Robustness and power of parametric, nonparametric, robustified and adaptive tests -: the multi-sample location problem

This paper deals with a survey of different types of tests, parametric, nonparametric, robustified and adaptive ones, and with an application to the two-sided c-sample location problem. Some concepts of robustness are discussed, such as breakdown point, influence function, gross-error sensitivity and especially alpha - and beta - robustness. A robustness study on level ct in the case of heteroscedasticity and nonnormal distributions is carried out via Monte Carlo methods and also a power comparison of ail the tests considered. It turns out that robustified versions of the F-test and Welch-test where the original observations are replaced by its ranks behave well over a broad class of distributions, symmetric ones with different tailweight and asymmetric ones, but, on the whole, an adaptive test is to prefer.