480 H. M. JOHNSON 



of the "probable difference" between Mi and Af 2 . This desig- 

 nation may be due to a typographical elision, although its use 

 might be justified. 



The ratio of the magnitude of the difference to the probable 

 error of the difference is given as a means of ascertaining from 

 the probability integral table of the function x + PE X what is 

 the probability for and against the difference being due to chance. 



Certain extreme reactions, indicated by asterisks in tables 

 2 to 5 inclusive, were not included in the averages. Their 

 exclusion was accomplished by the use of Chauvenet's criterion. 11 

 Its application to an asymmetrical distribution is not wholly 

 justifiable, but the calculation of a theoretically perfect one is 

 rather tedious and the gain in accuracy is not sufficient to justify 

 the labor. The arbitrary use of a standard criterion of exclusion 

 is evidently better than rendering judgment from simple inspec- 

 tion. In any set of data of this type a number of stray deter- 

 minations will be found which clearly do not belong to the same 

 distributions as the others and probably were not obtained 

 under comparable conditions. To admit them to a distribution 

 containing a limited number of cases may tend to distort com- 

 parisons with other distributions in which, owing to the limited 

 number of observations, similar strays had not yet appeared. 

 And yet, it is evidently unfair to apply an arbitrary criterion 

 of exclusion which may not apply uniformly to all the compared 

 distributions. 



The distributions, reduced to a percentage basis, are also 

 shown graphically in figures 3 to 6 inclusive. From inspection 

 of the graphs it is evident that all the distributions are multi- 

 modal. This is characteristic of all the reaction-time distribu- 

 tions which the author has seen. His attention was called to 

 the fact some five years ago by Professor Dunlap, who asserted 

 at the time that this form of distribution is typical, and does 

 not disappear with greater accumulation of data. This was 

 corroborated in an interesting manner in tallying the daily 

 records of the present work, according to classes of tune-values. 



11 Cf. Davenport, C. B. : op. cit., pp. 12 f. 



