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Traditional and Rank-Based Tests for Ordered Alternatives in a Cluster Correlated Model

Published online by Cambridge University Press:  01 January 2025

Yuanyuan Shao ,
Joseph W. McKean  and
Bradley E. Huitema
Yuanyuan Shao
Affiliation:
General Motors
Joseph W. McKean*
Affiliation:
Western Michigan University
Bradley E. Huitema
Affiliation:
Western Michigan University
*
Correspondence should be made to Joseph W. McKean, Department of Statistics, Western Michigan University, Kalamazoo, MI, USA. Email: joseph.mckean@wmich.edu
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Abstract

Methods for the analysis of one-factor randomized groups designs with ordered treatments are well established, but they do not apply in the case of more complex experiments. This article describes ordered treatment methods based on maximum-likelihood and robust estimation that apply to designs with clustered data, including those with a vector of covariates. The contrast coefficients proposed for the ordered treatment estimates yield higher power than those advocated by Abelson and Tukey; the proposed robust estimation method is shown (using theory and simulation) to yield both high power and robustness to outliers. Extensions for nonmonotonic alternatives are easily obtained.

Keywords

asymptotic theoryefficiencynonparametricsrandomized block designsrank-based fitsREML fitsrepeated-measures designsrobust analysis of covarianceWilcoxon procedures
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 3 , September 2020 , pp. 531 - 554
Copyright
Copyright © 2020 The Psychometric Society

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