8 EMPIRICAL STUDIES OF MEASUREMENT 



3. The Divergences of the Obtained from the True Measures by 

 Theory and by Experiment 



It is always interesting to compare the result of experiments in 

 chance with the expectations derived from the theory of probability. 

 Accordingly, I give the facts in Table IV. so as to save the reader 

 interested in this matter the time of collation and calculation from 

 the data of Tables II. and III. 



The figures under Theory were calculated not from the A.D.'s 

 of all the separate samplings, but once for all from the A.D. of the 

 total series. 



The figure under Theory is not in any case exactly the amount 

 to be expected under strictly correct theory, but is the amount to 



be expected from the formula A.D. tr -bt AT = ^5-, 



Vn 



This formula, applicable to cases of random sampling from a 

 distribution of the so-called normal type, will of course not suit 

 exactly distributions limited in extent and irregular in form. Com- 

 parison with it is however the important matter practically, since 

 it is the formula in universal use. 



TABLE IV. 

 Av. DEV. OF OBTAINED FROM TRUE AVERAGE 



