Testing Equality of Medians for Multiple Samples

TL;DR

This paper introduces a new non-parametric test for assessing the equality of medians across multiple independent samples, applicable to various quantiles, supported by theoretical analysis and simulation results.

Contribution

It develops a consistent, extendable non-parametric test for median equality among multiple samples, applicable to different quantile levels.

Findings

The test is consistent and theoretically justified.

Simulation studies demonstrate good performance.

Applicable to various quantile levels.

Abstract

In this paper, we construct a consistent non-parametric test for testing the equality of population medians for different samples when the observations in each sample are independent and identically distributed. This test can be further used to test the equality of unknown location parameters for different samples. The method discussed in this paper can be extended to any quantile level instead of the median. We present the theoretical results and also demonstrate the performance of this test through simulation studies.