14 BULLETIN 529, U. S. DEPARTMENT OF AGRICULTURE. 



Suppose the actual average for summer fallowed land, as determined 

 by the average of an indefinitely large number of trials extending 

 over a series of years sufficient to give average climatic effects, is 30 

 bushels per acre and that in a particular experiment it is 20 bushels. 

 Xow there is in this latter figure an inherent error of 10 bushels, and 

 this error can not be eliminated by any degree of accuracy in measur- 

 ing the 20-bushel yield. The only way to eliminate errors of this 

 kind is to get enough observations to allow the law of averages to 

 operate on them; that is, to insure the elimination of errors in one 

 direction by the occurrence of similar errors in the opposite direc- 

 tion. 



The relatively small importance of accuracy in the items to be 

 averaged as compared with the great importance of the number of 

 these items is well illustrated by the following facts concerning rain- 

 fall at Penn Yan, N. Y. The annual precipitation at this station has 

 been measured to the hundredth of an inch each year for a period of 

 60 years. The average of the 60 annual records is 29.113 inches. If 

 instead of the actual rainfall for each year we use the nearest multi- 

 ple of 10, thus recording 26.73 as 30, 23.87 as 20, and so on, we get an 

 average of 28.667, which is in error 1.532 per cent, assuming 29.113 

 inches to be the true average. If now we divide the 60-year period 

 into six periods of 10 years each, using the measurements to the hun- 

 dredth of an inch, the averages of these six periods are in error to 

 the extent of 3.24, 7.51, 2.95, 7.24, 2.94, and 3.52 per cent, respectively. 

 That is, the 60-year average based on measurements made to the 

 nearest multiple of 10 inches is more accurate than any one of the 

 10-year averages based on the most accurate measurements. 



It is not intended here to convey the impression that accuracy in 

 original data is a matter of small importance. Such accuracy is im- 

 portant. The main point to be made is that numbers of items to 

 be averaged is still more important. Our studies lead to the con- 

 clusion that errors in the farmer's knowledge of the details of 

 his business and of the work he does are in every way comparable 

 to the departures from the true mean in field plot experimental 

 work and that they distribute themselves about the true values in 

 approximately the same manner. The fact that the survey method 

 of investigation gives data sufficient to permit the law of averages 

 to eliminate plus errors by the occurrence of similar minus errors 

 while plot experiments ordinarily do not do this appears to justify 

 the statement that the survey method is a more reliable means of 

 arriving at those facts to which it is applicable than the field plot 

 experimental method. It appears, in fact, to occupy a place inter- 

 mediate between plot experiments on the one hand, where variations 



