1st Edition

Design and Analysis of Experiments with R

By John Lawson Copyright 2015
    628 Pages 162 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    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