An evaluation of parametric and non‐parametric tests on modified and non‐modified data

A number of studies have questioned the robustness of the parametric F ratio to assumption violation and have recommended alternative procedures. These procedures differ in terms of whether they are parametric or non-parametric, and whether they involve data modification or not. The present study compares Type I error rates and power of these approaches when they are calculated on data from a common mixed normal distribution. The tests investigated are F (parametric test, without data modification), Fm (parametric test, with data modification), Approximate randomization test (non-parametric test, without data modification), and Mann–Whitney U (non-parametric test, with data modification). Contrary to a previous study, the approximate randomization approach did not show good power characteristics. The Fm test and the Mann–Whitney U did show good power, with the former outperforming the latter.