# ANOVA and ANCOVA: A GLM Approach

John Wiley & Sons, Oct 25, 2011 - Mathematics - 344 pages
Provides an in-depth treatment of ANOVA and ANCOVA techniques from a linear model perspective

ANOVA and ANCOVA: A GLM Approach provides a contemporary look at the general linear model (GLM) approach to the analysis of variance (ANOVA) of one- and two-factor psychological experiments. With its organized and comprehensive presentation, the book successfully guides readers through conventional statistical concepts and how to interpret them in GLM terms, treating the main single- and multi-factor designs as they relate to ANOVA and ANCOVA.

The book begins with a brief history of the separate development of ANOVA and regression analyses, and then goes on to demonstrate how both analyses are incorporated into the understanding of GLMs. This new edition now explains specific and multiple comparisons of experimental conditions before and after the Omnibus ANOVA, and describes the estimation of effect sizes and power analyses leading to the determination of appropriate sample sizes for experiments to be conducted. Topics that have been expanded upon and added include:

• Discussion of optimal experimental designs

• Different approaches to carrying out the simple effect analyses and pairwise comparisons with a focus on related and repeated measure analyses

• The issue of inflated Type 1 error due to multiple hypotheses testing

• Worked examples of Shaffer's R test, which accommodates logical relations amongst hypotheses

ANOVA and ANCOVA: A GLM Approach, Second Edition is an excellent book for courses on linear modeling at the graduate level. It is also a suitable reference for researchers and practitioners in the fields of psychology and the biomedical and social sciences.

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### Contents

 Statistical Packages for Computers 15 Comparing Experimental Condition Means Multiple 53 Measures of Effect Size and Strength of Association 93 GLM Approaches to Independent Measures Factorial Designs 111 GLM Approaches to Related Measures Designs 139 The GLM Approach to Factorial Repeated Measures Designs 171 GLM Approaches to Factorial Mixed Measures Designs 199 The GLM Approach to ANCOVA 215
 Multilevel Analysis for the Single Factor 281 13 294 Repeated Measures Data 298 Appendix A 305 15 308 Appendix C 315 References 325 Index 339

 Assumptions Underlying ANOVA Traditional ANCOVA 235 Some Alternatives to Traditional ANCOVA 263