Testing for equality of distributions using the concept of (niche) overlap

In this paper, we propose a new non-parametric test for equality of distributions. The test is based on the recently introduced measure of (niche) overlap and its rank-based estimator. As the estimator makes only one basic assumption on the underlying distribution, namely continuity, the test is universal applicable in contrast to many tests that are restricted to only specific scenarios. By construction, the new test is capable of detecting differences in location and scale. It thus complements the large class of rank-based tests that are constructed based on the non-parametric relative effect. In simulations this new test procedure obtained higher power and lower type I error compared to two common tests in several settings. The new procedure shows overall good performance. Together with its simplicity, this test can be used broadly. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00362-021-01239-y.