The efficiency comparison of test for differences among several population means under heterogeneity of variances

摘要

The purpose of this study is to compare the efficiency of the statistical tests for testing differences among several population means under heterogeneity of variances. Heteroscedastic analysis of means test (HANOM), analysis of mean test (ANOM), Welch test, Brown-Forsythe test and Analysis of variance F-test (ANOVA-F) under 3 and 5 group means are investigated. The distributions of considered population are normal, beta, t and chisquare. The methods are compared by considering the ability to control the type I error rate and empirical power. The test is based on 0.05 levels of significance. In case of the under 3 group and 5 group means, HANOM test can control type I error rate. HANOM, ANOM, Welch test, Brown-Forsythe test and ANOVA-F exhibit highest empirical powers. However, Welch test has lower empirical power test of normal distribution and beta distribution for all sample sizes in case the number of treatment groups is 5 (k=5).