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A Likelihood Ratio Test for the Nonparametric Behrens‐Fisher Problem
Author(s) -
Troendle James F.
Publication year - 2002
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 - 10.1002/1521-4036(200210)44:7<813::aid-bimj813>3.0.co;2-a
Subject(s) - nonparametric statistics , mathematics , statistics , statistical hypothesis testing , exact test , null hypothesis , likelihood ratio test , score test , wilcoxon signed rank test , ratio test , cutoff , mann–whitney u test , physics , quantum mechanics
The nonparametric Behrens‐Fisher hypothesis is the most appropriate null hypothesis for the two‐sample comparison when one does not wish to make restrictive assumptions about possible distributions. In this paper, a numerical approach is described by which the likelihood ratio test can be calculated for the nonparametric Behrens‐Fisher problem. The approach taken here effectively reduces the number of parameters in the score equations to one by using a recursive formula for the remaining parameters. The resulting single dimensional problem can be solved numerically. The power of the likelihood ratio test is compared by simulation to that of a generalized Wilcoxon test of Brunner and Munzel. The tests have similar power for all alternatives considered when a simulated null distribution is used to generate cutoff values for the tests. The methods are illustrated on data on shoulder pain from a clinical trial.