474 H. M. JOHNSON 



RESULTS: AVERAGES 



The distributions and averages are presented in tables 2 to 

 5 inclusive. They are given for the benefit of any reader who 

 may wish to subject them to different treatment than the one 

 employed. 



It will be noted that the reaction-times of subject G are dis- 

 tributed in classes of iihr second, while the other subjects' reac- 

 tions are in classes of 0.01 second. The records of subject C 

 were made first of all, with the chronoscope motor operated at 

 720 revolutions per minute. Later, the speed was reduced for 

 the other subjects, to 600 revolutions per minute to give a 

 decimal unit of measurement. 



In all these tables the time values are given in classes of ten 

 units each, the designation of the class being the numerical 

 value of the median of the class. For example, the class of 

 0.31 includes all the reactions between 0.305 and 0.314 inclusive. 

 The unit of 0.001 second is smaller than is useful. The chrono- 

 scope is accurate to only 1 per cent, in the average, of the magni- 

 tude of the times measured in this work, as was shown by the 

 daily checks with the pendulum. 



Table 6 gives a summary of the averages and the probable 

 errors of the averages for each subject under each of the three 

 conditions; also, the differences between the compared averages, 

 and the probable error of the differences. The latter is computed 

 from the formula 



PE^-m = 0.6745 



in which a represents the root mean square deviation from the 

 mean, and N the number of terms included in the average M . 

 From inspection it will be noted that this formula is equiv- 

 alent to 



which is given by Davenport, 10 after Pearson, as the formula 



10 Davenport, C. B. : Statistical methods, with special reference to biological 

 variation. 3d ed. New York, J. Wiley & Sons, 1904, p. 15. 



