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Design and Analysis of Experiments with R

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Table of Contents

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
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
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
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
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
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
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
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
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
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
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
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



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.


"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

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