Comparing Medians: An Overview Plus New Results on Dealing With Heavy-Tailed Distributions

The author provides a review of methods for comparing medians, with an emphasis on comparing two groups. A fairly broad perspective is provided with a summary of the relative merits associated with different strategies. Included as a special case are well-known rank-based techniques. In addition, the author reports new results on comparing the medians of independent groups when sample sizes are small. A concern about virtually all methods for comparing measures of location is that the actual Type I error probability can be well below the nominal level when sampling from heavy-tailed distributions and simultaneously sample sizes are small. This has practical implications about power. Methods are described that correct this problem.