14 EMPIRICAL STUDIES OF MEASUREMENT 



MEASUREMENTS OF EELATIONSHIPS 



The importance to any science of exact and convenient methods 

 of measuring the relationships of the facts it studies should be 

 obvious. It is therefore unfortunate that students of psychology 

 and the social sciences have with few exceptions neglected both the 

 theoretical problem of correlated variations and the careful measure- 

 ment of such relationships as they have in fact found. 



The failure to utilize the methods devised by Galton, Pearson, 

 Sheppard, Spearman and others is due partly to an ignorant and 

 partly to an intelligent suspicion aroused by the mathematical 

 derivations of these methods. Ignorance of the rationale of their 

 derivations cooperating with ignorance of the conditions which re- 

 quire their use and of the necessity of some such refined methods has 

 caused the stupid suspicion and aversion. Inability to follow the 

 mathematics of the derivation of formula?, at least in detail, cooperat- 

 ing with the rational expectation that too abstract methods will fit 

 the concrete cases imperfectly and with the equally rational con- 

 fidence that proofs resting upon the assumption of close approxima- 

 tion of actual variations in mental and social facts to the probability 

 curve distribution are always unsafe and, perhaps, usually mislead- 

 ing, has caused the intelligent suspicion. 



It is probable that unless these methods are soon subjected to a 

 review by some one who can both make perfectly clear their presup- 

 positions to the rank and file of investigators in psychology and the 

 social sciences and prove their applicability to actual cases of rela- 

 tions to be measured, there will be damage done in two ways. Many 

 investigators will as in the past use hopelessly crude methods and 

 misinterpret relationships; and also many investigators will learn 

 off the formulas of the mathematical statisticians and apply them 

 to cases where they are out of place and give inadequate and mis- 

 leading results. To both of these errors the writer, for instance, 

 confesses himself guilty in the past. 



I am unable to make such a review but as no one of those who 

 are able seems willing, 1 I have made a partial and inferior substi- 

 tute for it which I hope may, in so far as it is sound, be instructive 

 to students of mental measurements and, in so far as it is unsound, 



1 Perhaps Mr. C. Spearman's article on ' The Proof and Measurement of 

 Association between Two Things' (in the^jw. J. of Psy., Vol. XV.) may be 

 considered as filling the need, but I fear that it is too technical in parts and 

 not inquisitive enough concerning the actual relations between (1) the indi- 

 vidual relationships, from which all our computations ought to start, and (2) 

 the general expressions or summaries of them. At all events I am not trying 

 to do over again, for better or worse, what Mr. Spearman has done, but some- 

 thing which is needed as introductory and accessory to his work. 



