A New Nonparametric Test for Testing Equality of Locations Against Umbrella Alternatives

Abstract

In this study, a distribution free new statistic is introduced to test the equality of locations against the umbrella alternative hypotheses. The Shan test known for the ordered alternatives hypotheses is arranged for the umbrella alternative hypotheses. This statistic can be considered as an extension of the sign and Mann-Whitney statistics. Using a comprehensive simulation design, the proposed test was compared with the Hettmansperger and Norton and, Mack-Wolfe tests according to the criteria of the power and type I error rate of the test. In the simulation outcomes, it was seen that the robustness condition for Bradley's type I error rate were ensured for all tests. The power comparison outcomes also showed that the proposed test is more powerful than the other tests.

Keywords

• Nonparametric statistics,Umbrella alternative,Monte Carlo Simulation

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