A first course in the design of experiments
A Linear Models Approach
Hardle, Donald Weber, John H. Skillings
Résumé
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
Scheff 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
Caractéristiques techniques
PAPIER | |
Éditeur(s) | Springer |
Auteur(s) | Hardle, Donald Weber, John H. Skillings |
Parution | 24/11/1999 |
Nb. de pages | 680 |
Format | 16 x 24 |
Couverture | Relié |
Poids | 1138g |
EAN13 | 9783540662075 |
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