Analysis and interpretation of interactions in agricultural research

Abstract

When reporting on well-conducted research, a characteristic of a complete and proper manuscript is one that includes analyses and interpretations of all interactions. Our purpose is to show how to analyze and interpret interactions in agronomy and breeding research by means of three data sets comprising random and fixed effects. Experiment 1 tested wheat (Triticum aestivum L.) at two N and four P fertilizer rates in two soil types. For this data set, we used a fixed-effect linear model with the highest order (three-way) interaction considered first and then worked down through the lower order interactions and main effects to illustrate the importance of interactions in data analysis. Experiment 2 evaluated maize (Zea mays L.) hybrids under four rates of N for 3 yr. For this data set, we used a linear mixed model and partitioned the four N rates into orthogonal polynomials. Experiment 3 evaluated genotypes in six environments where the objective was to show how to study genotype × environment interactions. Researchers must analyze all interactions, determine if they are due to changes in rank (crossover) or only to changes in scale, and then judge whether reporting on significant main effects or interactions would best explain the biological responses in their experiments. In an experiment with more than one factor, complete and correct analysis of interactions is essential for reporting and interpreting the research properly.