Can Analysis of Variance Be More Significant?

Abstract

Recent widespread criticism of the lack of statistical rigor in science journals has focused attention on the need to improve the standards for statistical design and analysis in research. This study examined the role of analysis of variance (ANOVA) in the context of current concerns regarding the validity and appropriateness of statistics in scientific publications. One objective was to suggest how ANOVA tables can be constructed to enhance the transparency and scientific integrity of scientific journals and better assist the interpretation of data. The broader goal of this study was to generate new discussion, debate, and ideas regarding ANOVA. The history and current status of ANOVA as the context for assessing the practical and statistical relevance of ANOVA tables for students, authors, reviewers, editors, and readers of scientific journals is discussed. Each component of an ANOVA table (sources of variation, degrees of freedom, sums of squares, mean squares, F values, and P values) is critiqued for its information and value. Using a criterion of including the components that provide essential information on key details of the experimental design and validating the appropriateness of the analysis, guidelines are provided for constructing an ANOVA table that is SIMPLE—Simple, Informative, Meaningful, Powerful, Logical, and Effective. A prototype SIMPLE ANOVA table is presented to encourage further consideration and debate regarding best practices for ANOVA tables.