Bülent ALTUNKAYNAK, Hamza GAMGAM, Merve BAGCACI

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

In this study, a distribution free new statistic is introduced to test the equality of locationsagainst the umbrella alternative hypotheses. The Shan test known for the orderedalternatives hypotheses is arranged for the umbrella alternative hypotheses. This statisticcan be considered as an extension of the sign and Mann-Whitney statistics. Using acomprehensive simulation design, the proposed test was compared with theHettmansperger and Norton and, Mack-Wolfe tests according to the criteria of the powerand type I error rate of the test. In the simulation outcomes, it was seen that the robustnesscondition for Bradley's type I error rate were ensured for all tests. The power comparisonoutcomes also showed that the proposed test is more powerful than the other tests.

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