Abstract
The paper considers the problem of comparing measures of lo cation associated with two dependent groups when values are missing at random, with an emphasis on robust measures of location. It is known that simply imputing missing values can be unsatisfactory when testing hypothe ses about means, so the goal here is to compare several alternative strategies that use all of the available data. Included are results on comparing means and a 20% trimmed mean. Yet another method is based on the usual median but differs from the other methods in a manner that is made obvious. (It is somewhat related to the formulation of the Wilcoxon-Mann-Whitney test for independent groups.) The strategies are compared in terms of Type I error probabilities and power.
Highlights
When comparing dependent groups, a commonly encountered concern is missing values
Liang et al (2008) suggested an approach to missing values using an empirical likelihood method, based on single imputation, which is readily adapted to the problem of computing a confidence interval for μD the population mean associated with D = X − Y, where X and Y are the dependent random variables being compared
There are many results on comparing robust measures of location (e.g. Wilcox, 2005), but when comparing robust measures of location associated with two dependent groups, it appears that there are no results on how to handle missing values beyond the complete case strategy
Summary
A commonly encountered concern is missing values. As is fairly evident, excluding missing data, known as complete case analysis, might result in inefficient estimation, which in turn might result in a substantial reduction in power when testing hypotheses (e.g., Liang, Wang, Robins, and Carroll, 2004). When the goal is to compare the marginal means and data are imputed, a simple strategy is to compute a confidence interval using a normal or t approximation in the usual manner It is known, that this approach can be unsatisfactory, as noted for example by Liang, Su and Zou (2008) as well as Wang and Rao (2002). Liang et al (2008) suggested an approach to missing values using an empirical likelihood method, based on single imputation, which is readily adapted to the problem of computing a confidence interval for μD the population mean associated with D = X − Y , where X and Y are the dependent random variables being compared. Wilcox, 2005), but when comparing robust measures of location associated with two dependent groups, it appears that there are no results on how to handle missing values beyond the complete case strategy. The method is extended to the case of missing values, but the impact of missing values is unknown
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