Nonparametric multiple-comparison methods for simply ordered medians

Recently, several multiple-comparison procedures for a simple order have been proposed. Most of these procedures are developed under the usual normality and equality-of-variances assumptions. In many applications, however, these assumptions may not be satisfied. For nonnormal data, two types of relatively simple nonparametric multiple-comparison methods for a simple order are proposed. The first is a rank-based method, which traces its roots to the one-sided Studentized-range test by Hayter, and the other is a two-stage method, which conducts the global test by Chacko, followed by one-sided pairwise tests. A simulation shows that the proposed procedures perform reasonably well with normal data, and that they are far superior to the parametric counterparts when data arise from a heavy-tailed distribution, such as Cauchy.