ANCOVA: A heteroscedastic global test when there is curvature and two covariates

TL;DR

This paper introduces a new heteroscedastic global test for comparing two groups across two covariates, demonstrating improved power over existing methods through simulations and real data application.

Contribution

The paper proposes a novel global testing method for heteroscedasticity with curvature and two covariates, showing enhanced power over existing techniques.

Findings

New method has higher power in simulations.

Method detects differences in real data example.

Outperforms existing nonparametric tests.

Abstract

For two independent groups, let $M_j(\mathbf{X})$ be some conditional measure of location for the $j$th group associated with some random variable $Y$ given $\mathbf {X}=(X_1, X_2)$. Let $\Omega=\{\mathbf{X}_1, \ldots, \mathbf{X}_K\}$ be a set of $K$ points to be determined. An extant technique can be used to test $H_0$: $M_1(\mathbf{X})=M_2(\mathbf{X})$ for each $\mathbf{X} \in \Omega$ without making any parametric assumption about $M_j(\mathbf{X})$. But there are two general reasons to suspect that the method can have relatively low power. The paper reports simulation results on an alternative approach that is designed to test the global hypothesis $H_0$: $M_1(\mathbf{X})=M_2(\mathbf{X})$ for all $\mathbf{X} \in \Omega$. The main result is that the new method offers a distinct power advantage. Using data from the Well Elderly 2 study, it is illustrated that the alternative method can make a practical difference in terms of detecting a difference between two groups.