A First Course in the Design of Experiments A Linear Models Approach

This text stands apart from other books on experiment design. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. It begins with a general introduction to the subject, then leads readers through the theoretical results, the various design models, and the analytical concepts that provide the techniques that enable analysis of virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. It features the SAS software package, but also demonstrates how any regression program can be used for analysis. With its clear, highly readable style, A First Course in the Design of Experiments proves ideal as both a reference and a text. TOC:Introduction to the Design of Experiments.- Definition of a Linear Model.- Least Squares Estimation and Normal Equations.- Linear Model Distribution Theory.- Distribution Theory for Statistical Inference.- Inference for Multiple Regression Models.- The Completely Randomized Design.- Planned Comparisons.- Multiple Comparisons.- Randomized Complete Block Design.- Incomplete Block Designs.- Latin Square Designs.- Factorial Experiments with Two Factors.- Analysis of Covariance.- Random and Mixed Models.- Nested Designs and Associated Topics.- Other Designs and Topics.- Appendix A: Matrix Algebra.- Appendix B: Tables.- References.- Index.

Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique.A First Course in the Design of Experiments: A Linear Models Approach stands apart. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. The authors begin with a general introduction then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. The authors use the SAS software package throughout the book, but also demonstrate how any regression program can be used for analysis.With its balanced presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.

INTRODUCTION TO THE DESIGN OF EXPERIMENTS Designing Experiments Types of Designs Topics in Text LINEAR MODELS Definition of a Linear Model Simple Linear Regression Least Squares Criterion Multiple Regression Polynomial Regression One-Way Classification LEAST SQUARES ESTIMATION AND NORMAL EQUATIONS Least Squares Estimation Solutions to Normal Equations-Generalized Inverse Approach Invariance Properties and Error Sum of Squares Solutions to Normal Equations-Side Conditions Approach LINEAR MODEL DISTRIBUTION THEORY Usual Linear Model Assumptions Moments of Response and Solutions Vector Estimable Functions Gauss-Markoff Theorem The Multivariate Normal Distribution The Normal Linear Model DISTRIBUTION THEORY FOR STATISTICAL INFERENCE Distribution of Quadratic Forms Independence of Quadratic Forms Interval Estimation for Estimable Functions Testing Hypotheses INFERENCE FOR MULTIPLE REGRESSION MODELS The Multiple Regression Model Revisited Computer-Aided Inference in Regression Regression Analysis of Variance SS( ) Notation and Adjusted Sums of Squares Orthogonal Polynomials Response Analysis Using Orthogonal Polynomials THE COMPLETELY RANDOMIZED DESIGN Experimental Design Nomenclature Completely Randomized Design Least Squares Results Analysis of Variance and F-Test Confidence Intervals and Tests Reparametrization for a Completely Randomized Design Expected Mean Squares, Restricted Model Design Considerations Checking Assumptions Summary Example-A Balanced CRD Illustration PLANNED COMPARISONS Introduction Method of Orthogonal Treatment Contrasts Nature of Response for Quantitative Factors Error Levels and Bonferroni Procedure MULTIPLE COMPARISONS Introduction Bonferroni and Fisher's LSD Procedures Tukey Multiple Comparison Procedure Scheffé Multiple Comparison Procedures Stepwise Multiple Comparison Procedures Computer Usage for Multiple Comparisons Comparison of Procedures, Recommendations RANDOMIZED COMPLETE BLOCK DESIGN Blocking Randomized Compete Block Design Least Squares Results Analysis of Variance and F-Tests Inference for Treatment Contrasts Reparametrization of a RCBD Expected Mean Squares, Restricted RCBD Model Design Considerations Summary Example INCOMPLETE BLOCK DESIGNS Incomplete Blocks Analysis for Incomplete Blocks-Linear Models Approach Analysis for Incomplete Blocks-Reparametrized Approach Balanced Incomplete Block Design LATIN SQUARE DESIGNS Latin Squares Least Squares Results Inferences for a LSD Reparametrization of a LSD Expected Mean Squares, Restricted LSD Model Design Considerations FACTORIAL EXPERIMENTS WITH TWO FACTORS Introduction Model for Two-Factor Factorial, Interaction Least Squares Results Inferences for Two-Factor Factorials Reparametrized Model Expected Mean Squares Special Cases for Factorials Assumptions, Design Considerations OTHER FACTORIAL EXPERIMENTS Factorial Experiments with Three or More Factors Factorial Experiments with Other Designs Special Factorial Experiments-2k Quantitative Factors, 3k Factorial Fractional Factorials, Confounded ANALYSIS OF COVARIANCE Introduction Inferences for a Simple Covariance Model Testing for Equal Slopes Multiple Comparisons, Adjusted Means Other Covariance Models Design Considerations RANDOM AND MIXED MODELS Random Effects Mixed Effects Models Introduction to Nested Designs-Fixed Case Nested Designs-Mixed Model Expected Mean Squares Algorithm Factorial Experiments-Mixed Model Pseudo F-Tests Variance Components NESTED DESIGNS AND ASSOCIATED TOPICS Higher Order Nested Designs Designs with Nested and Crossed Factors Subsampling Repeated Measures Designs OTHER DESIGNS AND TOPICS Split Plot Designs Crossover Designs Response Surfaces Selecting a Design Appendix A: Matrix Algebra Appendix B: Tables References Index Each chapter also includes exercises

John H. Skillings, Donald Weber