THE CRITERION OF LEARNING 69 



quired for learning. 2. With the increasing difficulty of the 

 problem there is an increase in the extent of variation between 

 the members of the same group so that the greater difference 

 between the groups looses its significance through the increase in 

 the probability of chance variation of the averages. 3. Hence 

 there is no advantage, for reliability of results, in prolonged 

 training where the problem is that of a statistical comparison of 

 different groups of animals by a single standard of achievement. 



These conclusions apply only to a specific technique, but one 

 which has been used extensively in studies of the effect of age, 

 sex, distribution of practice, etc., upon the rate of learning. It 

 may be argued that long training permits the comparative study 

 of the rate of learning at different stages of proficiency. This 

 is quite true, but the analysis of learning curves based upon 

 the averages of several animals has contributed remarkably 

 little to our knowledge of the mechanism of learning and in 

 statistical studies of the sort under discussion there is not time 

 for that detailed analysis of the individual behavior of the 

 subjects which is of value in the interpretation of the form of 

 the learning curve. On the other hand the results of studies 

 of the modifiability of the course of learning by environmental 

 factors are for the most part questionable because of the small 

 number of cases upon which they are based. In many cases 

 differences which are smaller than their probable errors have 

 been regarded as significant, seemingly only because they sup- 

 port the hypothese of the writers. 



The use of an adequate number of animals is difficult for 



the reason that the groups to be compared should be trained 



at the same time to rule out possible seasonal differences, of 



which we know nothing at present, while only a limited number 



of animals can be trained by one man at one time. A possible 



solution of the difficulty is the cooperation of several students 



upon a single problem but there is not enough data upon the 



influence of the experimenter's personal equation to permit of 



this as ye t. 3 The alternative seems to be the simplification of 



3 The use of two or more criteria as in the experiments reported, while reducing 

 the probable errors of the average difference found, removes hereditary and like 

 individual differences from the category of chance variations and places them 

 on an equal footing with the experimental differences (age, sex, or whatever differ- 

 ence is being studied) as the cause of the diverse rates of learning revealed by the 

 experiments. 



