Decembee 6, 1895.] 



SCIENCE. 



763 



Michel Angelo ' was born 300 years earlier 

 than Luther. 



Three questions were asked intended to 

 determine the average accuracy in estima- 

 ting weight, distance and time. These were 

 the weight of the text-book (James' Briefer 

 Course in Psychology) used by the class, 

 the distance between two buildings on the 

 college grounds and the time usually taken 

 by students to walk from the entrance door 

 of the building to the door of the lecture 

 room. The results are shown in the ac- 

 companying table, there being given the 

 approximate actual magnitude, the average 

 estimate with the constant error, the aver- 

 age departure of the estimates from the 

 average estimate and from the actual mag- 

 nitude and the median. 



It thus appears that in these cases there 

 was a marked tendency to under-estimate 

 weight and to over-estimate time. Length 

 was over-estimated, but to a less degree. 

 For the magnitudes used the average vari- 



ation was about one-third of the weight 

 and one-half of the distance or time. The 

 actual ei'rors were larger in the case of 

 weight and time, but not in the case of dis- 

 tance. The middle estimate or median 

 value is in all cases smaller than the aver- 

 age. The degree of confidence of the ob- 

 server does not in these cases seem to 

 measure objective accuracy. 



Curves are subjoined showing the distri- 

 bution of the estimates. The residuals are 

 divided into classes of the size of one-half 

 the theoretical probable errors, and the or- 

 di nates represent the percentages of the 

 whole number of observations falling with- 

 in each class. 



The curves approach the bell-shape re- 

 quired by the theory of probabilities, but 

 not very closely. The departures are 

 partly due to the limited number of obser- 

 vations (56 in each case), and the ten- 

 dency to estimate in round numbers; in esti- 

 mating time Y of the estimates were i, 1 or 

 2 minutes. But there is a large constant 

 error, and in addition there is an excess of 

 large positive errors which makes the aver- 

 age in all cases larger than the median. 

 This tendency obtains in nearly all varia- 

 tions and measurements and has not re- 

 ceived the attention it deserves. The aver- 



300 (,00 900 



M/e(3lit en ouncts Dhtaince. in feet 



Fig 1. The distribution of errors in estimating weight, distance and time. 





