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-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