Contributions to the Analysis of Genotype × Environment Interactions: Comparison of Different Parametric and Non‐parametric Tests for Interactions with Emphasis on Crossover Interactions

The objective of this study was to compare five statistical procedures (analysis of variance, the Azzalini/Cox test, the Hildebrand procedure, the Kubinger approach, and the de Kroon/van der Laan technique) for the analysis of genotype × environment interactions in cross‐classified data sets from cultivar performance yield trials with rows = cultivars and columns = environments (locations and/or years). The procedures Hildebrand, Kubinger and de Kroon/van der Laan are non‐parametric methods based on ranks, while analysis of variance and the Azzalini/Cox test proceed from the original absolute yield data. These very different statistical techniques were applied to extensive data sets from German official registration trials (1985–1989) with winter oilseed rape (Brassica napusL.), faba bean (Vicia fabaL.), oat (Avena sativaL.), fodder beet (Beta vulgarisL.) and sugar beet (Beta vulgarisL.). The Azzalini/Cox and de Kroon/van der Laan methods are based on the crossover concept of interaction (different rank orders) while the other methods are based on the usual concept of interaction (deviations from additivity of main effects). For an analysis of usual interactions the procedures Hildebrand, Kubinger and analysis of variance are approximately equivalent. For the crossover concept of interaction, the Azzalini/Cox approach is recommended, especially if one is particularly interested in rank changes between environments within genotypes.