Statistics and Its Interface

Volume 15 (2022)

Number 3

Paired-sample tests for homogeneity with/without confounding variables

Pages: 335 – 348

DOI: https://dx.doi.org/10.4310/21-SII695

Authors

Minqiong Chen (Southern China Research Center of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Ting Tian (Southern China Research Center of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Jin Zhu (Southern China Research Center of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Wenliang Pan (Southern China Research Center of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Xueqin Wang (Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui, China)

Abstract

In this article, we are concerned about testing the homogeneity on paired samples with or without confounding variables. These problems usually arise in clinical trials, psychological or sociological studies. We introduce new nonparametric tests for equality of two distributions or two conditional distributions of random vectors on paired samples. We show that their test statistics are consistent but have different asymptotic distributions under the null hypothesis, depending on whether confounding variables exist. The limit distribution of the test statistic is a mixed $\chi^2$ distribution when testing the equality of two paired distributions, while it is a normal distribution when testing the equality of two conditional distributions of paired samples. We conduct several simulation studies to evaluate the finite-sample performance of our tests. Finally, we apply our tests on real data to illustrate their usefulness in the applications.

Keywords

homogeneity, conditional distribution, paired samples, energy distance

Received 13 October 2020

Accepted 4 August 2021

Published 14 February 2022