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Design of Experiments

An Introduction Based on Linear Models

By Max Morris

Chapman and Hall/CRC – 2010 – 370 pages

Series: Chapman & Hall/CRC Texts in Statistical Science

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    978-1-58488-923-6
    July 26th 2010

Description

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.

Reviews

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

Contents

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 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

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

Additional guidelines for model editing

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

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

Introduction

Optimal design fundamentals

Optimality criteria

Algorithms

Appendices

References

Index

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

Author Bio

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.

Name: Design of Experiments: An Introduction Based on Linear Models (Hardback)Chapman and Hall/CRC 
Description: By Max Morris. 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...
Categories: Statistical Theory & Methods, Mathematics & Statistics for Engineers, Statistics for the Biological Sciences