17. ANCOVA for Ordered Treatments Designs

  1. Bradley E. Huitema

Published Online: 14 OCT 2011

DOI: 10.1002/9781118067475.ch17

The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, Second Edition

The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, Second Edition

How to Cite

Huitema, B. E. (2011) ANCOVA for Ordered Treatments Designs, in The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118067475.ch17

Author Information

  1. Department of Psychology, Western Michigan University, Kalamazoo, Michigan, USA

Publication History

  1. Published Online: 14 OCT 2011
  2. Published Print: 14 OCT 2011

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471748960

Online ISBN: 9781118067475

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Keywords:

  • Abelson-Tukey method;
  • analysis of covariance (ANCOVA);
  • multiple covariates;
  • ordered treatment levels;
  • rank-based monotone method;
  • reversed ordinal logistic regression;
  • robust linear model estimation

Summary

This chapter introduces generalizations of monotone methods that are appropriate for designs having both ordered treatment levels and one or more covariates. Both parametric and nonparametric monotone methods are described. Four different methods of combining the two are also explained. The first method is essentially an application of a modified version the parametric Abelson-Tukey method to adjusted means from analysis of variance (ANCOVA), but with an adjusted error term. The second method is a simple rank-based approach that can be computed using ordinary multiple regression software. The third approach involves the use of a reversed ordinal logistic regression model. The fourth approach utilizes recently developed robust linear model estimation. Each method can be expected to have power advantages over methods that do not incorporate a covariate; each method can incorporate more than one covariate.

Controlled Vocabulary Terms

analysis of covariance; covariate; generalized linear model; ordinal logistic regression