30 



CIRCULAR NO. 109, BUREAU OF PLANT INDUSTRY. 



Table I contains the probable error determinations made on five 

 groups of plats, one group at Scotts bluff, Nebr., and four at Huntley, 

 Mont., together with some other data associated with the probable 

 error in each case. Explanations of the various items are given after 

 the table under the respective numbers of the items. 



Table I. — Probable error determinations made on five groups of field plats at the Scotts- 



bluff and Huntley experiment farms . 



Items. 



1. Mean yield (groupsA,B,D,andEln pounds: group 



C in tons per acre) 



„ /Number of plats yielding above the mean 



\ Number of plats yielding below the mean 



3. Extreme range of plat yields, expressed in percent- 



age of mean yield of each group 



4. Mean deviation of plat yields, expressed in per- 



centage of mean yield of each group 



5. Probable error of asingle result expressed in terms 



of yield 



6. Probable error, expressed in percentage of mean 



yield of each group: 



a Of any single result 



6 Of the average of 10 results 



c Of the average of 20 results 



d Of the average of 30 results 



e Of the average of 40 results 



/Of the average of 46 results 



a Of the average of 66 results 



ft Of the average of 68 results 



7. Number of plat yields differing from mean: 



a By less than the probable error — 



Actual 



Theoretical 



6 By more than the probable error- 

 Actual 



Theoretical 



c By less than twice the probable error 



d By more than twice the probable error 



« By more than three times the probable error. 



/ By more than four times the probable error. . 



Groups. 



A. 



66 plats 



oats, 



Scotts- 



blufffleld 



K, 1911. 



287 

 35 

 31 



55.7 



9.8 



±23.9 



8.3 



2.6 

 1.9 

 1.5 

 1.3 

 1.2 

 1.0 



29 

 33 



37 

 33 



56 



10 



4 







B. 



68 plats 



oats, 



Huntley 



field K, 



1911. 



554 

 37 

 31 



106.0 



22.5 



±105.95 



19.1 



6.0 



4.3 



3.5 



3.0 



2.8 



2.34 



2.31 



26 

 34 



42 

 34 



63 

 5 

 

 



C 



46 plats 



beets, 



Huntley 



fields B II 



and Bill, 



1911. 



D. 



46 plats 



alfalfa, 



Huntley 



fields B II 



and B III, 



1912. 



11.71 



29 



17 



67.9 



12.9 



± 1.29 



±11.0 



3.5 

 2.4 

 2.0 

 1.7 

 1.6 



25 

 23 



21 

 23 



38 



8 

 4 

 



356 

 23 

 23 



52.5 



12.5 

 ±38.18 



±10.7 



3.4 

 2.4 

 1.9 

 1.7 

 1.6 



19 

 23 



27 

 23 



38 

 8 

 

 



E. 



10 plats 



alfalfa, 



Huntley 



field A II, 



1912. 



572 

 5 

 5 



51.5 



9.6 



±49.27 



± 8.6 



±2.7 



6 

 5 



4 

 ."> 

 7 

 3 

 1 

 



(1) The mean yield of each group of plats is expressed in pounds per plat, except 

 in the case of group C, where, for convenience, it is expressed as tons per acre. 



(2) This item is given to show how closely the plat yields in the different groups 

 agree with the assumption that approximately one-half the results will exceed the 

 mean. It is shown that in groups D and E the division is exactly equal; in A it is 

 very close, and in B and C it is rather noticeably unequal. It should be stated that 

 in group C, 7 of the 46 plats were spring plowed and the others fall plowed in prepara- 

 tion for beets. To this extent the treatment of the plats in group C was not uniform. 

 The mean yield of the 7 spring-plowed plats was 0.83 ton per acre less than the mean 

 yield of all 46 plats. The discrepancy introduces an error into the calculations, 

 but it has only a very slight effect on the probable error. 



(3) The extreme range in the yields obtained in each group is stated as a percentage 

 of the mean yield of each group so as to facilitate comparisons among the groups. 

 The extreme range in the plat yields at Scottsbluff was from 372 to 212 pounds per 



[Cir. 109] 



