A First Course in The Design of Experiments

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 to the subject, then lead readers through the theoretical results, the various design models, and the analytical concepts that provide the techniques that enable them to analyze virtually any design. Rife with examples and exercises illustrating its concepts, 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, integrated presentation of theory, methods, and applications, criteria for selecting the appropriate experimental design, and clear, highly readable style, A First Course in the Design of Experiments proves ideal as both a reference and a text.

Table of contents

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-Sit Conditions Approach

Linear Model Distribution Theory

Usual Linear Model Assumptions

Moments of Response and Solution 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 Sum of Squares

Orthogonal Polynomials

Response Analysis Using Orthogonal Polynomials

The Completely Randomized Design

Experimental Design Nomenclature

The Completely Randomized Design

Least Squares Results

Analysis of Variance and F-Test

Confidence Intervals and Tests

Reparametrization of 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

Scheffe 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 Square Designs

Least Squares Results

Inferences for an LSD

Reparametrization of an 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 Factorial

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

Inference 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