A note on consistency of non-parametric rank tests and related rank transformations

The extent to which rank transformations result in the same statistical decisions as their non-parametric counterparts is investigated. Simulations are presented using the Wilcoxon–Mann–Whitney test, the Wilcoxon signed-rank test and the Kruskal–Wallis test, together with the rank transformations and t and F tests corresponding to each of those non-parametric methods. In addition to Type I errors and power over all simulations, the study examines the consistency of the outcomes of the two methods on each individual sample. The results show how acceptance or rejection of the null hypothesis and differences in p-values of the test statistics depend in a regular and predictable way on sample size, significance level, and differences between means, for normal and various non-normal distributions.