Robust within Groups Anova: Dealing with Missing Values

The paper considers the problem of testing the hypothesis that J ≥ 2 dependent groups have equal population measures of location when using a robust estimator and there are missing values. For J = 2, methods have been studied based on trimmed means. But the methods are not readily extended to the case J > 2. Here, two alternative test statistics were considered, one of which performed poorly in some situations. The one method that performed well in simulations is based on a very simple test statistic with the null distribution approximated via a basic bootstrap technique. The method uses all of the available data to estimate each of the marginal (population) trimmed means. Other robust measures of location were considered, for which imputation methods have been derived, but in simulations the actual Type I error probability was estimated to be substantially less than the nominal level, even when there are no missing values.