MEASUREMENTS OF RELATIONSHIPS 29 



Comparison is thus more awkward with the Median Ratios than 

 with the Pearson Coefficients, because the latter method automat- 

 ically both divides through by the variability and gets a measure of 

 mutual implication. The superiority of the Pearson Coefficients is 

 to some extent specious for it makes comparison easy not by re- 

 moving difficulties but by presupposing that they do not exist. The 

 obvious additional steps needed in the case of comparison of Median 

 Ratios witness and emphasize the hypotheses on the basis of which 

 we do compare. They may also prevent us from inadequate com- 

 parison. For instance from the facts that the Pearson r for adult 

 brother's longevity with adult brother's longevity is .2853 and that 

 the Pearson r for stature with left middle finger length is .6608, we 

 have no right to conclude that the latter relationship is 2.3 times 

 a.s close. Any one who will study the individual relationships in 

 these two cases 1 will see that no single ratio can express the com- 

 parison of the two relationships. 



Speed of Calculation. 



Onee the correlation-table is written out the Median Ratio can be 

 calcinated iii from one tenth to one hundredth of the time taken for 

 the Pearson Coefficient. 



Divergence of Results Obtained from a Partial Sampling from the 



Results from the Entire Series Sampled. 



The Pearson Coefficient is for normal correlation by the theory 

 of error the more reliable. Whether in the actual cases of relation- 

 ship with which we work, where the distributions and correlations 

 are not exactly normal and where the theory of error does not apply 

 without modification, it is more reliable, is a matter to be determined. 

 Its use of the exact amount of every case of the relationships makes 

 for superior reliability, but its weighting of extreme cases may some- 

 what conterbalance this. 



The reason given by Professor Pearson for replacing Galton's 

 method of obtaining the Median Ratio by this product-moment 

 method was this superior reliability. No other reason has so far 

 as I am aware ever been advanced. It is doubtful if Professor 

 Pearson now would lay so much stress on greater reliability in the 

 case of normal correlation of normal distributions, since he has so 

 emphatically shown the rarity of both of these, and has been at 

 some pains to test empirically certain measures which are valid re- 

 gardless of the normality of distribution of the two facts. 



Since in almost every other respect the Median Ratio is a more 

 advantageous measure, it seems worth while to determine empir- 

 ically, for some typical relationships, the comparative freedom from 



1 See Biometrika, Vol. I., p. 84, and Vol. I., p. 2 1C. 



