A TEST BASED ON THE COMPUTATIONAL APPROACH FOR EQUALITY OF MEANS UNDER THE UNEQUAL VARIANCE ASSUMPTION

GÖKPINAR E., GÖKPINAR F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.41, sa.4, ss.605-613, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 4
  • Basım Tarihi: 2012
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.605-613
  • Anahtar Kelimeler: Brown-Forsythe Test, Computational Approach Test, Generalized F test, Parametric Bootstrap Test, Classic F Test, Welch Test, ANOVA
  • Gazi Üniversitesi Adresli: Evet

Özet

The classical F-test to compare several populations means depends on the assumption of homogeneity of variances of the population and on normality. When these assumptions - especially the equality of variance - is dropped, the classical F-test fails to reject the null hypothesis even if the data actually provide strong evidence for it. This can be considered a serious problem in some applications especially when the sample sizes are not large. To deal with this problem, a number of tests are available in the literature. Recently Pal, Lim and Ling (A computational approach to statistical inferences, J. Appl. Probab. Stat. 2 (1), 13-35, 2007) developed a computational technique, called the Computational Approach Test (CAT), which looks similar to a parametric bootstrap for hypothesis testing. Chang and Pal (A revisit to the Behren-Fisher Problem: Comparison of five test methods, Communications in Statistics - Simulation and Computation 37(6), 1064-1085, 2008) applied CAT to test the equality of two population means when the variances are unknown and arbitrary. In this study we apply a developed CAT to test the equality of k population means when the variances are unequal. Also the Brown-Forsythe, Weerahandi's Generalized F, Parametric Bootstrap and Welch tests are recalled and a simulation study performed to compare these tests according to type one errors and powers in different combinations of parameters and various sample sizes.