APPLICABILITY OF A COEFFICIENT OF CORRELATION 329 



does not give all of the information which is required concerning the 

 interrelationship of these two variables, and that a coefficient showing 

 whether the value of y becomes relatively larger or smaller with increas 

 ing values of x } would have considerable analytical value. 



I showed 1 then that if s = px, where p = y/lc, the bars denoting pop 

 ulation means, 



Vx TI 



The purpose of this paper is to illustrate the range of usefulness 

 of this coefficient by noting biological progress which has been made by 

 its use, and by actually applying it to series of data which have not been 

 heretofore fully analyzed by the higher statistical methods. 



Before passing to actual illustrations of applicability of the coefficient, 

 some questions of method should be considered. 



In cases in which the coefficient r xz is desired the correlation table 

 has usually been formed to determine r vu , where v -\- y = x. The mean 

 and standard deviation for x made up of any number of components 

 (HARRIS 1917 c) are well known (PEARL 1909, HARRIS 1918 a) ; 

 when x = v + y 



x = v + y, v x = V o- v 2 + a-y + 2 r vy &amp;lt;T v &amp;lt;T y 



If one has made his summations about zero as origin, as suggested 

 elsewhere (HARRIS 1910 b) it is quite easy to determine the necessary 

 moments from those alreadv available. 



The product moments are 



2(zry) is in each case the product moment already obtained in the cal 

 culation of r vy . 



In the original paper (HARRIS 1909 a), the method of determining the 

 value of cr x , which is essential for calculating the equation for the regres 

 sion of -s on x, was not indicated. 



1 The deduction of a usable formula for the problem then in hand was, as I have 

 elsewhere pointed out, due to Professor PEARSON who, with characteristic generosity 

 to his pupils, insisted that my name only appear in the paper. 



GENETICS 3: Jl 1918 



