Design and Analysis of Experiments Classical and Regression Approaches with SAS

About this book

Recently, there has been a welcome attempt to emphasize the analysis of experimental data as a regression problem involving dummy variables. With the growth of statistical computing and the availability of cutting-edge software, the time has come for such new approaches. Focusing on novel regression methods that make use of dummy variables, Design and Analysis of Experiments presents classical experimental design and data analysis using the invaluable tool of SAS. The text provides numerous examples and hands-on exercises to illustrate both the theoretical foundations and the computational approaches for different experimental designs. It also includes full code and outputs for SAS analyses.

Contents

Introductory Statistical Inference and Regression Analysis Elementary Statistical Inference Regression Analysis Experiments, the Completely Randomized Design (CRD)--Classical and Regression Approaches Experiments Experiments to Compare Treatments Some Basic Ideas Requirements of a Good Experiment One-Way Experimental Layout or the CRD: Design and Analysis Analysis of Experimental Data (Fixed Effects Model) Expected Values for the Sums of Squares The Analysis of Variance (ANOVA) Table Follow-Up Analysis to Check for Validity of the Model Checking Model Assumptions Applications of Orthogonal Contrasts Regression Models for the CRD (One-Way Layout) Regression Models for ANOVA for CRD Using Orthogonal Contrasts Regression Model for Example 2.2 Using Orthogonal Contrasts Coding (Helmert Coding) Regression Model for Example 2.3 Using Orthogonal Contrasts Coding Two-Factor Factorial Experiments and Repeated Measures Designs (RMDs) The Full Two-Factor Factorial Experiment (Two-Way ANOVA with Replication)--Fixed Effects Model Two-Factor Factorial Effects (Random Effects Model) Two-Factor Factorial Experiment (Mixed Effects Model) One-Way RMD Mixed Randomized Complete Block Design (RCBD) (Involving Two Factors) Regression Approaches to the Analysis of Responses of Two-Factor Experiments and RMDs Regression Models for the Two-Way ANOVA (Full Two-Factor Factorial Experiment) The Regression Model for Two-Factor Factorial Experiment Using Reference Cell Coding for Dummy Variables Use of SAS for the Analysis of Responses of Mixed Models Use of PROC Mixed in the Analysis of Responses of RMD in SAS Residual Analysis for the Vitamin Experiment Regression Model of the Two-Factor Factorial Design Using Orthogonal Contrasts Use of PROC Mixed in SAS to Estimate Variance Components When Levels of Factors Are Random Designs with Randomization Restriction--Randomized Complete Block, Latin Squares, and Related Designs RCBD Testing for Differences in Block Means Estimation of a Missing Value in the RCBD Latin Squares Some Expected Mean Squares Replications in Latin Square Design The Graeco--Latin Square Design Estimation of Parameters of the Model and Extracting Residuals Regression Models for Randomized Complete Block, Latin Squares, and Graeco--Latin Square Designs Regression Models for the RCBD SAS Analysis of Responses of Example 5.1 Using Dummy Regression (Effects Coding Method) Dummy Variables Regression Model for the RCBD (Reference Cell Method) Application of Dummy Variables Regression Model to Example 5.2 (Effects Coding Method) Regression Model for RCBD of Example 5.2 (Reference Cell Coding) Regression Models for the Latin Square Design Dummy Variables Regression Analysis for Example 5.5 (Reference Cell Method) Regression Model for Example 5.7 Using Effects Coding Method to Define Dummy Variables Dummy Variables Regression Model for Example 5.7 (Reference Cell Coding Method) Regression Model for the Graeco--Latin Square Design Regression Model for Graeco--Latin Square (Reference Cell Method) Regression Model for the RCBD Using Orthogonal Contrasts Factorial Designs--The 2k and 3k Factorial Designs Advantages of Factorial Designs The 2k and 3k Factorial Designs Contrasts for Factorial Effects in 22 and 23 Factorial Designs The General 2k Factorial Design Factorial Effects in 2k Factorial Designs The 3k Factorial Designs Extension to k Factors at Three Levels Regression Models for 2k and 3k Factorial Designs Regression Models for the 22 Factorial Design Using Effects Coding Method Regression Model for Example 7.1 Using Reference Cell to Define Dummy Variables General Regression Models for the Three-Way Factorial Design The General Regression Model for a Three-Way ANOVA (Reference Cell Coding Method) Regression Models for the Four-Factor Factorial Design Using Effects Coding Method Regression Analysis for a Four-Factor Factorial Experiment Using Reference Cell Coding to Define Dummy Variables Dummy Variables Regression Models for Experiment in 3k Factorial Designs Fitting Regression Model for Example 7.5 (Effects Coding Method) Fitting Regression Model 8.22 (Reference Cell Coding Method) to Responses of Experiment of Example 7.5 Fractional Replication and Confounding in 2k and 3k Factorial Designs Construction of the 2k 1 Fractional Factorial Design Contrasts of the 2k 1 Fractional Factorial Design The General 2k p Fractional Factorial Design Resolution of a Fractional Factorial Design Fractional Replication in 3k Factorial Designs The General 3k p Factorial Design Confounding in 2k and 3k Factorial Designs Confounding in 2k Factorial Designs Confounding in 3k Factorial Designs Partial Confounding in Factorial Designs Balanced Incomplete Blocks, Lattices, and Nested Designs The Balanced Incomplete Block Design Comparison of Two Treatments Orthogonal Contrasts in Balanced Incomplete Block Designs Lattice Designs Partially Balanced Lattices Nested or Hierarchical Designs Designs with Nested and Crossed Factors Methods for Fitting Response Surfaces and Analysis of Covariance Method of Steepest Ascent Designs for Fitting Response Surfaces Fitting a First-Order Model to the Response Surface Fitting and Analysis of the Second-Order Model Analysis of Covariance (ANCOVA) One-Way ANCOVA Other Covariance Models Multivariate Analysis of Variance (MANOVA) Link between ANOVA and MANOVA One-Way MANOVA MANOVA--The Randomized Complete Block Experiment Multivariate Two-Way Experimental Layout with Interaction Two-Stage Multivariate Nested or Hierarchical Design The Multivariate Latin Square Design Appendix: Statistical Tables Index Exercises and References appear at the end of each chapter.

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