COEKELATED VARIABILITY. 45 



The handling of long decimal fractions may be avoided by 

 the use of a method similar to that used at page 26 for find- 

 ing the average and standard deviation. The formula for r 

 may be written 



Assuming the class including or nearest to the true mean 

 of the subject values as the mean of the subjects, and the 

 class including or nearest to the true mean of the relative 

 values as the mean of the relatives, find for each variate the 

 product of its deviations x' and y' from the respective assumed 

 means, and (having regard for signs) find the algebraic sum 

 of these products. Divide this sum by the number of vari- 

 ates; the quotient is the average of the deviation products about 

 the assumed axes. To refer to the true axes, passing through 

 the true means, find the average moments, i^ (as on page 26), 

 both for the subject and the relative distributions about their 

 respective assumed means, and subtract the product of the 

 two values of v l from the average of the approximate devia- 

 tion products already found. Divide the difference by the 

 product of the standard deviations of the two frequency dis- 

 tributions. (Compare Yule, '97 b , pp. 12-17.) 



The probable error of the determination of r is 



= 0.6745(1 -r 2 ) 



v^ 



(Pearson and Filon, '98, p. 242.) 



Example. Correlation in number of Miillerian glands 

 on right and left legs of 2000 male swine. (See table on next 

 page.) 



For -f quadrants 2(x'y')= 5243 







