Design of Experiments: An Introduction Based on Linear Models
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Features
- Discusses the explicit relationship between experimental design and the quality of data analysis
- Presents the fundamental concepts and techniques of experimental design
- Describes specific forms or classes of experimental designs
- Contains an introduction to design for regression models
- Performs calculations using R, with commands provided in an appendix
- Incorporates actual experiments drawn from the scientific and technical literature
- Includes many end-of-chapter exercises
Solutions manual available upon qualified course adoption
Summary
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.
Table of 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(s)
Editorial Reviews
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
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| errata.pdf | Cross Platform | December 01, 2011 | Errata |
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