Date of Award

Fall 2023

Document Type

Open Access Dissertation

Department

Psychology

First Advisor

Michael Seaman

Abstract

The most common parametric procedure used to test main and interaction effects in the two- or more-groups factorial design is the analysis of variance (ANOVA) F test. Researchers in the behavioral and social sciences fields require statistical methods that are robust in the presence of deviations from the common parametric ANOVA assumptions of (a) normality, (b) homogeneity of variances among groups, and (c) independence of observations. When there is concern that the parametric assumptions are violated, nonparametric procedures can be employed that do not make as many initial assumptions about the parent populations. Of particular interest in the two-factor design is the test for interaction among the factors. This paper seeks to contribute to the research of nonparametric methods by exploring the properties of various nonparametric tests in detecting and inferring interaction effects when the population distributions are skewed or asymmetrical. A review of rank-based nonparametric tests for interaction is provided to determine what methods have been proposed to test for interaction and how these methods have performed in comparative research studies. This review includes research findings regarding normal scores to determine the potential of a normal scores transformation when testing for interaction. A comparative study of nonparametric methods that have been shown by past research to provide reasonable power and Type I error control is conducted to determine if these methods also perform well when testing for interaction effects using Monte Carlo simulated data with skewed and asymmetric distributions. A second comparative study explores the performance of three novel nonparametric tests for interaction. These three tests are the rank transform test, aligned rank transform test, and McSweeney test with a Van der Waerden normal scores transformation in place of a rank transformation. For the studied designs, the aligned rank transform test, the aligned rank transform test using normal scores, and the McSweeney test using normal scores provide nonparametric tests of interaction that maintain Type I error rate, are as powerful as the ANOVA F test when the underlying population is normal, and have more power when the underlying population is not normal.

Rights

© 2024, Michael Ethan Hornsby Brown

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