Parametric and Nonparametric Multiple Comparisons in Repeated Measures
Abstract
Many experiments in psychology, biology, medicine, etc., result in repeated measures data, i.e., multiple dependent observations over time. Researchers in these fields are often interested in reporting effect sizes; however, there currently is not a one-step procedure to deal with such a scenario. We achieve this through an application of the multivariate delta method, which enables us to derive an effect size generalization of the General Parametric Model (GPM) of Hothorn et al. (2008) which we refer to as the General Parametric Model with Effect Size (GPM-ES). We then utilize the GPM-ES framework to develop a one-step multiple contrast test procedure (MCTP). We demonstrate these methods by working out a real-world example with boys' dental growth data, and discuss how this framework can be applied to the nonparametric multiple comparisons -- extending the work of Noguchi et al. (2020) to the case of repeated measures data.