A Simulation Study on the Sample Size in the Mann‑Whitney Test in the Case of Pareto Distribution

Abstract

In the paper, the problem of determination of the number of observations necessary for the appropriate use of the non‑parametric Mann‑Whitney test in the case of Pareto distribution is presented. Using the method provided by Noether, the sample size is calculated which guarantees that the Mann‑Whitney U test at a given significance level α has the pre‑assumed power 1 –β. The presented method is examined by calculating empirical power in computer simulations. Moreover, different techniques of rounding the estimated sample size to an even integer number are studied. It is important when two equinumerous samples are to be compared.

Keywords

• test Manna‑Whitneya
• rozmiar próby
• moc testu
• moc empiryczna
• rozkład Pareto
• metoda Noethera