Consider the problem of performing all pair-wise comparisons among J dependent groups based on measures of location associated with the marginal distributions. It is well known that the standard error of the sample mean can be large relative to other estimators when outliers are common. Two general strategies for addressing this problem are to trim a fixed proportion of observations or empirically check for outliers and remove (or down-weight) any that are found. However, simply applying conventional methods for means to the data that remain results in using the wrong standard error. Methods that address this problem have been proposed, but among the situations considered in published studies, no method has been found that gives good control over the probability of a Type I error when sample sizes are small (less than or equal to thirty); the actual probability of a Type I error can drop well below the nominal level. The paper suggests using a slight generalization of a percentile bootstrap method to address this problem.