Factors affecting experimental error in field plot tests with corn

Bryan, Arthur A.
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1. Data are presented showing the variability among the yields of 2,304 hills of each of three commonly-grown strains of yellow dent corn. The variability among the mean yields of different numbers of randomly drawn perfect-stand hills decreased in close agreement with theoretical expectancy, as the number of hills increased to a total of 192. The reduction was rather small, however, after 48 hills were drawn so that this number may be considered about sufficient to represent a variety.

2. In a comparison of open-pollinated varieties and crosses of inbred lines equal degrees of precision were attained with about one-half as many plants or hills of crosses as of open-pollinated varieties.

3. The variability of plot yields decreased as the size of plot increased from 8 to 16, to 24 and to 48 hills, but the decrease was not proportional to the size of plot. The experimental error for a given area, therefore, would be lower with larger numbers of smaller plots.

4. Variability among the means of dummy "varieties" decreased as the number of hills devoted to a "variety" increased from 96 to 144 and to 192. The decrease in variability was in close agreement with theoretical expectancy when the effect of correlated variation was considered.

5. The results agree with those of other investigations in that single-row (long, narrow) plots had a lower experimental error than plots of the same size but more nearly square. Shape was less important with smaller plots.

6. Correlation among the plots within replications was relatively large only when the number of "varieties" was relatively small. Maximum correlations were obtained in two experiments with 32 single-row plots in a replication. In the third experiment about equal correlations were obtained with 24, 32 and 48 single-row plots in a replication. Correlations within 4 and 6-row groups of plots such as would be used with the moving average method were markedly higher than the above. The variation that can be eliminated by analysis is restricted to that between replications. Analysis of variance, therefore, will be the most efficient when only a few items are being compared. Some of the variation within replications can be eliminated by adjusting to regression on a moving average.

7. The significance of differences approximating 7.6, 8.9 and 9.9 percent of the mean was determined with 18 8-hill, nine 16- hill and six 24-hill plots, respectively. Although the significance was not shown in every comparison of plot sizes or numbers of replications, the tendency was toward the greater efficiency of the smaller plot and toward a reduction in the estimated variance in fairly good agreement with theoretical expectancy as the, number of replications was increased.