Inferences about which of J dependent groups has the largest robust measure of location

Recently, a multiple comparisons procedure was derived with the goal of determining whether it is reasonable to make a decision about which of J independent groups has the largest robust measure of location. This was done by testing hypotheses aimed at comparing the group with the largest estimate to the remaining J - 1 groups. It was demonstrated that for the goal of controlling the familywise error rate, meaning the probability of one or more Type I errors, well-known improvements on the Bonferroni method can perform poorly. A technique for dealing with this issue was suggested and found to perform well in simulations. However, when dealing with dependent groups, the method is unsatisfactory. This note suggests an alternative method that is designed for dependent groups.