Abstract
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.
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