1st Edition

Design of Experiments An Introduction Based on Linear Models

By Max Morris Copyright 2011
    376 Pages 13 B/W Illustrations
    by Chapman & Hall

    376 Pages 13 B/W Illustrations
    by Chapman & Hall

    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.

    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.

    Biography

    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.

    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