Modified tests for comparison of group means under heteroskedasticity and non-normality caused by outlier(s)

Creative Commons License

ÇAVUŞ M., YAZICI B., SEZER A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.46, no.3, pp.493-510, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.15672/hjms.2017.417
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.493-510
  • Keywords: Outlier, Heteroskedasticity, Unbalanced, Huber's M-Estimators, Generalized F-test, GENERALIZED P-VALUES, UNEQUAL VARIANCES, ROBUST ANALYSIS, ANOVA, MODELS
  • Anadolu University Affiliated: Yes

Abstract

There are several approximate tests proposed such as Welch's F-test (W), the Parametric Bootstrap Test (PB) and Generalized F-test (GF) for comparing several group means under heteroskedasticity. These tests are powerful and have nominal type 1 error rates but they are not performing satisfactorily under non-normality caused by outlier(s). To handle this problem, we investigate tests that are powerful and provide nominal type 1 error rates by using robust estimators both for location and scale parameters. The performance of the modified tests are examined with Monte-Carlo simulation studies. Results of simulations clearly indicate that Generalized F-test modified with Huber's M-estimators achieves the nominal type 1 error rate and provide higher power than alternative methods.