EMPIRICAL STUDIES IN THE THEORY OF 

 MEASUREMENT 



IN the present condition of psychology, sociology and education, 

 convenience, economy and directness are as important desiderata in 

 methods of measurement as refinement with respect to precision. 

 The results of these studies justify certain methods which have the 

 decided advantage of giving measures which are direct functions of 

 the data, independent of any hypothesis about the prevalence of the 

 so-called 'normal' distribution, but which have been somewhat dis- 

 countenanced or at least neglected in both the theory and the prac- 

 tice of statistics. 



The section on correlation attempts also to make clear just what 

 is measured by a coefficient of correlation and what the dangers are 

 in the application of correlation formulas without constant super- 

 vision by an adequate sense for the concrete individual facts to be 

 related. 



MEASUREMENTS OF TYPE AND VARIABILITY 



1. The Comparative Accuracy of the Average and the Median 



The median as a measure of the central tendency of a series of 

 measures"~has the advantages of greater quickness of calculation, 

 freedom from the influence of erroneous measurements, ease of in- 

 terpretation and often greater practical significance. It is, there- 

 fore, important to know whether the accuracy, with which the 

 median actually obtained from a small sampling of a series conforms 

 to the true median of the total series, is much less than the similar 

 accuracy in the case of the more commonly used measure, the average. 



It is possible with any given form of distribution to calculate on 

 the basis of the theory of probability the accuracy in either case. 

 Trusting that some one will soon do this for typical forms of dis- 

 tribution other than the so-called 'normal' I have chosen to get 

 empirical data on the same question from actual experiments with 

 random samplings from certain large series of measures. 



The median was calculated for each sampling by regarding the 

 total series as measures of a continuous variable, quantity 61, for 

 instance, equalling from 60.0 up to 62.0, quantity 63 equalling from 

 62.0 up to 64.0, etc. Where the median fell within a unit of the 

 scale, as of course it usually did, the fractional part was taken 



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