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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
Additional resources:

April 2013 | 344 pages | SAGE Publications, Inc
The goal of this book is to demonstrate basic statistical concepts from two different perspectives, giving the reader a conceptual understanding of how to interpret statistics and their use. Those two perspectives are a focus on the traditional tests that are used such as t-test, correlation and ANOVA, and a model-comparison approach using General Linear Methods. This text is intended for upper-level undergraduate courses, or first year graduate students. It is not for courses where students have no basic understanding of statistics.
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.

“I believe that when students are taught about statistics using the approach of this text, they have a MUCH deeper understanding and appreciation of the material. It is really fantastic.”

Jeffrey A. Ciesla
Kent State University

“The author does a really nice job of explaining the General Linear Model (GLM) by comparing it to hypothesis testing and showing [some of] its real-world applicability.”

Alfred F. Mancuso
Georgian Court University

“The text includes simple descriptions of complex mathematical concepts that are the foundation of statistics in the social sciences.”

Lela Rankin Williams
Arizona State University

“I think the book provides a nice step-by-step approach to understanding ANOVA and regression techniques. The author does an excellent job breaking down the different components of these statistical techniques while capturing the attention of the reader.”

Manfred van Dulmen
Kent State University

“…the author really takes the readers step by step and makes the material easy to follow even for readers without extensive mathematics backgrounds.”

Kamala London
University of Toledo

The book stands out with its clarity and structure which allows students to easily orientate themselves in elementary methods of empirical research. The genral approach enables student's to derive further methods and adopt knowledge to various kinds of statistical software.

Mr Joachim Müller
Faculty 2: Educational Sciences, University of Essen
February 16, 2016

A very useful book which focuses on some of the more commonly used tests for biological sciences

Dr Emma Coulthard
All Saints Campus, Manchester Metropolitan University
October 15, 2015

Vik covers clearly and simply the mathematical concepts underlying vast tools in statistical methods. The examples are very helpful and are well explained in that a student with no statistical background can grasp the concepts therein without much difficulty. I would recommend students to supplement this text with their primary text when they take courses in statistics.

Dr Lorenz Neuwirth
Psychology Dept, Cuny College Of Staten Island
February 15, 2015

Although I really like this book (and recommend it as a supplemental text for my students), I did not adopt it. The book has very little support material (e.g., PowerPoint slide, images, homework and test problems, sample data sets), which makes it very difficult for me to choose it over other texts that have this material -- note: this is especially true for the data sets, which are difficult to create. Also, book does not have much coverage for follow-up analyses for interactions in multiple regression or factorial ANOVA. Although this is a complex topics and somewhat beyond the scope of the book, it is one that I have to cover in my class.

Mr Keith Donohue
Psychology Dept, North Dakota State University
October 29, 2014

Clealry laid out text with good examples. Stress free reading !

SPEECH AND HEARING SCIENCES, Queen Margaret University College, Edinburgh
April 29, 2014

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