MEASUREMENTS OF RELATIONSHIPS 



17 



make the deviations from it toward closer correlation equal to the ' 

 deviations from it towards less correlation, but is so calculated as 

 to make the sumof the squares of the deviationsT-from it least 



This of course weights the extreme deviations much more than 

 those near the jenterof the ..sn^fapp^ f r the same change in the 

 slope^oFthe Ime alters the sum of the squares of the deviations from 

 the line near the center of the surface far less than that of the re- 

 mote deviations. This is a possibly questionable feature of the 

 Pearson Coefficient. 



Moreover it is calculated as the slope of this line of so-called 

 ' regression ' as found when the two traits are reduced to equivalence 

 of variability and double entries are made in the correlation table, 

 *. e., B's as related to A's and A's as related to B's, the two sets 

 of entries being so superposed that the intersection of the means in 

 the one case coincides with the intersection of the means in the 

 other case. 



Professor Pearson gives many readers the impression that his 

 coefficient of correlation is calculated as the slope of the straight line 



Fi 



F( 3 . 3. 

 -7 -5" -3 -I +1 +3 +S +1 



-S 

 -3 

 -I 

 + l 

 +3 



through to fit the points in the correlation diagram that represent 

 the means of the arrays 1 (the two related series being reduced to 

 an equivalence in variability and entered doubly), but in fact it 

 is the slope of the line from which the sum of the squares of the 

 deviations of all the dots each representing one relationship is least, 

 not the slope of the line from which the sum of the squares of the 

 deviations of the dots representing each the mean of one array is 

 least. It is in onr illustration a line to fit the dots of_Fig. 3 r jnot 

 fhnsy ft f Figr. 2. That is, an array of 100 cases is (quite properly) 



given greater weight than one of 2 cases. 



1 See, for instance, ' Grammar of Science,' 2d edition, 1900, p. 393 and p. 396. 



