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On the W ILCOXON ‐M ANN ‐W HITNEY ‐Test as Nonparametric Analogue and Extension of t ‐Test
Author(s) -
Hilgers R.
Publication year - 1982
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710240102
Subject(s) - extension (predicate logic) , mathematics , estimator , test (biology) , nonparametric statistics , test statistic , distribution (mathematics) , combinatorics , statistics , statistical hypothesis testing , computer science , mathematical analysis , paleontology , biology , programming language
Abstract In the present paper some basic aspects of the W ILCOXON ‐M ANN ‐W HITNEY ‐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 W ILCOXON ‐M ANN ‐W HITNEY ‐test being a test on ‘differences in distribution’ in general is misleading. As an example of an extended application of the W ILCOXON ‐M ANN ‐W HITNEY ‐statistic the test of P OTT‐HOFF (1963) on differences in medians of symmetric distributions is treated together with a discussion on suitable variance estimators to guarantee appropriate asymptotic distribution.