362 H M - JOHNSON 



experiment there was no economic basis for assigning any given 

 weight to errors. 



Fortunately, the problem permitted the early acquisition of 

 perfect accuracy. In very few cases did the errors exceed two 

 per cent after three or four days of practice; while some subjects 

 made only sporadic and single errors after the first day. The 

 factor of speed therefore chiefly determines the measure of per- 

 formance. 



Each daily sitting yields two scores of performance:, one for 

 light (PJ and one for darkness (P D ). The conventional method 

 of treatment would be to average the P J S and P D 's for each sub- 

 ject over the duration of the study and to compare the differ- 

 ence between the two averages with its probable error in order to 

 establish its significance. This treatment, however, is appro- 

 priate only if the results tend to group themselves about a mean 

 in accordance with the laws of probability. It is not appropriate 

 if a large constant source of variation operates together with the 

 fortuitous factors. 



Such a condition is presented in the present case, due to the 

 effect of practice, which in a few days' time multiplied the degree 

 of skill exhibited in the initial stages of learning. Two alterna- 

 tives were presented: (1) to train the subjects until the increase 

 of skill from day to day became negligibly small, and discard the 

 results obtained before this point is reached; or (2) to correct for 

 the effect of practice. Considerations of economy necessitated 

 the adoption of the latter plan. 



The correction was accomplished as follows : Each P L is dimin- 

 ished by the corresponding P D , and the difference (A) is ex- 

 pressed as a percentage of P D . In mathematical notation, 



100 (P L - P D ) 



Then, for each subject, the average differential effect (M A ) is 

 expressed by 2 A -T- N, in which N represents the number of 

 averaged terms. 



Practically the result was obtained simply by expressing each 

 P L as a ratio per cent P D ; averaging the ratios; and then dimin- 



