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On non‐parametric and generalized tests for the two‐sample problem with location and scale change alternatives
Author(s) -
Podgor Marvin J.,
Gastwirth Joseph L.
Publication year - 1994
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780130535
Subject(s) - parametric statistics , robustness (evolution) , sample size determination , mathematics , type i and type ii errors , statistics , statistical hypothesis testing , semiparametric model , parametric model , rank (graph theory) , scale (ratio) , computer science , econometrics , combinatorics , biochemistry , chemistry , gene , physics , quantum mechanics
Various tests have been proposed for the two‐sample problem when the alternative is more general than a simple shift in location: non‐parametric tests; O'Brien's generalized t and rank sum tests; and other tests related to the t. We show that the generalized tests are directly related to non‐parametric tests proposed by Lepage. As a result, we obtain a wider, more flexible class of O'Brien‐type procedures which inherit the level robustness property of non‐parametric tests. We have also computed the tests' empirical sizes and powers under several models. The non‐parametric procedures and the related O'Brien‐type tests are valid and yield good power in the settings investigated. They are preferable to the t ‐test and related procedures whose type I errors differ noticeably from nominal size for skewed and long‐tailed distributions.