How to Address Non-normality: A Taxonomy of Approaches, Reviewed, and Illustrated - Pek, Jolynn; Wong, Octavia; Wong, Augustine C. M. (Frontiers in Psychology, 2018)
The linear model often serves as a starting point for applying statistics in psychology. Often, formal training beyond the linear model is limited, creating a potential pedagogical gap because of the pervasiveness of data non-normality. We reviewed 61 recently published undergraduate and graduate textbooks on introductory statistics and the linear model, focusing on their treatment of non-normality. This review identified at least eight distinct methods suggested to address non-normality, which we organize into a new taxonomy according to whether the approach: (a) remains within the linear model, (b) changes the data, and (c) treats normality as informative or as a nuisance. Because textbook coverage of these methods was often cursory, and methodological papers introducing these approaches are usually inaccessible to non-statisticians, this review is designed to be the happy medium. For the purpose of promoting best practice in the application of the linear model, we provide a relatively non-technical review of advanced methods which can address non-normality. We also present three empirical examples to highlight distinctions between these methods' motivations and results. It is anticipated that our taxonomy will provide a useful overview and starting place for researchers interested in extending their knowledge in approaches developed to address non-normality from the perspective of the linear model.