7-^1:4 EXPERIMENT STATION RECOED. [Vol. 38 



ing to the varying productivity of fruit trees, together wltti studies dealing 

 with errors in field trials, are reviewed, and a bibliography of cited literature 

 is appended. 



The results of this investigation, which are presented in a series of tables and 

 fully discussed, are summarized as follows : " Studies have been made upon the 

 variability of the yields of orange, lemon, apple, and walnut trees. The 

 orchards studied were selected on account of uniformity of treatment and ap- 

 pearance, 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 coefficient was somewhat higher, reaching 53.91±1.92 per cent. The varia- 

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

 bility may be assumed to be the result of ' casual ' factors which are beyond the 

 control and possibly the recognition of a careful experimenter. 



" The effect upon variability of combining trees into plats of various sizes 

 and shapes has been investigated. As the number of trees per plat is increased, 

 the coefficient of variability decreases. The coefficient of variability does not 

 decrease, however, in proportion to the increased number of trees per plat. In 

 most cases there is little gained in accuracy by increasing the plat to include 

 more than eight adjacent trees. 



" One of the great causes of variability in yields appears to be the hetero- 

 geneity of apparently uniform soil. While a combination of a sufficient number 

 of adjacent trees into a plat will overcome largely the fluctuations of individ- 

 uals, nevertheless the plats 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 distribution of plats 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 variability for an average plat of 16 adjacent trees was 

 22.58±1.01, while 16 trees in 4 scattered ultimate plats each of 4 ti*ees have 

 a coefficient of variability of .9.29it0.4. The larger the number of units in a 

 combination plat the more typical is the sample of the area obtained. A 16-tree 

 plat can be expected to give more reliable results if divided into four equal plats 

 and repeated at four regularly placed intervals than can either two 8-tree 

 plats, or 16 adjacent trees. The same principle holds true for larger units. A 

 given number of unit plats wiU give a greater accuracy than half the number of 

 units vsdth twice as many trees per unit 



" Four repetitions of an ultimate plat reduced the coefficient of variability to 

 a point considered practical for cultural operations. Farther repetitious, 

 though reducing the coefficient In less degree, did not appear to justify the ad- 

 ditional number of trees required. A minimum of 8 to 10 trees is required for 

 plats involving cultm-al experiments. In case of rootstock, pruning, or variety 

 trials, twice as many plats each containing 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 plats yield aUke, even on soUs which were chosen because of 

 their apparent uniformity, is well shown by applying the formula proposed by 

 Harris [E. S. R., 33, p. 727] for measuring the coefficient of correlation between 

 neighboring plats of the field. Applying this to the Arlington navel oranges, the 

 writers have calculated the correlation between the yield of the 8-tree plat as 

 the ultimate unit and the yield of the combination of four such adjacent plats, 

 and it was found that 



r=+0.533±0.0S5. 



