248 Journal of Agricultural Research voi. xii. No. s 



that the coefficient of variability decreases as the plots are enlarged, but 

 not proportionally to the size of the plot. 



The limitations of field experiments were discussed by Carleton (ic^og), 

 who called the attention of experimenters to the various uses of control 

 plots, and to the general precautions necessary to obtain reliable results. 



Hall {igog), Mercer and Hall (igii), and Hall and Russell (igii) 

 recorded extensive studies of the soil variations in experimental grounds 

 and the influence of size and repetition of plots upon accuracy. This 

 work was done largely with the yields of wheat, mangel, and hay crops. 

 The conclusions from the above work are that the error in field trials 

 diminishes as the size of the plot increases, but that the reduction is 

 small when the plot is enlarged to a size greater than one-fortieth of an 

 acre. The error may be further diminished by increasing the number of 

 plots similarly treated and scattering them about the area under experi- 

 ment; but there is not much to be gained by increasing the number of 

 plots above five. 



Wood and Stratton (igio) sounded notes of caution concerning the 

 interpretation of experimental results. Frequency distribution is dis- 

 cussed from the point of view of its bearing on the reliability of averag- 

 ing results. The applications of the probable-error methods to questions 

 of sampling for analysis, to field experiments, and to feeding experi- 

 ments are illustrated. The probable error of field experiments was 

 investigated by two independent methods and found to be about 5 

 per cent of the mean yield. Tables are given showing the number of 

 duplicate plots or number of animals in a feeding trial which must be 

 employed to give any desired precision in the result. It is shown that 

 more accurate results may be obtained by employing large numbers of 

 small scattered plots than by using one large plot. 



The estimation of errors in field-plot tests has been given consid- 

 erable attention by Lyon {igi2) and coworkers. It was shown that it 

 is not possible to establish a schedule of relative yields for a series of 

 plots, even after several years' comparison. Also, there seems to be 

 little gain by using plots larger than one-fiftieth of an acre in size when 

 the comparative yield of the crops is made the criterion. An area of 

 one-twenty-fifth of an acre of land distributed in four widely separated 

 plots, devoted to any one test, secures a much greater degree of accuracy 

 than the same area of land in one body. The probable error was reduced 

 from 4.5 to 2 per cent by such distribution. 



Pickering (igii), from studies on apples and pears, concluded that 

 experimental plots should include 6 to 12 fruit trees. Precautionary 

 advice was also given concerning the measurement of results b)^ crop 

 production, foliage, and tree characteristics. In comparing the results 

 on the treated plots with the controls, instead of taking the average of 

 the controls, he prefers to plot these results out and to draw a smoothed 



