RAYMOND PEARL. 



It is of some interest to examine the trend of the total devia- 

 tions given in the last column. The data are shown 

 in Fig. 5, arranged in order from the smallest to tin 

 deviation. 



This diagram illustrates a point frequently overlooked. It is 

 commonly argued that the more independent judgments one ob- 

 tains regarding any point the more accurate will the average 

 result be. We are apt to say that if ten men measure a stick 

 the average of their measurements will necessarily be nearer to 

 the true dimension than if but three men measure and their 

 average be taken. But it is plainly evident from Fig. 5 and 

 Tables VI. and YIII. that the inclusion of observers I., II., III. 

 added nothing to the accuracy of the mean. The point which is 

 forgotten in assuming that greater numbers necessarily mean 

 greater accuracy is apparent if we examine the equation for the 

 probable error of a mean which is 



P.E.J, .67449 



V n 



The probable .error, to be sure, varies inversely with n, but 

 it also varies directly with a, the standard deviation. And, what 

 is here of primary importance, the standard deviation tends to 

 increase as n increases. Whether the probable error shall be 

 smaller or not as the number of observations is increased depends 

 upon what has happened in the meantime to the standard devia- 

 tion. When n is small, as in the case here under discussion, the 

 effect on the standard deviation of taking n + I observations as 

 compared with n may greatly outweigh its effect in the denomina- 

 tor of the probable error fraction. 



IV. 



The next point to be considered is the relative constancy of 

 the same observer's error. If each of the fifteen observers had 

 made a second count of all the ears at some considerable interval 

 of time after the first, how closely would the recounts tally with 

 the original counts? Such an experiment really tests, of course, 

 the stability or constancy of an observer's judgment . It indicates 

 the degree to which his standard of sorting is absolute, and to 

 what extent it fluctuates. 



