Within groups analysis of covariance: multiple comparisons at specified design points using a robust measure location when there is curvature

Abstract

Consider the situation where measurements are taken at two different times and let M_j(x) be some conditional robust measure of location associated with the random variable Y at time j, given that some covariate X=x. The goal is to test H₀: M₁(x)=M₂(x) for each x∈ x₁, … , x_K such that the probability of one or more Type I errors is less than α, where x₁, … , x_K are K specified values of the covariate. The paper reports simulation results comparing two methods aimed at accomplishing this goal without specifying some parametric form for the regression line. The first method is based on a simple modification of the method in Wilcox [Introduction to robust estimation and hypothesis testing. 3rd ed. San Diego, CA: Academic Press; 2012, Section 11.11.1]. The main result here is that the second method, which has never been studied, can have higher power, sometimes substantially so. Data from the Well Elderly 2 study, which motivated this paper, are used to illustrate that the alternative approach can make a practical difference. Here, the estimate of M_j(x) is based in part on either a 20% trimmed mean or the Harrell–Davis quantile estimator, but in principle the more successful method can be used with any robust location estimator.

Keywords:

• ANCOVA
• trimmed mean
• Harrell–Davis estimator
• smoothers
• bootstrap methods
• Well Elderly 2 study
• cortisol
• depressive symptoms
• perceived health

Acknowledgements

We thank Xiao He for supplying the C++ code used in this study.