Robustness to non-normality of common tests for the many-sample location problem

Abstract

This paper studies the effect of deviating from the normal distribution assumption when considering the power of two many-sample location test procedures: ANOVA (parametric) and Kruskal-Wallis (non-parametric). Power functions for these tests under various conditions are produced using simulation, where the simulated data are produced using MacGillivray and Cannon's [10] recently suggested g-and-k distribution. This distribution can provide data with selected amounts of skewness and kurtosis by varying two nearly independent parameters.