On the WILCOXON-MANN-WHITNEY-Test as Nonparametric Analogue and Extension of t-Test

In the present paper some basic aspects of the WILCOXON-MANN-WHITNEY-test under various assumptions concerning the underlying distributions are studied. Starting with a formal analogy to Student's t-test its specific sensibility is worked out and the connexion to the problem of testing differences in location is discussed in detail as well as to the model with ordered alternatives. Further a counter example is given showing that the common verbal formulation the WILCOXON-MANN-WHITNEY-test being a test on ‘differences in distribution’ in general is misleading. As an example of an extended application of the WILCOXON-MANN-WHITNEY-statistic the test of POTT-HOFF (1963) on differences in medians of symmetric distributions is treated together with a discussion on suitable variance estimators to guarantee appropriate asymptotic distribution.

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