264 Journal of Agricultural Research voi. xii, no. s 



unit and could be expected to give more reliable results if repeated at 

 four regularly-placed intervals than either two 8-tree units, or 16 ad- 

 jacent trees — that is, such a regular scattering of the several units 

 which make up the combination plot reduces the error of the final com- 

 parisons which is caused by the variation in soil productivity. 



The fact that marked soil variations occur which tend to make ad- 

 jacent trees or adjacent plots yield alike, even on soils which were 

 chosen because of their apparent uniformity, is well shown by the work 

 of Harris (19 13). The criterion for the measurement of such variability 

 proposed by this author is the coefficient of correlation between neigh- 

 boring plots of the field.* Applying this to the Arlington 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 combination of 

 four such adjacent plots and it was found that 



r= +0.533 ±0.085. 



This shows a marked correlation, indicating a pronounced hetero- 

 geneity in the soil of this grove, influencing fruit production. 



However, when we calculate the correlation between the 8-tree plot as 

 the ultimate unit and the yield of the combination of four such system- 

 atically scattered plots, it is found that — 



r= -f o.i37±o.i20 



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

 regarded as significantly zero. This is merely another means of calcu- 

 lating the value of scattering a 32-tree plot in four ultimate plots of 8 

 trees each rather than selecting 32 adjacent trees. 



DEGREE OF ACCURACY EXPECTED WITH A PLOT OF A GIVEN SIZE 



Assuming, for example, that experimental plots have been laid out 

 in the navel oranges (Arlington) with a total of 32 trees to the plot in 

 four scattered units of eight trees each, the question might logically be 

 asked, "What differences in the yields of such plots can safely be at- 

 tributed to differential treatment as different methods of irrigation or 

 fertilization, and what may probably be due to mere chance because of 

 soil heterogeneity and the fluctuating variation of the trees?" 



Table IV shows a coefficient of variability of 14.85 ±1.30 in this 

 plantation laid out in 32-tree plots of four scattered units of eight trees 

 each. The probable error,^ then, in this example, that such a plot of 

 32 trees is typical of the area in question, is 14.85X0.6745= ± 10.02 



• The formula used is , 2 



r_ . <[S(C P)-S(P^)]lm[n(n-j)]}-p 



where />== yield of an individual plot; ot= number of larger plots, each made up of n contiguous ultimate 

 units; Cp= yield of the larger combination plots; S= summation of the yields of all the ultimate or com- 

 bination plots of the field. 



* The probable error of a single variant of a population may be defined as that departure from the mean 

 on either side, within which exactly one-half of the variants are found. Expressed as a percentage of 

 the mean, it is determined by multiplying the coefficient of variabihty by 0.6745. 



