1st Edition

# Design of Experiments An Introduction Based on Linear Models

376 Pages 13 B/W Illustrations
by Chapman & Hall

376 Pages 13 B/W Illustrations
by Chapman & Hall

376 Pages
by Chapman & Hall

Also available as eBook on:

Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems.

The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix.

This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.

Introduction
Example: rainfall and grassland
Basic elements of an experiment
Experiments and experiment-like studies
Models and data analysis

Linear Statistical Models
Linear vector spaces
Basic linear model
The partitioned linear model
The reduced normal equations
Estimation and information
Hypothesis testing and information
Blocking and information

Completely Randomized Designs
Introduction
Models
Matrix formulation
Influence of design on estimation
Influence of design on hypothesis testing

Randomized Complete Blocks and Related Designs
Introduction
A model
Matrix formulation
Influence of design on estimation
Influence of design on hypothesis testing
Orthogonality and "Condition E"

Latin Squares and Related Designs
Introduction
Replicated Latin squares
A model
Matrix formulation
Influence of design on quality of inference
More general constructions: Graeco-Latin squares

Some Data Analysis for CRDs and Orthogonally Blocked Designs
Introduction
Diagnostics
Power transformations
Basic inference
Multiple comparisons

Balanced Incomplete Block Designs
Introduction
A model
Matrix formulation
Influence of design on quality of inference
More general constructions

Random Block Effects
Introduction
Inter- and intra-block analysis
CBDs and augmented CBDs
BIBDs
Combined estimator
Why can information be "recovered"?
CBD reprise

Factorial Treatment Structure
Introduction
An overparameterized model
An equivalent full-rank model
Estimation
Partitioning of variability and hypothesis testing
Factorial experiments as CRDs, CBDs, LSDs, and BIBDs
Model reduction

Split-Plot Designs
Introduction
SPD(R,B)
SPD(B,B)
More than two experimental factors
More than two strata of experimental units

Two-Level Factorial Experiments: Basics
Introduction
Example: bacteria and nuclease
Two-level factorial structure
Estimation of treatment contrasts
Testing factorial effects

Two-Level Factorial Experiments: Blocking
Introduction
Complete blocks
Balanced incomplete block designs
Regular blocks of size 2f−1
Regular blocks of size 2f−2
Regular blocks: general case

Two-Level Factorial Experiments: Fractional Factorials
Introduction
Regular fractional factorial designs
Analysis
Example: bacteria and bacteriocin
Comparison of fractions
Blocking regular fractional factorial designs
Augmenting regular fractional factorial designs
Irregular fractional factorial designs

Factorial Group Screening Experiments
Introduction
Example: semiconductors and simulation
Factorial structure of group screening designs
Group screening design considerations
Case study

Regression Experiments: First-Order Polynomial Models
Introduction
Polynomial models
Designs for first-order models
Blocking experiments for first-order models
Split-plot regression experiments
Diagnostics

Regression Experiments: Second-Order Polynomial Models
Introduction
Designs for second-order models
Design scaling and information
Orthogonal blocking
Split-plot designs
Bias due to omitted model terms

Introduction to Optimal Design
Introduction
Optimal design fundamentals
Optimality criteria
Algorithms

Appendices

References

Index

A Conclusion and Exercises appear at the end of each chapter.

### Biography

Max D. Morris is a professor in the Department of Statistics and the Department of Industrial and Manufacturing Systems Engineering at Iowa State University. A fellow of the American Statistical Association, Dr. Morris is a recipient of the National Institute of Statistical Sciences Sacks Award for Cross-Disciplinary Research and the American Society for Quality Wilcoxon Prize.

A distinctive feature of this excellent book is that it actually focuses on how to design an experiment. … In all, an original and very useful book for students and instructors.
—Stat Papers (2014) 55:1225–1226

the author has succeeded in striking a balance between the choice of topics and depth in discussion for teaching a course. The book is written with a refreshing style and succeeds in conveying the concepts to a reader. The treatment of the subject matter is thorough and the theory is clearly illustrated along with worked examples. Other books are available on similar topics but this book has the advantage that the chapters start with the classical non-matrix-theory approach to introduce the linear model and then converts it into a matrix theory-based linear model. This helps a reader, particularly a beginner, in clearly understanding the transition from a non-matrix approach to a matrix approach and to apply the results of matrix theory over linear models further.
—Shalabh, Journal of the Royal Statistical Society, Series A, 2012

Overall, this is a book that is easy to like, with good definitions of designs, few typographical errors, and consistent, straightforward explications of the models … I can picture a lot of students using a text aimed at a broad market design course but who need to understand more about what is going on behind the curtain. Morris’ text also fills that gap very well.
—Gary W. Oehlert, Biometrics, May 2012

It is truly my pleasure to read this book … after reading this book, I benefitted by gaining insights into the modeling aspect of experimental design, and consequentially it helps me appreciate the idea of statistical efficiency behind each design and understand the tools used in data analysis. … an excellent reference book that I would recommend to anyone who is serious about learning the nuts and bolts of experimental design and data analysis techniques.
—Rong Pan, Journal of Quality Technology, Vol. 43, No. 3, July 2011