Modified Welch test statistic for ANOVA under Weibull distribution

Abstract

A modification to Welch test statistic is proposed to test the equality of population means of various groups under a Weibull distribution. The proposed test statistic is simple and corresponds to the standard Welch test statistic in which the maximum likelihood mean and variance estimators are replaced with robust estimators based on quantile, quantile least square and repeated median. The influence function and breakdown point of these robust estimators are obtained to show their robustness properties. In the simulation study, various experimental designs are considered to evaluate the performance of proposed modified Welch classical ANOVA tests in terms of the type I-errors studies via simulation study.