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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About the Author
Andrew Rutherford, PhD, is Senior Lecturer in the School of Psychology at Keele University (United Kingdom). Dr. Rutherford's research interests include encoding and retrieval processes in recall and recognition and the effect of mild head injury on cognition, as well as general linear modeling.
Table of Contents
CHAPTER 1 AN INTRODUCTION TO GENERAL LINEAR MODELS: REGRESSION, ANALYSIS OF VARIANCE AND ANALYSIS OF COVARIANCE.
1.1 Regression, analysis of variance and analysis of covariance.
1.2 A pocket history of regression, ANOVA and ANCOVA.
1.3 An outline of general linear models (GLMs).
1.4 The "general" in GLM.
1.5 The "linear" in GLM.
1.6 Least squares estimates.
1.7 Fixed, random and mixed effects analyses.
1.8 The benefits of a GLM approach to ANOVA and ANCOVA.
1.9 The GLM presentation.
1.10 Statistical packages for computers.
CHAPTER 2 TRADITIONAL AND GLM APPROACHES TO INDEPENDENT MEASURES SINGLE FACTOR DESIGNS.
2.1 Independent measures designs.
2.2 Balanced data designs.
2.3 Factors and independent variables.
2.4 An outline of traditional ANOVA for single factor designs.
2.6 Traditional ANOVA calculations for single factor designs.
2.7 GLM approaches to single factor ANOVA.
CHAPTER 3 COMPARING EXPERIMENTAL CONDITION MEANS, MULTIPLE HYPOTHESIS TESTING, TYPE 1 ERROR AND A BASIC DATA ANALYSIS STRATEGY.
3.2 Comparisons between experimental condition means.
3.3 Linear contrasts.
3.4 Comparison sum of squares.
3.5 Orthogonal contrasts.
3.6 Testing multiple hypotheses.
3.7 Planned and unplanned comparisons.
3.8 A basic data analysis strategy.
3.9 The Role of the Omnibus F-Test.
CHAPTER 4 SIGNIFICANCE TESTING, CONFIDENCE INTERVALS, EFFECT SIZE AND POWER.
4.2 Effect size as a standardized mean difference.
4.3 Effect size as strength of association (SOA).
4.4 Small, medium and large effect sizes.
4.5 Effect size in related measures designs.
4.6 Overview of standardized mean difference and SOA measures of effect size.
CHAPTER 5 GLM APPROACHES TO INDEPENDENT MEASURES FACTORIAL DESIGNS.
5.1 Factorial designs.
5.2 Factor main effects and factor interactions.
5.3 Regression GLMs for factorial ANOVA.
5.4 Estimating effects with incremental analysis.
5.5 Effect size estimation.
5.6 Further analyses.
CHAPTER 6 GLM APPROACHES TO RELATED MEASURES DESIGNS.
6.2 Order effect controls.
6.3 The GLM approach to single factor repeated measures designs.
6.4 Estimating effects by comparing Full and Reduced repeated measures design GLMs.
6.5 Regression GLMs for single factor repeated measures designs.
6.6 Effect size estimation.
6.7 Further analyses.
CHAPTER 7 GLM APPROACHES TO FACTORIAL RELATED MEASURES DESIGNS.
7.1 Factorial related measures designs.
7.2 Fully related factorial design.
7.3 Estimating effects by comparing Full and Reduced experimental design GLMs.
7.4 Regression GLMs for the fully related factorial ANOVA.
7.5 Effect size estimation.
7.6 Further analyses.
CHAPTER 8 GLM APPROACHES TO FACTORIAL MIXED MEASURES DESIGNS.
8.1 Factorial mixed measures designs.
8.2 Estimating effects by comparing Full and Reduced experimental design GLMs.
8.3 Regression GLM for the two factor mixed measures ANOVA.
8.4 Effect size estimation.
8.5 Further analyses.
CHAPTER 9 THE GLM APPROACH TO ANCOVA.
9.1 The nature of ANCOVA.
9.2 Single factor independent measures ANCOVA designs.
9.3 Estimating effects by comparing Full and Reduced ANCOVA GLMs.
9.4 Regression GLMs for the single factor single covariate ANCOVA.
9.5 Further analyses.
9.6 Effect size estimation.
9.8 Other ANCOVA designs.
CHAPTER 10 ASSUMPTIONS UNDERLYING ANOVA, TRADITIONAL ANCOVA AND GLMs.
10.2 ANOVA and GLM assumptions.
10.3 A strategy for checking ANOVA and traditional ANCOVA assumptions.
10.4 Assumption checks and some assumption violation consequences.
10.5 Should the assumptions underlying the main statistical analysis be checked?.
CHAPTER 11 SOME ALTERNATIVES TO TRADITIONAL ANCOVA.
11.1 Alternatives to traditional ANCOVA.
11.2 The heterogeneous regression problem.
11.3 The heterogeneous regression ANCOVA GLM.
11.4 Single factor independent measures heterogeneous regression ANCOVA.
11.5 Estimating heterogeneous regression ANCOVA effects.
11.6 Regression GLMs for heterogeneous ANCOVA.
11.7 Covariate - experimental condition relations.
11.8 Other alternatives.
11.9 The role of ANCOVA.
CHAPTER 12 MULTILEVEL ANALYSIS FOR THE SINGLE FACTOR REPEATED MEASURES DESIGN.
12.1 Introduction to multilevel analysis.
12.2 Review of the single factor repeated measures experimental design GLM and ANOVA.
12.3 The multilevel approach to the single factor repeated measures experimental design.
12.4 Parameter estimation in multilevel analysis.
12.5 Applying multilevel models with different error variance-covariance structures.
12.6 Empirically Assessing different multilevel models.