A First Course in the Design of Experiments: A Linear Models Approach

by Skillings; John H.

• ISBN13: 9780849396717
• ISBN10: 0849396719
• eBook ISBN(s): 9781351469968
• Format: Hardcover
• Copyright: 1999-11-24
• Publisher: CRC Press
• More Book Details

Summary

Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique.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 then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, 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 presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.

Table of Contents

Introduction to the Design of Experiments	1	(8)
Designing Experiments	1	(4)
Types of Designs	5	(1)
Topics in Text	6	(3)
Linear Models	9	(26)
Definition of a Linear Model	9	(2)
Simple Linear Regression	11	(2)
Least Squares Criterion	13	(6)
Multiple Regression	19	(3)
Polynomial Regression	22	(3)
One-Way Classification	25	(10)
Exercises	29	(6)
Least Squares Estimation and Normal Equations	35	(28)
Least Squares Estimation	35	(7)
Solutions to Normal Equations -- Generalized Inverse Approach	42	(4)
Invariance Properties and Error Sum of Squares	46	(3)
Solutions to Normal Equations -- Side Conditions Approach	49	(14)
Exercises	53	(10)
Linear Model Distribution Theory	63	(40)
Usual Linear Model Assumptions	63	(3)
Moments of Response and Solutions Vector	66	(6)
Estimable Functions	72	(6)
Gauss-Markoff Theorem	78	(10)
The Multivariate Normal Distribution	88	(3)
The Normal Linear Model	91	(12)
Exercises	93	(10)
Distribution Theory for Statistical Inference	103	(36)
Distribution of Quadratic Forms	103	(7)
Independence of Quadratic Forms	110	(3)
Interval Estimation for Estimable Functions	113	(7)
Testing Hypotheses	120	(19)
Exercises	132	(7)
Inference for Multiple Regression Models	139	(46)
The Multiple Regression Model Revisited	139	(3)
Computer-Aided Inference in Regression	142	(12)
Regression Analysis of Variance	154	(6)
SS() Notation and Adjusted Sums of Squares	160	(2)
Orthogonal Polynomials	162	(8)
Response Analysis Using Orthogonal Polynomials	170	(15)
Exercises	176	(9)
The Completely Randomized Design	185	(68)
Experimental Design Nomenclature	185	(3)
Completely Randomized Design	188	(2)
Least Squares Results	190	(4)
Analysis of Variance and F-test	194	(8)
Confidence Intervals and Tests	202	(4)
Reparametrization of a Completely Randomized Design	206	(6)
Expected Mean Squares, Restricted Model	212	(5)
Design Considerations	217	(2)
Checking Assumptions	219	(16)
Summary Example -- A Balanced CRD Illustration	235	(18)
Exercises	241	(12)
Planned Comparisons	253	(28)
Introduction	253	(1)
Method of Orthogonal Treatment Contrasts	253	(8)
Nature of Response for Quantitative Factors	261	(6)
Error Levels and Bonferroni Procedure	267	(14)
Exercises	276	(5)
Multiple Comparisons	281	(26)
Introduction	281	(1)
Bonferroni and Fisher's Least Significant Difference Procedures	282	(3)
Tukey Multiple Comparison Procedure	285	(5)
Scheffe Multiple Comparison Procedure	290	(2)
Stepwise Multiple Comparison Procedures	292	(5)
Computer Usage for Multiple Comparisons	297	(6)
Comparison of Procedures, Recommendations	303	(4)
Exercises	304	(3)
Randomized Complete Block Design	307	(56)
Blocking	307	(5)
Randomized Complete Block Design	312	(4)
Least Squares Results	316	(6)
Analysis of Variance and F-Tests	322	(7)
Inference for Treatment Contrasts	329	(4)
Reparametrization of an RCBD	333	(13)
Expected Mean Squares, Restricted RCBD Model	346	(2)
Design Considerations	348	(2)
Summary Example	350	(13)
Exercises	354	(9)
Incomplete Block Designs	363	(22)
Incomplete Blocks	363	(2)
Analysis for Incomplete Blocks -- Linear Models Approach	365	(6)
Analysis for Incomplete Blocks -- Reparametrized Approach	371	(5)
Balanced Incomplete Block Design	376	(9)
Exercises	379	(6)
Latin Square Designs	385	(28)
Latin Squares	385	(2)
Least Squares Results	387	(4)
Inference for an LSD	391	(8)
Reparametrization of an LSD	399	(3)
Expected Mean Squares, Restricted LSD Model	402	(1)
Design Considerations	403	(10)
Exercises	406	(7)
Factorial Experiments with Two Factors	413	(46)
Introduction	413	(2)
Model for Two-Factor Factorial and Interaction	415	(4)
Least Squares Results	419	(7)
Inferences for Two-Factor Factorials	426	(9)
Reparametrized Model	435	(4)
Expected Mean Squares	439	(1)
Special Cases for Factorials	440	(8)
Assumptions, Design Considerations	448	(11)
Exercises	449	(10)
Other Factorial Experiments	459	(38)
Factorial Experiments with Three or More Factors	459	(7)
Factorial Experiments with Other Designs	466	(5)
Special Factorial Experiments -- 2k	471	(8)
Quantitative Factors, 3k Factorial	479	(4)
Fractional Factorials, Confounded	483	(14)
Exercises	489	(8)
Analysis of Covariance	497	(22)
Introduction	497	(2)
Inferences for a Simple Covariance Model	499	(7)
Testing for Equal Slopes	506	(3)
Multiple Comparisons, Adjusted Means	509	(3)
Other Covariance Models	512	(1)
Design Considerations	513	(6)
Exercises	514	(5)
Random and Mixed Models	519	(40)
Random Effects	519	(2)
Mixed Effects Models	521	(2)
Introduction to Nested Designs -- Fixed Case	523	(9)
Nested Designs -- Mixed Model	532	(5)
Expected Mean Squares Algorithm	537	(4)
Factorial Experiment -- Mixed Model	541	(3)
Pseudo F-Tests	544	(3)
Variance Components	547	(12)
Exercises	553	(6)
Nested Designs and Associated Topics	559	(20)
Higher Order Nested Designs	559	(4)
Designs with Nested and Crossed Factors	563	(2)
Subsampling	565	(2)
Repeated Measures Designs	567	(12)
Exercises	573	(6)
Other Designs and Topics	579	(40)
Split-Plot Designs	579	(9)
Crossover Designs	588	(7)
Response Surfaces	595	(12)
Selecting a Design	607	(12)
Exercises	610	(9)
Appendix A Matrix Algebra	619	(18)
A.1 Matrices	619	(6)
A.2 Vectors	625	(1)
A.3 Rank of a Matrix	626	(1)
A.4 Linear and Quadratic Forms	627	(2)
A.5 Matrix Factorizations	629	(1)
A.6 Differentiation of Vectors and Quadratic Forms	630	(7)
Exercises	632	(5)
Appendix B Tables	637	(24)
References	661	(4)
Solutions for Selected Odd-Numbered Exercises	665	(12)
Index	677