Onyiah Design and Analysis of Experiments

Classical and Regression Approaches with SAS
1. Auflage 2011
ISBN: 978-1-4200-6055-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 856 Seiten

Reihe: Statistics: A Series of Textbooks and Monographs

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.

Zielgruppe

Undergraduate students in statistics; graduate students and researchers in applied statistics, pharmaceuticals, business, biology, engineering, and computer science.

Autoren/Hrsg.

Onyiah, Leonard C.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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.