Additive Main Effects and Multiplicative Interaction Analysis Based on Ranks

Additive Main effects and Multiplicative Interaction (AMMI) model is one of the statistical model that depends on normality assumption. That is, the error terms of AMMI model is normally distributed with mean zero and constant variance. However, many of the data used in agricultural screening trials involving AMMI model are non-normal, skewed or heavy-tailed. The application of AMMI to such data may be misleading due to violation of normality assumption. The procedures to address the violation of the normality assumption such as rank methods to AMMI analysis are either not developed or not common in the literature. The purpose of this study is to proposed rank transform procedure for AMMI analysis. The rank transform is carried out by replacing original observations with their ranks and then applies the usual parametric AMMI analysis to the ranks. In this study, the proposed rank method was applied to the seven genotypes of ten New York environments data set. The results indicate that the proposed rank method for AMMI gives similar results as when the raw data were used for analysis on the biplot. The results also show that the tests for testing AMMI multiplicative term give different p-values.