MEASUREMENTS OF -RELATIONSHIPS 



the relationship is a very valuable measure but one the calculation 

 of which takes a long time and involves presuppositions about the 

 form of distribution of the relationship. 



In all cases the investigator of a relationship should be observ- 

 ant of the form of distribution of the individual relationships and 

 of their approximate mode. Where the correlation table shows any 

 marked eccentricity in the distribution of the relationships the ob- 

 served modal relationship at least should probably be stated, even 

 though the more reliable Median Ratio or Pearson Coefficient has 

 been calculated. 



The correlation (in the sense of the slope of the line which the 

 Pearson Coefficient measures) may be inferred from the frequencies 

 of certain types of pairs, as in the case, r = cos. irl] (U equalling 

 the percentage of unlike-signed pairs with median sectioning). 



The methods of making this inference are especially valuable 

 when we wish to compare two relationships, one (or both) of which 

 is measured very crudely, for instance, the relation between health 

 and cheerfulness and the relation between intellect and morality. 

 From such measures as the following : 



g Much 

 g Little 



Health 



Sickly Healthy 



150 150 



Inferior 



Intellect 

 Dull Bright 



315 285 



250 



450 



1 2 Superior 145 



2G5 



of 



one can not compare directly the closeness of relationship 

 health and cheerfulness with that of intellect and morality. 



The following formulas, suggested by Pearson, are probably the 

 best available for dealing with such casesT In all N= the total 



FIG. 9. 



number of pairs; a, b, c and d mean respectively the numbers of 

 ^Wi, 2 2/i x \y-t an d x 2 y 2 pairs where Xj. means measures above any 

 given degree of x and x 2 , measures below it, and similarly for y 1 and 

 3/ 8 (see Fig. 9). 



