough approximation to the coeffi- 

 cient of correlation. 



But Pearson ('00 C ) has shown that this simple relation is 

 not nearly as close to the true r as the following: 



where 



The superiority of the value r s as an approximation to r, 

 justifies the additional work its determination demands. 



SPURIOUS CORRELATION IN INDICES. 



When two characters a and b are measured in each indi- 

 vidual of a series of individuals, and each absolute magnitude 

 is transformed into an index by dividing it by the magnitude 

 of a third character c as found in the same individuals, a 

 spurious correlation will be found to exist between the indices 



of and (Pearson, J 97). 

 c c 



Let C 1 = the coefficient of variability of a; 

 C 2 = " " " " " b; 



ri _ (t (( (t (t tf r . 



U 3 c, 



r = " " " SDurious correlation. 



