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 11 

 tion r= whenever the distributions of frequencies of 



na 1 a 2 



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 

 T *~~ ad + bc' 



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 



4abcd . \ 



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, '97). 

 c c 



Let Cj=the coefficient of variability of a; 



C_ f f < ( ( ( (I I ( -L. 



2= b; 



C__<< t f t ( 1 1 ( ( . 

 3~~ C, 



r Q = " " spurious correlation. 



C 2 



