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.