Analysis of combined experiments revisited

Abstract

Agronomic experiments are often replicated over time and space to evaluate how treatments perform across a range of environments. of eanalysis of experiments conducted for more than one growing season (years) and/or places (locations) is commonly referred to as analysis of combined experiments. Common analyses of these studies treat some effects as fixed, treat others as random, and usually include interactions between fixed and random effects, which we call mixed interactions. Recommendations for how to treat mixed interactions has changed. In the traditional practice, the effects of interactions between fixed and random effects were assumed to sum to zero within each level of a fixed factor. Contemporary practice considers these effects to be mutually independent.This latter assumption is used to construct F tests by many of the statistical analysis programs that are widely used to analyze data from agronomic experiments but is inconsistent with that used in many previously published studies. The assumptions made about mixed interactions in the analysis of variance can result in very different interpretations and can potentially lead to different conclusions. We address the discrepancy between the analyses that were formerly recommended and those that are currently implemented by popular software programs and provide recommendations for analyzing data from combined experiments.