No. 530] SHORTER ARTICLES AND DISCUSSION 127 



a row and column with the same heading (37 in this case). 



(3) We employ the ordinary frequencies in the body of the 

 table in getting the sum of the deviations of (xy) for use in the 

 formula for the coefficient of correlation, just as in ordinary cor- 

 relation tables. The computation of the coefficient is of course 



(as in the case of symmetrical tables) considerably simpler 

 than in the usual case, since we have but one standard deviation 

 and one quantity d to deal with. 



Only one other point in the computation is peculiar, requiring 

 careful observance. If we let n signify the number of pairs 

 and N the number of individuals (so that N — 2n), then in find- 

 ing the mean, standard deviation, and coefficient of variation, 

 we use N (just as in symmetrical tables), so that the formula for 

 the standard deviation is 



But in getting the coefficient of correlation, the sum S(xy) 

 which we get from our unsymmetrical table is just half what we 

 should get from a symmetrical table (as we have already seen). 

 Therefore, to make the computations identical with those for 

 symmetrical tables, we must either double this sum in the for- 

 mula for the coefficient of correlation, or what is simpler, in 

 place of doubling this sum we may halve the number by which 

 we divide this sum, that is, we may use n in place of N. Thus 

 the formula for the coefficient of correlation becomes by this 

 method 



This method lends itself readily to the valuable procedure 

 recently described by Harris (1910) for finding the coefficient 

 of correlation, the only point requiring careful attention being 

 the fact that in finding the standard deviation we must use 

 N (number of individuals), while in the formula for the coeffi- 



present plan is likewise well adapted for finding the coefficient 

 of correlation by the "difference method" (see Harris, 1909). 



If the method we have described is us d. the pairs are entered 

 in the table but once, in any way that is convenient; the correla- 

 tion computed will always be the same, and identical with that 

 from symmetrical tables. It avoids the cumbersome and labo- 



