Rethinking the Analysis of Non‐Normal Data in Plant and Soil Science

• Published in: Agronomy journal Vol. 107; no. 2; pp. 811 - 827
• Main Author: Stroup, Walter W.
• Format: Journal Article
• Language: English
• Published: The American Society of Agronomy, Inc 01-03-2015
• ISSN: 0002-1962; 1435-0645
• DOI: 10.2134/agronj2013.0342

The introduction of high‐quality, useable generalized linear mixed model (GLMM) software in the mid‐2000s changed the conversation regarding the analysis of non‐normal data from designed experiments. For well over half a century, the reigning paradigm called for using analysis of variance (ANOVA), either assuming approximate normality of the original data or applying a variance‐stabilizing transformation. The appearance of GLMMs creates a dilemma. The ANOVA‐based analyses and GLMM‐based analyses often yield mutually contradictory results. What results should a researcher report, and how should the choice be justified? If GLMM‐based analysis is preferred—and there is increasing evidence that this is the case—approaches to data analysis ingrained while learning ANOVA must be unlearned and relearned. The basic issues associated with the analysis of non‐normal data are reviewed here, the thought processes required for GLMMs and how they differ from traditional ANOVA are introduced, and three examples are presented, giving an overview of GLMM‐based analysis. The three examples include discussions of what is known to date about the relative merits of GLMM‐ and ANOVA‐based analysis of non‐normal data.