Is It Really Robust? Reinvestigating the Robustness of ANOVA Against Violations of the Normal Distribution Assumption

Empirical evidence to the robustness of the analysis of variance (ANOVA) concerning violation of the normality assumption is presented by means of Monte Carlo methods. High-quality samples underlying normally, rectangularly, and exponentially distributed basic populations are created by drawing samples which consist of random numbers from respective generators, checking their goodness of fit, and allowing only the best 10% to take part in the investigation. A one-way fixed-effect design with three groups of 25 values each is chosen. Effect-sizes are implemented in the samples and varied over a broad range. Comparing the outcomes of the ANOVA calculations for the different types of distributions, gives reason to regard the ANOVA as robust. Both, the empirical type I error a and the empirical type II error beta remain constant under violation. Moreover, regression analysis identifies the factor type of distribution'' as not significant in explanation of the ANOVA results.