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



These figures show that there is less error in this case by the use of 

 formulas (2) and (4) and that there was very little difiference between 

 these two. 



This question of a "normal" yield of a plot depends obviously upon 

 the portion of the population chosen as a standard and upon the method 

 of calculation. Investigators differ in the choice of both of these factors. 



An illustration may be given to show the results of calculating the 

 normal from different standards. The coefficient of variability of the 

 lo-tree plot of Arlington navel oranges was computed, taking the devia- 

 tions from (a) the mean of all plots, (b) the mean of all control plots, 

 and (c) the "normal" calculated by formula 2. The results are shown 

 in Table XIII. 



TabIvE XIII. — Deviation of yields from mean of area compared with deviation from lo-iree 



linear control plot 



Since no differential treatments had been given these plots, the mean 

 of all plots differs little from the mean of all control plots, the respective 

 means being 1,376 and 1,367 pounds. The variability of plots calcu- 

 lated from these two standards is not significantly different. In the 

 case of the deviation taken from the normal yield, however, there is a 

 very significant decrease in variability, since there are discontinuous soil 

 variations not recognizable in the general average of the area which are 

 taken into account by this formula. 



CHANCE ARRANGEMENT OF CONTROL PLOTS 



A weakness of this system of comparison with interpolated plots lies 

 in the possibility that the series of control plots may not be representa- 

 tive of the area. The plots chosen for controls may be on soil superior 

 or inferior to that of the intervening plots. There are indications that 

 this possibility may be more real than one would expect from purely 

 random sampling. 



A few computations will show the extent to which the different methods 

 of choosing control plots may affect the results. The Arlington grove 

 records were recomputed, shifting the control plots back one row. The 

 yield of the first control plot (see Table XI) was 1,051 pounds instead of 

 800, and the last was 1,160 instead of 1,520 pounds. The first arrange- 

 ment will be termed "arrangement A," the second "arrangement B." 

 The mean yield of all control plots is not greatly changed by the different 



