MEASUREMENTS OF RELATIONSHIPS 27 



fectly fit to compare only when the form of distribution of the 

 relationship A B is the same as that of the relationship C D. 

 So also of the median B/A and median D/C, or of the median 

 A/B and median C/D, or of any measure of the central tendency 

 of relationship which may be inferred from them. In so far as what 

 we wish to compare is the modal relationship, however, there is a 

 smaller error as a rule in inferring from the comparison of the 



Median Ratios _of unlike distributions of relationships than in in- 

 ferring from the comparison of their Pearson Coefficients. 



Convenience of Calculation. 



Provided the original measures are on a sufficiently fine scale, 

 as they ought for every reason to be where relationships are to 

 be measured by a Pearson Coefficient or a Median Ratio or a Modal 

 Ratio, the Median Ratio is of course far more convenient than the 

 Pearson Coefficient. Once a correlation table is written out the 

 Median Ratios can be obtained with very little computation or eye 

 strain. Inspection of the correlation table will tell about what they 

 will be and only a few of the ratios will need to be ranged in order. 

 I append a sample calculation (Fig. 8). 



First one makes an exact median sectioning of the #'s and the 

 y 's and then counts the cases that give negative ratios. 



By inspection one then chooses for the y/x ratios an approximate 

 median (here of about .25) and for convenience draws a line to 

 include these cases and counts them. One then increases their 

 number by adding the cases of the next smallest ratios not included 

 or by taking away the cases of the largest ratios included until one 

 reaches the Median Ratio (here .333). One then repeats the process 

 oi: guessing at an approximate median for the y/x ratios and cor- 

 recting it, 



In making comparisons on the basis of the median ratios we 

 must of course bear in mind the variabilities of our A, B, C and D. 

 In the Pearson Coefficients the series concerned are reduced to an 

 equivalence in variability in the process of calculation. With the 

 Median Ratios, if we wish to make this reduction to terms of the 

 variability as a unit we must do it as a separate operation. For 

 instance let A, B, C and D be series with variabilities 1, 2, 4 and 5. 

 If then the Median Ratios found are 



B/A = 1.00, A/B = .25, D/C = .625 and <7/D = .40, 

 the Median Ratios that would be found if the differences in varia- 

 bility were eliminated would be B/A -=-2/1, A/B-+-1/2, etc., that 

 is .50, .50, .50 and .50. If we wish to compare the mutual implica- 

 tion of A and B with the mutual implication of C and D we must 



go further still and combine the median - --'- - with the median 



