BYU-Idaho Math326: Design and Analysis of Experiments

A Customizable Textbook

This book is meant to be a starting point for you to learn design and analysis of experiments. If you get the files used to create this website from your inctructor, you can edit the Quarto files so that the book becomes your own!

How to Use This Book

Under Basics of Design the most foundational issues that face each experimenter are described.

The Specific Designs section addresses specific designs we will learn about in this course. Each design will have an image next to it representing the diagram of the structural factors. Within each of these designs there are subsections:

  • Overview contains the model, factor structure and hypotheses
  • Design discusses how the randomization is implemented and why
  • Decomposition is a bridge between the design and analysis. It walks through creating an ANOVA table by hand for the given design to allow you to see how the factor structure affects the analysis.
  • R instructions provides code illustrating how to run the model
  • Resources contains worked examples and a space for you to store other links and info

The section labeled Broad Topics seeks to address topics that are relevant to many experiment designs.

Finally, a section dedicated to R code that can be used in multiple designs. This includes numerical and graphical data summaries as well as code for model diagnostics/assumption checking.

You should add additional topics and designs as you learn more, even after the course is over. The book is meant to be fully customizable and growing to reflect your growing understanding.

Suggested Sequence of Topics for Teaching

This book was specifically designed for the Math326 Design and Analysis of Experiments class at BYU-Idaho, as it stands in 2022. BYU-I follows a 14 week semester. After introducing some foundational principles of experimental design, the recommended sequence follows the general pattern of

  • Introduce a specific design: suitability/benefits of the design, explanation of the design, factor structure and decomposition, steps for analysis (including R code)
  • Discuss new topics/complexities/considerations associated with that design located in the Broad Topics list.

Here is a specific, suggested reading schedule:

  2. Read the pages under the Basics of Design menu in order

  3. Read the following pages in order under “Broad Topics” menu: Factor Structure through Assumptions

  4. Read Basic Factorial Introduction and BF[1] under Specific Designs menu

  5. Pages under the R Instructions menu can act as a resource. They may fit well as a review here

  6. Under Broad Topics menu Read Contrasts and Multiple Comparisons

  7. Read BF[2] under Specific Design menu

  8. Read Unbalanced Datasets under Broad Topics menu

Book Scope

This is an introductory book intended to familiarize students with foundational concepts and vocabulary in the design and analysis of experiments. The designs covered in this book are the most basic and all assume a continuous response variable. Hopefully with this foundation students will be prepared to excel in experimental design and analysis courses in grad school, or be able to extend these principles to more complex designs as practitioners.