A CLASSIFICATION OF GROUPS 283 



Considering the latter first, it is evident that there are several 

 groups which are beat with frequencies above the average fre- 

 quency of all other groups, because: 



(a) the total number of groups beat = 303 



(b) the total number of different groups beat = 69 



(c) the average frequency = 4.4 



The numbers 47, 62, 13, and 18 which represent the frequencies 

 of the four groups 22, 46, 70, and 94 give the following percent- 

 age frequencies: 15.5 per cent, 22.1 per cent, 4.2 per cent and 6 

 per cent. These percentages are, with one exception, quite above 

 the average frequency of all groups, and still greater than 2.4 

 per cent which represents the average frequency of all groups, 

 the above four excepted. Clearly there are certain groups that 

 are beat more often than others and more often than they would 

 be beat, were their distribution a matter of chance. Graphi- 

 cally this is shown on graph 1 from which it appears that the 

 groups 3, 7, 22, 46, 70 and 94 have maxima that are perceptibly 

 greater than the average for all groups. 



It will have to be asked and answered how often a group must 

 be beat or must recur in any given series before it can be said 

 that its frequency of recurrence is significant. Clearly, but only 

 generally, this is the case when its frequency rises appreciably 

 over the average frequency of all other groups. In this it is 

 assumed that on a chance basis all groups are equally likely to 

 occur. If certain groups occur more frequently and particularly 

 when these same groups recur on different days of experimenta- 

 tion, or indeed in different observers, then such recurrence must 

 have some significance. On this principle the groups 22, 46, 

 70 and 94 are significant, whatever the nature of the significance, 

 and speaking generally again, the 303 groups of observer R may 

 presently be divided into the two classes, those that are signifi- 

 cant and those that are insignificant by the frequency criterion. 

 Obviously no hard and fast line can be drawn between the 

 members of the two classes of groups, and consequently the fre- 

 quency principle cannot be considered as the sole or as an abso- 



