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The powers of several two-sample tests are compared by simulation for small samples from exponential and Weibull distributions with and without censoring. The tests considered include the F test, a modification for samples that are from Weibull distributions, Cox's test, Peto & Peto's log rank test, their generalized Wilcoxon test, a modified log rank test, and a generalized Wilcoxon test of Gehan. When samples are from exponential distributions, with or without censoring, the F test is the most powerful followed by two general groupings of tests: first the three non-Wilcoxon tests and then the two Wilcoxon tests. There is little difference in the power characteristics of the tests within each grouping. Estimates of the asymptotic relative efficiencies of the various tests relative to F are obtained from the normal probability plots of the power curves. When the samples are taken from Weibull distributions with constant hazard ratio, the F test is not robust and a modification is used. The results for this case are essentially the same as in the case of exponential distributions, with the modified F test as the most powerful. However, when the hazard ratio is nonconstant, the two generalizations of the Wilcoxon test have more power than the other tests.
Lee et al. (Fri,) studied this question.