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Design and Analysis of Experiments

Classical and Regression Approaches with SAS

By Leonard C. Onyiah

Chapman and Hall/CRC – 2008 – 856 pages

Series: Statistics: A Series of Textbooks and Monographs

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    978-1-42-006054-6
    July 28th 2008

Description

Unlike other books on the modeling and analysis of experimental data, Design and Analysis of Experiments: Classical and Regression Approaches with SAS not only covers classical experimental design theory, it also explores regression approaches. Capitalizing on the availability of cutting-edge software, the author uses both manual methods and SAS programs to carry out analyses.

The book presents most of the different designs covered in a typical experimental design course. It discusses the requirements for good experimentation, the completely randomized design, the use of orthogonal contrast to test hypotheses, and the model adequacy check. With an emphasis on two-factor factorial experiments, the author analyzes repeated measures as well as fixed, random, and mixed effects models. He also describes designs with randomization restrictions, before delving into the special cases of the 2k and 3k factorial designs, including fractional replication and confounding. In addition, the book covers response surfaces, balanced incomplete block and hierarchical designs, ANOVA, ANCOVA, and MANOVA.

Fortifying the theory and computations with practical exercises and supplemental material, this distinctive text provides a modern, comprehensive treatment of experimental design and analysis.

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 2k1 Fractional Factorial Design

Contrasts of the 2k1 Fractional Factorial Design

The General 2kp Fractional Factorial Design

Resolution of a Fractional Factorial Design

Fractional Replication in 3k Factorial Designs

The General 3kp 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.

Name: Design and Analysis of Experiments: Classical and Regression Approaches with SAS (Hardback)Chapman and Hall/CRC 
Description: By Leonard C. Onyiah. Unlike other books on the modeling and analysis of experimental data, Design and Analysis of Experiments: Classical and Regression Approaches with SAS not only covers classical experimental design theory, it also explores regression approaches...
Categories: Statistics for the Biological Sciences, Mathematics & Statistics for Engineers, Statistical Theory & Methods