Some Robust and Adaptive Tests Versus F-Test for Several Samples

Summary

Testing the equality of c means the application of the F-test depends on very restrictive assumptions such as normality and equal variances of the c populations. If these assumptions are not satisfied it is more appropriate to apply a robust version of the F-test. We consider the Welch test, a rank version of the Welch test, the trimmed Welch test and some nonparametric counterparts where each of them is very efficient for a special class of distributions. But usually the practising statistician has no clear idea of the underlying distribution. Therefore, an adaptive test should be applied which takes into account the given data. We compare the F-test with its robust and adaptive competitors under normality and nonnormality as well as under homoscedasticity and heteroscedasticity. The comparison is referred to level α and power β of the test and is carried out via Monte Carlo simulation. It turns out that the Welch test is the best one in the case of unequal variances, for equal variances, however, special rank tests are to prefer. It is also shown that the adaptive test behaves well over a broad class of distributions.