28o Journal of Agricultural Research voi. xii, no. s 



account of uniformity of treatment and appearance, yet the variability 

 in productivity was considerable. The coefficient of variability for the 

 yield of individual trees of the clonal varieties ranged from 29.27 ±0.69 

 to 41 .23 ± 1 .52 per cent, but for the individual seedling walnuts, the coeffi- 

 cient was somewhat higher, reaching 53.91^:1.92 per cent. The varia- 

 bility of these tree yields approaches the normal curve of errors. This 

 variability may be assumed to be the result of "casual" factors which are 

 beyond the control and possibly the recognition of a careful experimenter. 



(3) The effect upon variability of combining trees into plots of various 

 sizes and shapes has been investigated. As the number of trees per 

 plot is increased, the coefficient of variability decreases. The coeffi- 

 cient of variability does not decrease, however, in proportion to the in- 

 creased number of trees per plot. In most cases there is little gained in 

 accuracy by increasing the plot to include more than eight adjacent trees. 



(4) One of the great causes of variability in yields appears to be the 

 heterogeneity of apparently uniform soil. While a combination of a 

 sufficient number of adjacent trees into a plot will overcome largely the 

 fluctuations of individuals, nevertheless the plots may not sufficiently 

 include both high- and low-yielding areas to give a typical average. 

 Greater reliability may be secured by a systematic repetition and dis- 

 tribution of plots through the experimental area. A consistent gain in 

 reliability resulting from this method of repetition is shown by the use 

 of several different methods of computing the variability. 



The coefficient of variabiHty for an average plot of 16 adjacent trees 

 was 22. 58 ±1.01, while 16 trees in four scattered ultimate plots each of 

 four trees have a coefficient of variability of 9.29^0.40. The larger the 

 number of units in a combination plot the more typical is the sample of 

 the area obtained. A i6-tree plot can be expected to give more reliable 

 results if divided into four equal plots and repeated at four regularly 

 placed intervals than can either two 8-tree plots, or 6 adjacent trees. 

 The same principle holds true for larger units. A given number of unit 

 plots will give a greater accuracy than half the number of units with 

 twice as many trees per unit. 



Four repetitions of an ultimate plot reduced the coefficient of variability 

 to a point considered practical for cultural operations. Further repeti- 

 tions, though reducing the coefficient in less degree, did not appear to 

 justify the additional number of trees required. A minimum of 8 to 10 

 trees is required for plots involving cultural experiments. In the case of 

 rootstock, pruning, or variety trials, twice as many plots each contain- 

 ing half as many trees might be used to obtain greater accuracy. 



The fact that marked soil variations occur which tend to make adjacent 

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

 because of their apparent uniformity, is well shown by applying the 

 formula proposed by Harris {191 5) for measuring the coefficient of correla- 

 tion between neighboring plots of the field. Applying this to the Arlington 



