Global comparisons of medians and other quantiles in a one-way design when there are tied values

TL;DR

This paper develops and evaluates a bootstrap-based method for testing the equality of medians and other quantiles across multiple independent groups, especially addressing issues with tied values and extending beyond simple two-group comparisons.

Contribution

It introduces a bootstrap approach combined with the Harrell--Davis estimator for robustly testing quantile equality in multi-group settings with ties.

Findings

Bootstrap method performs well in simulations.

Method effectively handles tied values.

Illustrated with real data from Well Elderly 2 study.

Abstract

For $J \ge 2$ independent groups, the paper deals with testing the global hypothesis that all $J$ groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes suggested for comparing medians, but it is well known that under general conditions they do not adequately address this goal. Extant methods based on the usual sample median are unsatisfactory when there are tied values except for the special case $J=2$. A variation of the percentile bootstrap used in conjunction with the Harrell--Davis quantile estimator performs well in simulations. The method is illustrated with data from the Well Elderly 2 study.