Kimihiro Noguchi, PhD

Let us consider a typical set-up where multiple independent samples are compared using various contrasts. We frequently encounter the situation where these samples do not follow typical distributional assumptions such as normality or homoscedasticity. Moreover, these samples may contain outliers or may be unbalanced, making a robust nonparametric multiple comparison procedure highly desirable. To overcome these problems, we discuss a rank-based nonparametric multiple contrast testing procedure and its modification which accommodates different effect size measures. Specifically, we start by describing relative effects and how their log-odds type transformation leads to effect sizes analogous to Cohen’s d for easier interpretation. Then, we propose a testing procedure which accommodates the transformation so that simultaneous confidence intervals directly corresponding to the effect sizes can be easily constructed. Finally, we examine its robustness via a simulation study and illustrate its real-life application with an example from a neuropsychological study.