The performance of some two-sample tests in small samples with and without censoring

The power curves of three two-sample tests are compared in small samples from the exponential and four forms of the Weibull distribution with and without censoring. The tests considered are: F ratio, modified F ratio (F′ test), and a generalized Wilcoxon test (W test). Monte Carlo methods are used to obtain power curves for each test with sample sizes 20 and 50. The F test is known to be most efficient when sampling is from exponential distributions. If sampling is from exponential distributions and either there are no censored observations or all censored observations equal T, the F′ and W tests are nearly as powerful as F, with F′ being more powerful than W. If the times to censoring are not equal, the F′ test is not appropriate and the W test is nearly as powerful as F. When sampling is from Weibull distributions, with or without censoring, the F test is not robust; for example, its size is too small when the coefficient of variation is less than one. When sampling is from Weibull distributions and either there is no censoring or all censored observations have the same value, the F′ test is more powerful than the W test. If the times to censoring are not equal, the F′ test is not appropriate; the W test has the proper size and is a valid test.