Abstract
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 avail- able 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.
Highlights
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
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
Consider J ≥ 2 dependent groups and let θj (j = 1, . . . , J) be some robust measure of location associated with the jth marginal distribution
Summary
Exclude any rows of data where there are missing values and analyze the data that remain. This approach might result in a reduction in power when testing hypotheses (e.g., [15]). When testing (1), a simple strategy is to impute missing values and use some conventional test statistic in the usual manner. It is known, that this approach can be unsatisfactory, as noted for example by Liang et al [15] as well as Wang and Rao [32]
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