10. Assumptions Underlying ANOVA, Traditional ANCOVA, and GLMs

  1. Andrew Rutherford

Published Online: 30 SEP 2013

DOI: 10.1002/9781118491683.ch10

Anova and Ancova, Second Edition

Anova and Ancova, Second Edition

How to Cite

Rutherford, A. (2011) Assumptions Underlying ANOVA, Traditional ANCOVA, and GLMs, in Anova and Ancova, Second Edition, John Wiley & Sons, Inc., Hoboken, New Jersey. doi: 10.1002/9781118491683.ch10

Publication History

  1. Published Online: 30 SEP 2013
  2. Published Print: 7 OCT 2011

ISBN Information

Print ISBN: 9780470385555

Online ISBN: 9781118491683

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Keywords:

  • ANOVA;
  • covariate;
  • general linear model (GLM);
  • independent measures designs;
  • regression assumptions;
  • traditional ANCOVA

Summary

A least squares general linear model (GLM) specification includes more than an equation describing the data in terms of model parameters and error terms. There is also a set of assumptions specifying restrictions on the model parameters and error terms. This chapter presents the typical expression of ANOVA assumptions and the typical expression of GLM and regression assumptions. It explains why these two sets of assumptions are equivalent and that all GLMs make this small single set of statistical assumptions. Subsequently, the further assumptions made to simplify parameter estimation and interpretation when related ANOVA and traditional ANCOVA are applied, are discussed. The set of assumptions underlying all GLM analyses are most apparent in the context of independent measures designs. To illustrate graphical and significance test methods, some of the assessment techniques described are applied to the single factor independent measures ANCOVA with one covariate example.

Controlled Vocabulary Terms

analysis of covariance; analysis of variance; covariate; regression