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5.4 Inferences Based on a Percentile Boo... > 5.4.2 Comparing Trimmed Means and Me... - Pg. 172

172 Introduction to Robust Estimation and Hypothesis Testing independent groups, the percentile bootstrap again is the best method based on current results. As in the one-sample case, there are bootstrap methods that have not been examined via simulations when comparing M-measures of location, so it is not being suggested that all other bootstrap techniques have no practical value for the problem at hand. A confidence interval based on an estimate of the standard error will provide good probability coverage when the sample sizes are sufficiently large, assuming the estimated difference is normally distributed, but it is unknown just how large the sample sizes should be before this approach can be recommended, particularly when distributions are skewed. If both distributions are symmetric, confidence intervals based on estimated standard errors seem to have merit when Student's t-distribution is used to determine an appropriate critical value, but there is no good decision rule, based on available empirical data, whether distributions are sufficiently symmetric. (One could test the assumption that distributions are symmetric, but how much power should such a test have to justify the use of a method that assumes symmetric distributions?) A bootstrap-t method might also be advantageous in certain situations, but it is unknown when, if ever, this approach should be used over the percentile bootstrap. When sample sizes are small, all indications are that the percentile bootstrap is best, so it is recommended until there is good evidence that some other method should be used instead.