Estimating Spatial Variation in Analysis of Data from Yield Trials: A Comparison of Methods

In large yield trials, variation in soil fertility (or, more generally, yield potential) can result in substantial heterogeneity within blocks and, thus, poor precision in treatment estimates. Precision may be improved using statistical analyses in which this spatial variation is accounted for in estimation of treatment or entry means. Three such types of spatial analysis are trend analysis, the Papadakis method, and analyses based on correlated errors models (which account for spatial variation through correlations between yields of neighboring plots). We reviewed the theory and empirical performance of these spatial analyses and compared them with the classical analyses. The classical analyses can be justified solely on the basis of randomization; spatial analyses depend on the model specified for the variation in yield potential. Performance depends on the polynomial used to describe yield potential in trend analysis, on the neighboring plots used to estimate fertility in the Papadakis analysis, and on the correlation structure in the correlated errors models. Empirical comparisons were based on data from 11 corn ( Zea mays L.) yield trials and 1 soybean ( Glycine max L.) trial, each showing evidence of heterogeneity within blocks. In comparison with the classical randomized blocks analysis, precision tended to be best for the trend and the trend plus correlated errors analyses, with the Papadakis method intermediate. Ranking of entries differed across analyses, because each analysis adjusts for spatial variation in a different way. Using a spatial analysis technique can improve precision, but selecting the most appropriate analysis for a given data set can be hard.