Feb.4,i9i8 Variability of Yields of Fruit Trees and Field Trials 281 



navel oranges, the writers have calculated the correlation between the 

 yield of the 8-tree plot as the ultimate unit and the yield of the com- 

 bination of four such adjacent plots, and it was found that 



r= +0.533 ±0.085. 



This result shows a marked correlation, indicating a pronounced 

 heterogeneity in the soil of this grove influencing fruit production. 



However, when the correlation between the 8-tree plot as the ultimate 

 unit and the yield of the combination of four such systematically scattered 

 plots was calculated it was found that 



r= +o.i37±o.i20. 



This coefficient is practically equal to its probable error and can be 

 regarded as significantly zero. 



(5) In the computations made by the writers emphasis is also laid 

 upon the nature and magnitude of the probable error. It is shown in 

 several cases that the probable error of comparison between plots may be 

 so large that relatively large differences must be evident between treated 

 and untreated plots for a reasonable assurance that it is due to the 

 factors being experimented upon. With the plots of 16 to 32 adjacent 

 trees which were studied, a difference of from 62.94 to 81.97 per cent of 

 the mean production would be necessary in order to obtain chances of 10 

 to I that the results were due to differential treatment and not to casual 

 variation in the productivity of the trees. With the same number of trees 

 in scattered units, a difference of 28.42 to 50.02 per cent would be necessary 

 for the same odds. It seems probable, therefore, that a difference between 

 two tree plots of less than 50 per cent of the mean production should 

 be considered with caution before attributing it to differential treatment. 



(6) The relation between the shape of a plot and its variability was in- 

 vestigated by making comparisons betvveen square plots and linear plots 

 containing the same number of trees. Except in the case of large plots, the 

 difference in the variability of plots of different shapes was insignificant. 



(7) In any method of field experimentation where a standard of com- 

 parison is desired the theoretical or "normal" yield of a plot is a question 

 of importance. By the use of certain formulas the "normal" yield may 

 be computed from control plots. As a standard, one may use the average 

 yields of the control plots of the entire area, or of the nearest control 

 plots, or a combination of the two. In cases studied, the coefficient of 

 variability was reduced 50 per cent by calculating the normal yield from 

 the nearest controls in place of using the mean of the entire area. The 

 employment of every alternate row as a control plot was not sufficient 

 to offset the variability due to soil heterogeneity. 



(8) Computations made on the yields of orange, walnut, and apple 

 trees for several consecutive years showed little annual fluctuation in 

 their variability. One or two crops may not show greater variability 

 than the average of six or seven crops. 



