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Regression, ANOVA, and the General Linear Model

Regression, ANOVA, and the General Linear Model
A Statistics Primer

  • Peter Vik - Pacific University, Forest Grove, OR, USA, Idaho State University, Pocatello, USA

January 2013 | 344 pages | SAGE Publications, Inc
Peter Vik's Regression, ANOVA, and the General Linear Model: A Statistics Primer demonstrates basic statistical concepts from two different perspectives, giving the reader a conceptual understanding of how to interpret statistics and their use. The two perspectives are (1) a traditional focus on the t-test, correlation, and ANOVA, and (2) a model-comparison approach using General Linear Models (GLM). This book juxtaposes the two approaches by presenting a traditional approach in one chapter, followed by the same analysis demonstrated using GLM. By so doing, students will acquire a theoretical and conceptual appreciation for data analysis as well as an applied practical understanding as to how these two approaches are alike.

Chapter 1: Introduction
Part I: Foundations of the General Linear Model
Chapter 2: Predicting Scores: The Mean and the Error of Prediction
Chapter 3: Bivariate Regression
Chapter 4: Model Comparison: The Simplest Model Versus a Regression Model
Part II: Fundamental Statistical Tests
Chapter 5: Correlation: Traditional and Regression Approaches
Chapter 6: T-test: Concepts and Traditional Approach
Chapter 7: Oneway Analysis of Variance (ANOVA): Traditional Approach
Chapter 8: T-test, ANOVA, and the Bivariate Regression Approach
Part III: Adding Complexity
Chapter 9: Model Comparison II: Multiple Regression
Chapter 10: Multiple Regression: When Predictors Interact
Chapter 11: Two-way ANOVA: Traditional Approach
Chapter 12: Two-way ANOVA: Model Comparison Approach
Chapter 13: One-way ANOVA with Three Groups: Traditional Approach
Chapter 14: ANOVA with Three Groups: Model Comparison Approach
Chapter 15: Two by Three ANOVA: Complex Categorical Models
Chapter 16: Two by Three ANOVA: Model Comparison Approach
Chapter 17: Analysis of Covariance (ANCOVA): Continuous and Categorical Predictors
Chapter 18: Repeated Measures
Chapter 19: Multiple Repeated Measures
Chapter 20: Mixed Between and Within Designs
A: Research Designs
B: Variables, Distributions, & Statistical Assumptions
C: Sampling and Sample Sizes
D: Null Hypothesis, Statistical Decision-Making, & Statistical Power


Student Study Site
A selection of diverse conceptual and computational practice problems is provided for each chapter of the book, minus the introduction. Students are encouraged to use them as a study aid and instructors are encouraged to use them as a homework and/or testing tool.

This book provides a very clearly written step-by-step approach of GLM, without using too many statistical formulations.

Dr Elisabeth Dorant
Fac: Health, Medicine & Life Sciences, Maastricht University
December 16, 2013

Alternative way at looking at statistics compared to other texts. Use to show student the links between statistical tests and manage hand calculations

Dr Robert Hogg
Dept of Sport & Exercise Science, University of Sunderland
October 30, 2013

An indispensable reference that redefines the position of the linear model and clarifies statistical approaches in research. The text is engaging and provides relevance as both an introductory tome and dip-in reference.

Mr Philip Bright
Research Department, European School of Osteopathy
October 21, 2013

An extremely good book that breaks down the subject in to understandable pieces

Mr Joel Harris
Sports Therapy, University of Hertfordshire
July 22, 2013

Excellent book for anybody performing research in sports science.

Ms Bettina Karsten
Life and Sports Science, Greenwich University
June 17, 2013

This is an excellent and unique statistics text that bridges the gap between linear modelling approaches and the traditional test-focussed perspective. Worthy of comparison with Rich Zeller and Ed Carmines classic text, explaining the essential underpinning concepts rather than trying to teach statistical tests by rote.

Professor Brian Taylor
Social Work , University of Ulster
June 13, 2013

Not what I had anticipated. Had hoped for something that also incorporated SPSS.

Dr Helen Scott
Psyc, Staffordshire University
June 7, 2013

Easy to read even for the undegraduates with limited knowledge of statistics as provides a step-by-step approach to understanding ANOVA and regression techniques.

Miss Magdalena Marczak
Faculty of Health & Life Sciences, Coventry University
May 12, 2013

A useful text for students completing a Masters programme and doing a research dissertation. Good level of detail included and step by step process in various statistical tests is easy to follow.

In my opinion slightly too detailed for undergraduates

Dr Pauline Meskell
School of Nursing and Midwifery, National University of Ireland, Galway
May 8, 2013
Key features


  • A demonstration of statistical analysis using both traditional and GLM approaches as offers a path to conceptual understanding of data analysis as well as a practical applied knowledge.
  • A single data set was used throughout the book to the extent possible, so as to demonstrate model-building by creating successively enhanced models based on the same data set.

For instructors

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