Robust Post-Hoc Multiple Comparisons: Skew t Distributed Error Terms

Abstract

The pairwise comparisons or post-hoc methods are used for determining the source of the difference of group means in one-way ANOVA. These methods are mostly depend on normality assumption. However, nonnormal distributions are more prevalent than normal distribution. Therefore, robust estimation methods become very important tools in statistical analysis. In this paper, we assume that the distribution of the error terms is Azzalini's skew $t$ and obtain the robust estimators in order to make post-hoc tests in one-way ANOVA. We use maximum likelihood (ML) methodology and compare this methodology with some of robust estimators like M estimator, Wave estimator, trimmed mean and modified maximum likelihood (MML) methodology with Monte Carlo simulation study. Simulation results show that the proposed methodology is more preferable. We also compare power values of the test statistics and conclude that the test statistics based on the ML estimators are more powerful than the test statistics based on other methods.

Teachers' Perception of Artificial Intelligence Integration in Learning: A Cross-Sectional Online Questionnaire Survey

“…ANOVA was chosen because it is able to compare means between groups to detect signi cant differences in the dependent variable (Kara, 2023; T. K. Kim, 2017). Teaching experience categories include < 5 years, 5-10 years, > 10 years, while age categories include < 35 years, 35-50 years, > 50 years.Post hoc tests were conducted when ANOVA showed signi cant differences in order to identify different groups (Celik, 2022). The study paid attention to ethics by implementing voluntary participation, data con dentiality, and minimizing risks (Ajemba & Arene, 2022).…”