Abstract
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.
Highlights
Analyzing data sets appropriately is of immense importance in any discipline
In production one would like to know which process is more efficient or which product has higher quality, or in ecology one is interested in the overlap of the survival space of two species, just to name some examples
We propose a new and motivated non-parametric test with competitive performance and straightforward interpretation
Summary
Analyzing data sets appropriately is of immense importance in any discipline. Are the numerical characteristics of the individual data sets of interest, but often their distribution in comparison to other data sets. In production one would like to know which process is more efficient or which product has higher quality, or in ecology one is interested in the overlap of the survival space of two species, just to name some examples
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