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 are available here.
This book is 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.
1. Learning from Data. 1.1. Cause-Effect Relationships. 1.2. Experimental Studies. 2. Completely Randomized Designs. 2.1. One-Way Analysis of Variance. 2.2. Checking Model Assumptions. 2.3. Nonparametric Approaches. 2.4. Power or "What Sample Size Do I Need?". 2.5. Adjusting for Covariates. 2.6. Appendix. 3. Contrasts and Multiple Testing. 3.1. Contrasts. 3.2. Multiple Testing. 4. Factorial Treatment Structure. 4.1. Introduction. 4.2. Two-Way ANOVA Model. 5. Complete Block Designs. 5.1. Introduction. 5.2. Randomized Complete Block Designs (RCBD). 5.3. Nonparametric Alternatives. 5.4. Outlook: Multiple Block Factors. 6. Random and Mixed Effects Models. 6.1. Random Effects Models. 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 (BIBD). 8.3. Analysis of Incomplete Block Designs. 8.4. Outlook. 8.5. Concluding Remarks. Bibliography. Index
Biography
Lukas Meier is a senior scientist at the Seminar für Statistik at ETH Zürich. His main interests are teaching statistics at various levels, the application of statistics in many fields of applications using advanced ANOVA or regression models, and high-dimensional statistics. He co-leads the statistical consulting service at ETH Zürich and is the director of a continuing education program in applied statistics.
"I found this to be a well-written, practical, concise, and very clear handbook on the appropriate analysis of data from randomized experiments using the freely available R software. The book comes in at 187 pages including the references and the index, so it gets right to the point without a lot of extra words. This book will be easy to understand for practitioners from many different fields who are collecting and analyzing data from randomized experiments, and the consistent focus on data management and data analysis using R is excellent. This is a wonderful little handbook that should be on a lot of desks. Who is it best for? First, I see this as a supplemental textbook/handbook for an undergraduate or graduate course on the design and analysis of randomized experiments. Some background in probability and statistics is needed, so this could be used for a year-3 or year-4 class in an undergraduate sequence in statistics or a graduate course on experimental design taught in a non-statistics department to students with some prior coursework in statistics. Second, professional researchers and data analysts who are comfortable with R and frequently find themselves analyzing the results of randomized experiments will also find this book very useful. I enjoyed reading it and will definitely make use of it in my work as an applied statistician and survey methodologist."
~Brady T.West, The American Statistician"The material is presented in an easy-to-read format targeting readers who seeks to understand the general principles of popular experimental designs with examples showcasing how to analyze corresponding data and interpret the outputs in RI feel this book succeeds in giving a good introduction to ANOVA and mixed effects models using R. It shows the importance of understanding the scientific question at hand when planning an experiment to enable meaningful analyses. For those who teach courses where analyzing data with ANOVA and mixed effects models are needed with a reduced theoretical overhead and an increased emphasis on interpretation and application of the methods in R, this book merits consideration."
~Oluwagbenga David Agboola, Journal of Quality Technology
