Design of Experiments An Introduction Based on Linear Models

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.

IntroductionExample: rainfall and grassland Basic elements of an experimentExperiments and experiment-like studies Models and data analysis Linear Statistical ModelsLinear vector spaces Basic linear model The hat matrix, least-squares estimates, and design information matrixThe partitioned linear model The reduced normal equations Linear and quadratic forms Estimation and information Hypothesis testing and informationBlocking and information Completely Randomized DesignsIntroductionModels Matrix formulation Influence of design on estimation Influence of design on hypothesis testing Randomized Complete Blocks and Related DesignsIntroductionA modelMatrix formulation Influence of design on estimation Influence of design on hypothesis testing Orthogonality and "Condition E" Latin Squares and Related DesignsIntroductionReplicated Latin squaresA modelMatrix formulation Influence of design on quality of inference More general constructions: Graeco-Latin squares Some Data Analysis for CRDs and Orthogonally Blocked Designs Introduction DiagnosticsPower transformations Basic inferenceMultiple comparisons Balanced Incomplete Block DesignsIntroductionA modelMatrix formulationInfluence 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 StructureIntroduction An overparameterized modelAn equivalent full-rank model Estimation Partitioning of variability and hypothesis testing Factorial experiments as CRDs, CBDs, LSDs, and BIBDs Model reduction Split-Plot DesignsIntroduction SPD(R,B) SPD(B,B) More than two experimental factors More than two strata of experimental units Two-Level Factorial Experiments: BasicsIntroduction Example: bacteria and nuclease Two-level factorial structure Estimation of treatment contrastsTesting factorial effectsAdditional guidelines for model editing Two-Level Factorial Experiments: BlockingIntroductionComplete 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 FactorialsIntroduction Regular fractional factorial designs Analysis Example: bacteria and bacteriocin Comparison of fractions Blocking regular fractional factorial designs Augmenting regular fractional factorial designsIrregular fractional factorial designs Factorial Group Screening Experiments Introduction Example: semiconductors and simulation Factorial structure of group screening designsGroup screening design considerationsCase 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 ModelsIntroduction 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 criteriaAlgorithms Appendices References Index A Conclusion and Exercises appear at the end of each chapter.

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.