16 EMPIRICAL STUDIES OF MEASUREMENT 



Each of these pairs represents a relationship, the entire series 

 reading: A deviation in A of 7 from the central tendency of A 

 brought with it a deviation in B of 5 from the central tendency of 

 B; a deviation of 5 brought in one case a deviation in B of 5, 

 in a second case one of 3, and in a third case of 1, etc. 



Consider now two measures each expressing an important fact 

 concerning this series of 30 individual relationships. The first is, 



.634. The second is, The median of the 30 B/ A 



ratios = .65. The former is of course the Pearson Coefficient of 

 correlation for A B; the latter is. the Median or Mid Ratio B/A. 



What the former measures can not be stated except in terms not 

 yet given by the individual relationships themselves. Professor 

 Pearson's own statements for instance are in terms of certain facts 

 of a correlation diagram such as Fig. 1, not in terms of the indi- 

 vidual relationships. 



It is clear that in the case of Fig. 1, which represents our 30 

 relationships graphically, the slope of the straight line LL 1 through 



-7 -S -3 -I 



-3 



+3 



+7 



O so drawn that the sum of the deviations of the individual dots from 

 it is zero (measuring deviations in the direction of the B line and 

 calling deviations above the line in the left hand half of the surface 

 and below the line in the right hand half of the surface +, and 

 calling deviations below the line in the left half and above the line 

 in the right hand half ) is a measure of an important fact about 

 the series of relationships. 



I The Pearson Coefficient does not, however, measure the slope of. 

 / just such a line as we have supposed to be drawn in Fig. 1 and 

 I described in the last paragraph. Its line is not so calculated as to 



1 In this case the slope is roughly 73 per cent, of 45, the slope which would 

 be found were correlation perfect. The slope for the A's taken as dependent on 

 the B's is roughly 64 per cent, of 45. 



