Robust ANOVA tests for exponentially distributed data

Abstract

The presence of variance heterogeneity and non-normality many data may frequently invalidate the use of the analysis of variance (ANOVA) F test in one-way independent groups designs. In this study, we consider the violations of the assumptions in the one-way ANOVA. Robust Welch (RW), Brown-Forsythe (RBF) and also Modified Brown-Forsythe (MBF) test statistics for the one-way ANOVA under heteroscedasticity are developed for the non-normal data assumed to have exponential distribution with outliers. In order to get these robust test statistics, robust estimators of mean and variance of exponential distribution are obtained by using robust estimators of this distribution parameter. The influence function and breakdown point of these estimators are obtained to show that these estimators are robust. We consider balanced and unbalanced sample sizes with homogeneous and heterogeneous variances. The simulations results show up that the proposed robust tests have a good performance.