Design of Experiments: An Introduction Based on Linear Models, 1st Edition (Paperback) book cover

Design of Experiments

An Introduction Based on Linear Models, 1st Edition

By Max Morris

Chapman and Hall/CRC

376 pages | 13 B/W Illus.

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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.


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

Table of Contents


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 hat matrix, least-squares estimates, and design information matrix

The partitioned linear model

The reduced normal equations

Linear and quadratic forms

Estimation and information

Hypothesis testing and information

Blocking and information

Completely Randomized Designs



Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

Randomized Complete Blocks and Related Designs


A model

Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

Orthogonality and "Condition E"

Latin Squares and Related Designs


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



Power transformations

Basic inference

Multiple comparisons

Balanced Incomplete Block Designs


A model

Matrix formulation

Influence of design on quality of inference

More general constructions

Random Block Effects


Inter- and intra-block analysis

CBDs and augmented CBDs


Combined estimator

Why can information be "recovered"?

CBD reprise

Factorial Treatment Structure


An overparameterized model

An equivalent full-rank model


Partitioning of variability and hypothesis testing

Factorial experiments as CRDs, CBDs, LSDs, and BIBDs

Model reduction

Split-Plot Designs




More than two experimental factors

More than two strata of experimental units

Two-Level Factorial Experiments: Basics


Example: bacteria and nuclease

Two-level factorial structure

Estimation of treatment contrasts

Testing factorial effects

Additional guidelines for model editing

Two-Level Factorial Experiments: Blocking


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


Regular fractional factorial designs


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


Example: semiconductors and simulation

Factorial structure of group screening designs

Group screening design considerations

Case study

Regression Experiments: First-Order Polynomial Models


Polynomial models

Designs for first-order models

Blocking experiments for first-order models

Split-plot regression experiments


Regression Experiments: Second-Order Polynomial Models


Quadratic polynomial models

Designs for second-order models

Design scaling and information

Orthogonal blocking

Split-plot designs

Bias due to omitted model terms

Introduction to Optimal Design


Optimal design fundamentals

Optimality criteria





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

About the Author

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.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General