DYNAMOGENIC INFLUENCE OF LIGHT 365 



The low statistical reliability of a number of the averages in- 

 cluded in the second group in table 2 is probably due to the 

 small number of measurements. I consider the difficulty of 

 getting a sufficient number of measurements to be one of the 

 most serious objections which can be urged against the work- 

 method as a means of exhibiting differential effects when the 

 effects, as in the present case, are small. 



The fact of individual differences being established, one may 

 inquire whether the performance of the group of subjects, as a 

 whole, was better in the light than in the dark, or the contrary. 

 In other words, in case the whole population to which this group 

 is a sample were experimented upon in groups of 16, what is the 

 probability that the average performance of a group would be 

 better in the light than in the dark? 



These questions are met by including in one distribution all 

 the A's of all the subjects and calculating the constants of the 

 distribution. The average (M A ) and the standard deviation (o-) 

 were obtained by the method of tabulation. Extreme measure- 

 ments which failed to satisfy Chauvenet's criterion were ex- 

 cluded, and the probable error of the average (PE MA ) was taken 

 as 0.6745 0- -r- \/N. The distribution is shown in classes each 

 having a range of 1 per cent, and each class is designated by the 

 numerical value of the mean of the measurements included in it. 

 For example, the class designated as 5.45 includes all the meas- 

 urements between 5 per cent and 5.9 per cent inclusive and the 

 value of each of the measurements included in the class is taken 

 as 5.45 per cent. 



The general distribution is shown statistically in table 3 and 

 graphically in figure 1. The results indicate that the average 

 performance of the entire group is 2.09 per cent better in the 

 light than in the dark; and that the probability is of the order of 

 1 X 10~ 14 that the direction of the difference would be reversed 

 by repetition of the experiment. 



The form of the empirical frequency curve suggests that the 

 deviations from normality of distribution are due to limitations 

 of simple sampling. 



