Feb.4,i9i8 Variability of Yields of Fruit Trees and Field Trials 273 



proportional to their distance from the plot. This would obviously be 

 In the case of a large number of trees, where a linear plot is long 

 enough to include both high- and low-yielding areas in each plot, there 

 appears to be an advantage in favor of the hnear plot. The great advan- 

 tage of the hnear plot in most cases is the economy of cultural operations. 

 Another advantage will be discussed in the following section on the 

 interpolation of control plots. 



A carefully conducted fertilizer experiment with orchard trees requires 

 a guard row between adjacent plots in order to eliminate the possibility 

 of the fertilizer's affecting the margin of the next plot, since there are 

 many observations which show that tree roots extend considerable dis- 

 tances and often reach the lines of adjoining rows (Hedrick, 1914; Ballan- 

 tyne, 1916). It is obvious that it is more reliable to employ guard rows 

 rather than to divide cultural treatments midway between tree rows. 

 The number of guard trees required for square plots is smaller than for 

 a linear plot containing the same number of trees. A 9-tree plot in the 

 form of a square requires 7 guard trees; in the form of a linear plot it ■ 

 requires 1 1 guard trees. In the former case seven-sixteenths of all trees 

 are in the guard rows, in the latter eleven-twentieths. As the size of the 

 plot increases, the difference becomes greater. It thus becomes a ques- 

 tion of the extent to which one is willing to go in enlarging the size of the 

 linear plot before the increase in the number of trees in guard rows offsets 

 the economy in cultural operations thus obtained. 



USE OF CONTROL PLOTS 

 INTERPOLATED CONTROL PLOT 



Agronomists are in the habit of using every third, fourth, or fifth row 

 or plot in the experimental tract as a standard from which the normal 

 yield of any intervening treated plot may be calculated. The nature of 

 the crops and the cultural methods used commend this system of arrange- 

 ment. 



This method, like others, has its advantages and disadvantages. After 

 the results are obtained there is still a need for a proper method of com- 

 parison. There are several different methods of estimating the ' ' normal ' ' 

 yield of any plot. The "normal" (A^) may be estimated by the formalu 



Q-fQ-f- ...Cn 

 n 



which is simply the mean of all the control plots in the area. If the 

 soil of the area were uniform and all variations in the yield of the controls 

 were purely chance variations, this method would give a satisfactory 

 result. Again N may be estimated from the yields of the two nearest 

 control plots. For example, if every third plot is a control and the ar- 

 rangement is Cj, A, B, Cj, and so on, the normal for A would be 

 yiC^ + y^C^- In this way the yields of the controls receive weights in- 

 versely proportional to their distance from the plot. This would ob- 



