Statistical Analysis of a Yield Trial

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Abstract
Yield trials frequently have both significant main effects and a significant genotype X environment (GE) interaction. Traditional statistical analyses are not always effective with this data structure: the usual analysis of variance (ANOVA), having a merely additive model, identifies the GE interaction as a source but does not analyze it; principal components analysis (PCA), on the other hand is a multiplicative model and hence contains no sources for additive genotype or environment main effects; and linear regression (LR) analysis is able to effectively analyze interaction terms only where the pattern fits a specific regression model. The consequence of fitting inappropriate statistical models to yield trial data is that the interaction may be declared nonsignificant, although a more appropriate analysis would find agronomically important and statistically significant patterns in the interaction. Therefore, agronomists and plant breeders may fail to perceive important interaction effects. This paper compares the above three traditional models with the additive main effects and multiplicative interaction (AMMI) Model, in an analysis of a soybean [Glycine max (L.) Merr.] yield trial. ANOVA fails to detect a significant interaction component, PCA fails to identify and separate the significant genotype and environment main effects, and LR accounts for only a small portion of the interaction sum of squares. On the other hand, AMMI analysis reveals a highly significant interaction component that has clear agronomic meaning. Since ANOVA, PCA, and LR are sub‐cases of the more complete AMMI model, AMMI offers a more appropriate first statistical analysis of yield trials that may have a genotype X environment interaction. AMMI analysis can then be used to diagnose whether or not a specific sub‐case provides a more appropriate analysis. AMMI has no specific experimental design requirements, except for a two‐way data structure.

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