INTERPRETING THE VARIATION OF PLAT YIELDS. 29 



The 66 plats at Scottsbluff are not a sufficient number to form a 

 "perfect" series, where the variations are so great, but they afford an 

 opportunity of calculating the probable error with sufficient accuracy 

 for practical purposes. The mean yield of the 66 plats is 287 pounds 

 and the probable error of any single result is found to be ±23.9 

 pounds, or 8.3 per cent of the mean yield. This is equivalent to 3 

 bushels per acre. According to the above definition of probable, error, 

 33 plats should yield within 23.9 pounds of the mean, and the yield of 

 the other 33 plats should vary from the mean by more than 23.9 

 pounds. It was actually found that 29 plats varied from the mean by 

 less than the probable error and 37 varied by more. While those 

 numbers 29 and 37 are not equal, they are as close as can be expected 

 in a series of only 66 observations and close, enough for practical 

 purposes. 



The specific application of these determinations to field experiments 

 is this: In a series of plats planted to a single crop and given uniform 

 treatment marked variations may occur and from these variations 

 the probable error may be determined. If, then, in the same series of 

 plats later planted to a single crop and given different treatments, the 

 variations in yield do not exceed the probable error as previously 

 determined, these variations can not properly be attributed to the 

 effects of the treatments and they should not be considered as sig- 

 nificant. In other words, the probable error may be employed as a 

 measure of the confidence which can safely be placed in experimental 

 results. The more a variation, supposedly due to a treatment, ex- 

 ceeds the probable error the greater the. confidence which can properly 

 be placed in the supposition that the treatment is responsible for the 

 variation. If a variation is greater than twice the probable error, its 

 significanee is very materially increased, antl if it is so large as to 

 exceed three, four, or five times the probable error, its significance 

 approaches a practical certainty. 



In the series of plats at Scottsbluff only ten plat yields Varied from 

 the mean by more than twice the probable, error, and only four varied 

 by more than three times the probable error. There were no vari- 

 ations from the mean equal to four times the probable error. In 

 other words, to have obtained a variation equal to four times the 

 probable error it would have been necessary to introduce, a variation 

 in the treatment. If under this different treatment a variation in 

 yield greater than four times the probable, error were obtained, it 

 would be a practical certainty that the variation was due to the 

 treatment. But any variation less than this would be subject to the 

 suspicion that it might be due to accidental errors, such as soil irregu- 

 larity, etc., rather than to treatment, and the suspicion would increase 

 as the size of the variation decreased. 



[Cir. 109] 



