inequality is satisfied: with t1 − α/2 the (1 − α/2)-quantile of the t-distribution. Comparison with the Kruskal-Wallis test The most common non-parametric test for the one-factor model is the Kruskal-Wallis test. The Kruskal-Wallis test is based on the ranks of the data. The advantage of the Van Der Waerden test is that it provides the high efficiency of the standard ANOVA analysis when the normality assumptions are in fact satisfied, but it also provides the robustness of the Kruskal-Wallis test when the normality assumptions are not satisfied. References van der Waerden, B.L. (1952). "Order tests for the two-sample problem and their power", Indagationes Mathematicae, 14, 453–458. van der Waerden, B.L. (1953). "Order tests for the two-sample problem. II, III", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Serie A, 564, 303–310, 311–316. Statistical tests Nonparametric statistics