28 CIRCULAR NO. 109, BUREAU OP PLANT 'INDUSTRY. 



field A II at Huntley. In each case the plats were harvested sep- 

 arately, and the yields obtained form the basis of the material pre- 

 sented in this paper. 



The results obtained with 66 plats of oats on field K at Scottsbluff 

 in 1911 will serve as an illustration of the method pursued. These 

 plats received uniform treatment throughout the season, so that 

 without a consideration of accidental errors it would be expected that 

 the plat yields would be equal ; or, in other words, it would be expected 

 that the yield of any plat taken at random would fairly represent the 

 yield of any other plat in the field. Such an expectation is, of course, 

 never realized. It was found in the case of the oat plats at Scotts- 

 bluff that the yields varied from 372 pounds to 212 pounds — an 

 extreme range of 160 pounds per plat. This variation is equivalent 

 to 20 bushels per acre, or 55.7 per cent of the mean yield. Where a 

 difference of 20, or even 10 or 5, bushels per acre is obtained from two 

 plats receiving different treatments the difference is commonly con- 

 sidered significant and attributable to the treatments. But it is 

 obvious that a difference of 5 bushels per acre would not have been 

 significant on field K in 1911 if the oat plats had received different 

 treatments. 



It is commonly found that approximately one-half the results 

 observed in a series will be greater than the mean of all the results 

 and that approximately one-half the results will be less than the mean, 

 and also that the number of results differing from the mean will 

 decrease as the magnitude of the difference increases. For example, 

 there are 29 plats in field K which yielded within 24 pounds of the 

 mean yield, while only 10 plats differed from the mean yield by more 

 than 48 pounds. Because of this tendency for the majority of the 

 results to lie relatively close to the mean, the mean is taken as a basis 

 upon which to calculate the probable error. 



In a "perfect" series " The probable error is such that, talcing any 

 single result at random, the chances are even for or against that result 

 differing from the average by the amount of the probable error. In other 

 words, half the results should differ from the mean by less than the 

 probable error, the other half by more." 1 



The probable error is calculated in the following manner: The 

 mean of all the results is determined. This mean is subtracted from 

 each result to obtain the difference, each difference is squared, and 

 the sum of these squares, disregarding the sign, is found. Then the 

 following formula is employed: 



The probable error of a single result= 



P fi7 .r /The sum of the squares of the differences. 

 yThe number of results less 1. 



i Wood and Stratton. Journal of Agricultural Science (Cambridge), v. 3, pt. 4, p. 417. December, 1910. 

 [Cir. 109] 



