ANOVA and Mixed Models: A Short Introduction Using R

✍ Scribed by Lukas Meier

• Publisher: CRC Press/Chapman & Hall
• Year: 2022
• Tongue: English
• Leaves: 202
• Series: Chapman & Hall/CRC The R Series
• Category: Library

✦ Synopsis

ANOVA and Mixed Models: A Short Introduction Using R provides both the practitioner and researcher a compact introduction to the analysis of data from the most popular experimental designs. Based on knowledge from an introductory course on probability and statistics, the theoretical foundations of the most important models are introduced. The focus is on an intuitive understanding of the theory, common pitfalls in practice, and the application of the methods in R. From data visualization and model fitting, up to the interpretation of the corresponding output, the whole workflow is presented using R. The book does not only cover standard ANOVA models, but also models for more advanced designs and mixed models, which are common in many practical applications.

Features

• Accessible to readers with a basic background in probability and statistics
• Covers fundamental concepts of experimental design and cause-effect relationships
• Introduces classical ANOVA models, including contrasts and multiple testing
• Provides an example-based introduction to mixed models
• Features basic concepts of split-plot and incomplete block designs
• R code available for all steps
• Supplementary website with additional resources and updates available at https://stat.ethz.ch/~meier/teaching/book-anova/

This bookis primarily aimed at students, researchers, and practitioners from all areas who wish to analyze corresponding data with R. Readers will learn a broad array of models hand-in-hand with R, including the applications of some of the most important add-on packages.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
1. Learning from Data
1.1. Cause-Effect Relationships
1.2. Experimental Studies
1.2.1. Predictors or Treatments
1.2.2. Randomization
1.2.3. Experimental and Measurement Units
1.2.4. Response
1.2.5. Experimental Error
1.2.6. More Terminology
1.2.7. A Few Examples
2. Completely Randomized Designs
2.1. One-Way Analysis of Variance
2.1.1. Cell Means Model
2.1.2. Parameter Estimation
2.1.3. Tests
2.2. Checking Model Assumptions
2.2.1. Residual Analysis
2.2.2. Transformations Affect Interpretation
2.2.3. Checking the Experimental Design and Reports
2.3. Nonparametric Approaches
2.4. Power or “What Sample Size Do I Need?”
2.4.1. Introduction
2.4.2. Calculating Power for a Certain Design
2.5. Adjusting for Covariates
2.6. Appendix
2.6.1. Ordered Factors: Polynomial Encoding Scheme
2.6.2. Connection to Regression
3. Contrasts and Multiple Testing
3.1. Contrasts
3.1.1. Introduction
3.1.2. Some Technical Details
3.2. Multiple Testing
3.2.1. Bonferroni
3.2.2. Bonferroni-Holm
3.2.3. Scheffé
3.2.4. Tukey Honest Significant Differences
3.2.5. Multiple Comparisons with a Control
3.2.6. FAQ
4. Factorial Treatment Structure
4.1. Introduction
4.2. Two-Way ANOVA Model
4.2.1. Parameter Estimation
4.2.2. Tests
4.2.3. Single Observations per Cell
4.2.4. Checking Model Assumptions
4.2.5. Unbalanced Data
4.3. Outlook
4.3.1. More Than Two Factors
4.3.2. Nonparametric Alternatives
5. Complete Block Designs
5.1. Introduction
5.2. Randomized Complete Block Designs
5.3. Nonparametric Alternatives
5.4. Outlook: Multiple Block Factors
6. Random and Mixed Effects Models
6.1. Random Effects Models
6.1.1. One-Way ANOVA
6.1.2. More Than One Factor
6.1.3. Nesting
6.2. Mixed Effects Models
6.2.1. Example: Machines Data
6.2.2. Example: Chocolate Data
6.2.3. Outlook
7. Split-Plot Designs
7.1. Introduction
7.2. Properties of Split-Plot Designs
7.3. A More Complex Example in Detail: Oat Varieties
8. Incomplete Block Designs
8.1. Introduction
8.2. Balanced Incomplete Block Designs
8.3. Analysis of Incomplete Block Designs
8.3.1. Example: Taste Data
8.3.2. Intraand Inter-block Analysis
8.4. Outlook
8.5. Concluding Remarks
Bibliography
Index