Testing the equality of treatment means in one-way ANOVA: Short-tailed symmetric error terms with heterogeneous variances

GÜVEN G.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.51, sa.6, ss.1736-1751, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.1055277
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1736-1751
  • Anahtar Kelimeler: One-way ANOVA, short tailed symmetric distribution, fiducial based test, generalized F test, modified maximum likelihood, Monte Carlo simulation, PARAMETRIC BOOTSTRAP APPROACH, EXPERIMENTAL-DESIGN, UNEQUAL VARIANCES
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

We propose two tests based on fiducial and generalized p -value approaches for testing the equality of treatment means in one-way analysis of variance (ANOVA). Modified maximum likelihood (MML) estimators are used in the proposed tests. In contrast to least squares (LS) estimators, MML estimators are highly efficient and robust to plausible deviations from an assumed distribution and to mild data anomalies. In this study, error terms are assumed to have short-tailed symmetric (STS) distributions with heterogeneous variances. The performances of the proposed tests are compared with the fiducial based test using bias-corrected LS estimators via an extensive Monte Carlo simulation study. Finally, two real datasets are analyzed for illustrative purposes.