Robust Post-Hoc Multiple Comparisons: Skew t Distributed Error Terms Compararciones múltiples a posteriori robustas con errores siguendo una t-student sesgada

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Celik N.

Revista Colombiana de Estadistica, vol.45, no.2, pp.363-372, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15446/rce.v45n2.100837
  • Journal Name: Revista Colombiana de Estadistica
  • Journal Indexes: Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.363-372
  • Keywords: One-way ANOVA, Post-Hoc Comparison, Robustness, Skew t distribution
  • Kocaeli University Affiliated: No

Abstract

© 2022, Universidad Nacional de Colombia. All rights reserved.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.