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A Robust Test for Multi‐Sample Location Problems with Unequal Group Variances and Nonnormality
Author(s) -
Tabatabai M. A.,
Tan W. Y.
Publication year - 1988
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.4710300303
Subject(s) - statistics , mathematics , test statistic , normality , statistic , estimator , test (biology) , normality test , monte carlo method , z test , f test , f test of equality of variances , statistical hypothesis testing , paleontology , biology
A robust test (to be referred to as M * test) is proposed for testing equality of several group means without assuming normality and equality of variances. This test statistic is obtained by combining Tiku's MML robust procedure with the James statistic. Monte Carlo simulation studies indicate that the M * test is more powerful than the Welch test, the James test, and the tests based on Huber's M ‐estimators over a wide range of nonnormal universes. It is also more powerful than the Brown and Forsythe test under most of nonnormal distributions and has substantially the same power as the Brown and Forsythe test under normal distribution. Comparing with Tan‐Tabatabai test, M * is almost as powerful as Tan‐Tabatabai test.