Design and Analysis of Experiments with R: 1st Edition (Hardback) book cover

Design and Analysis of Experiments with R

1st Edition

By John Lawson

Chapman and Hall/CRC

620 pages | 162 B/W Illus.

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pub: 2014-12-17
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Description

Design and Analysis of Experiments with R presents a unified treatment of experimental designs and design concepts commonly used in practice. It connects the objectives of research to the type of experimental design required, describes the process of creating the design and collecting the data, shows how to perform the proper analysis of the data, and illustrates the interpretation of results.

Drawing on his many years of working in the pharmaceutical, agricultural, industrial chemicals, and machinery industries, the author teaches students how to:

  • Make an appropriate design choice based on the objectives of a research project
  • Create a design and perform an experiment
  • Interpret the results of computer data analysis

The book emphasizes the connection among the experimental units, the way treatments are randomized to experimental units, and the proper error term for data analysis. R code is used to create and analyze all the example experiments. The code examples from the text are available for download on the author’s website, enabling students to duplicate all the designs and data analysis.

Intended for a one-semester or two-quarter course on experimental design, this text covers classical ideas in experimental design as well as the latest research topics. It gives students practical guidance on using R to analyze experimental data.

Reviews

"This is an excellent but demanding text. … This book should be mandatory reading for anyone teaching a course in the statistical design of experiments. … reading this text is likely to influence their course for the better."

MAA Reviews, March 2015

"In my opinion, this is a very valuable book. It covers the topics that I judge should be in such a book including what might be called the standard designs and more … it has become my go to text on experimental design."

David E. Booth, Technometrics

Table of Contents

Introduction

Statistics and Data Collection

Beginnings of Statistically Planned Experiments

Definitions and Preliminaries

Purposes of Experimental Design

Types of Experimental Designs

Planning Experiments

Performing the Experiments

Use of R Software

Completely Randomized Designs with One Factor

Introduction

Replication and Randomization

A Historical Example

Linear Model for Completely Randomized Design (CRD)

Verifying Assumptions of the Linear Model

Analysis Strategies When Assumptions Are Violated

Determining the Number of Replicates

Comparison of Treatments after the F-Test

Factorial Designs

Introduction

Classical One at a Time versus Factorial Plans

Interpreting Interactions

Creating a Two-Factor Factorial Plan in R

Analysis of a Two-Factor Factorial in R

Factorial Designs with Multiple Factors—Completely Randomized Factorial Design (CRFD)

Two-Level Factorials

Verifying Assumptions of the Model

Randomized Block Designs

Introduction

Creating a Randomized Complete Block (RCB) Design in R

Model for RCB

An Example of a RCB

Determining the Number of Blocks

Factorial Designs in Blocks

Generalized Complete Block Design

Two Block Factors Latin Square Design (LSD)

Designs to Study Variances

Introduction

Random Sampling Experiments (RSE)

One-Factor Sampling Designs

Estimating Variance Components

Two-Factor Sampling Designs—Factorial RSE

Nested SE

Staggered Nested SE

Designs with Fixed and Random Factors

Graphical Methods to Check Model Assumptions

Fractional Factorial Designs

Introduction to Completely Randomized Fractional Factorial (CRFF)

Half Fractions of 2k Designs

Quarter and Higher Fractions of 2k Designs

Criteria for Choosing Generators for 2k-p Designs

Augmenting Fractional Factorials

Plackett–Burman (PB) Screening Designs

Mixed-Level Fractional Factorials Orthogonal Array (OA)

Definitive Screening Designs

Incomplete and Confounded Block Designs

Introduction

Balanced Incomplete Block (BIB) Designs

Analysis of Incomplete Block Designs

Partially Balanced Incomplete Block (PBIB) Designs—Balanced Treatment Incomplete Block (BTIB)

Row Column Designs

Confounded 2k and 2k-p Designs

Confounding 3 Level and p Level Factorial Designs

Blocking Mixed-Level Factorials and OAs

Partially CBF

Split-Plot Designs

Introduction

Split-Plot Experiments with CRD in Whole Plots (CRSP)

RCB in Whole Plots (RBSP)

Analysis Unreplicated 2k Split-Plot Designs

2k-p Fractional Factorials in Split Plots (FFSP)

Sample Size and Power Issues for Split-Plot Designs

Crossover and Repeated Measures Designs

Introduction

Crossover Designs (COD)

Simple AB, BA Crossover Designs for Two Treatments

Crossover Designs for Multiple Treatments

Repeated Measures Designs

Univariate Analysis of Repeated Measures Design

Response Surface Designs

Introduction

Fundamentals of Response Surface Methodology

Standard Designs for Second-Order Models

Creating Standard Response Surface Designs in R

Non-Standard Response Surface Designs

Fitting the Response Surface Model with R

Determining Optimum Operating Conditions

Blocked Response Surface (BRS) Designs

Response Surface Split-Plot (RSSP) Designs

Mixture Experiments

Introduction

Models and Designs for Mixture Experiments

Creating Mixture Designs in R

Analysis of Mixture Experiment

Constrained Mixture Experiments

Blocking Mixture Experiments

Mixture Experiments with Process Variables

Mixture Experiments in Split-Plot Arrangements

Robust Parameter Design Experiments

Introduction

Noise Sources of Functional Variation

Product Array Parameter Design Experiments

Analysis of Product Array Experiments

Single Array Parameter Design Experiments

Joint Modeling of Mean and Dispersion Effects

Experimental Strategies for Increasing Knowledge

Introduction

Sequential Experimentation

One-Step Screening and Optimization

An Example of Sequential Experimentation

Evolutionary Operation

Concluding Remarks

Appendix: Brief Introduction to R

Answers to Selected Exercises

Bibliography

Index

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

About the Author

John Lawson is a professor in the Department of Statistics at Brigham Young University.

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General