Spatial Heterogeneity Affects Variety Trial Interpretation
- Shane T. Ball ,
- David J. Mulla and
- Calvin F. Konzak
Observations in neighboring plots of variety trials are often spatially dependent. This may reduce the utility of applying the classical analysis of variance (ANOVA) due to trends and correlated errors. Identifying the presence, magnitude, and pattern of spatial heterogeneity is useful for assessing the utility of ANOVA. Our objectives were to estimate the effects of spatial heterogeneity on the independence of errors, and appraise a nearest-neighbor analysis (NNA) to improve the analysis of a variety trial experiment. A semivariogram for organic C at one field site showed a substantial soil spatial dependence and was consistent with the semivariogram for residuals in grain yield. Semivariograms of classical residuals for grain yield had large nugget variances and exhibited spatial structure. Similarly, semivariograms of the nonclassical residuals showed large spatial dependence, accounting for 40 to 80% of the sample variance. Genotype effects were not alwaystatistically significant when the raw data were analyzed using ANOVA. The NNA was used to adjust data for the effects of large- and small-scale spatial dependencies in the variety trial experiment. The ANOVA on NNA-adjusted data showed highly significant P ≤ 0.01) genotypic effects. The improved analysis also showed reduced error variance (from 57–78%), and dramatically increased 2 values compared with the ANOVA on unadjusted data. The estimates of variance between genotypes from ANOVA on unadjusted data were from 99% smaller to 63% larger than the error variance. On the other hand, the variance component estimates between genotypes from ANOVA on adjusted data ranged from 0 to 300% larger than the error variance. The spatial heterogeneity can have serious effects on the interpretation of variety trials experiments. In general, nonclassical deviations appear more sensitive to the effects of spatial heterogeneity than classical residuals, and are more useful as a test for violations in the classical assumption of spatial independence.
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