A Likelihood Ratio Test for the Nonparametric Behrens-Fisher Problem

✍ Scribed by James F. Troendle

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 97 KB
• Volume: 44
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/1521-4036(200210)44:7<813::aid-bimj813>3.0.co;2-a

✦ Synopsis

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.