Description
Introduction to the Design & Analysis of Experiments introduces readers to the design and analysis of experiments. It is ideal for a one-semester, upper-level undergraduate course for majors in statistics and other mathematical sciences, natural sciences, and engineering. It may also serve appropriate graduate courses in disciplines such as business, health sciences, and social sciences. This book assumes that the reader has completed a two-semester sequence in the application of probability and statistical inference.
Features
- The strong emphasis on design helps students learn to minimize variation of response variables in their experiments, producing more meaningful results with less random error.
- A documentation form at the beginning of the book gives students a detailed checklist so they can develop experiments in a consistent way.
- A graphical approach to the analysis of the sample data imparts a visual understanding of the impending results.
- Detailed, worked-out examples in each chapter illustrate important concepts and methods. Probing and "what if" questions teach students to consider alternative designs to adapt to specific conditions.
- Statistics software is integrated throughout the text to help students develop a conceptual understanding of methods, without getting lost in the mathematical techniques.
- Step-by-step Minitab® instructions in the appendices show students how to arrive at the results presented in the chapters.
Table of Contents
1. An Introduction to the Design of Experiments
1.1 Introduction
1.2 The Use of Designed Experiments in Process Studies
1.3 Fundamental Aspects of Designed Experiments
1.4 Documentation Form for a Designed Experiment
1.5 Summary
References
Exercises
2. Investigating a Single Factor: Completely Randomized Experiments
2.1 Introduction and Graphical Analysis of Sample Data
2.2 The Analysis of Variance Approach: Partitioning the Total Variation in the Data
2.2.1 Analysis of Variance for a Fixed Effects Model
2.2.2 Analysis of Variance for a Random Effects Model
2.3 Methods for Multiple Comparisons
2.3.1 Tukey's Method for Multiple Comparisons
2.3.2 Scheffé's Method for Multiple Comparisons
2.4 Potential Consequences of Violating Analysis of Variance Assumptions
2.5 The Use of P-values in Testing Statistical Hypotheses
2.6 Summary
References
Exercises
Appendix 2: Introduction to and Computer Instructions for Using Minitab, Release 15
3. Investigating a Single Factor: Randomized Complete and Incomplete Block and Latin Square Designs
3.1 Introduction
3.2 Analysis of Variance for Blocked Data: Partitioning the Total Variation in the Data
3.3 Assumptions and Validity of Analysis of Variance for Randomized Complete Block Designs
3.4 Tukey and Scheffé's Procedures for a Randomized Complete Block Design
3.5 Balanced Incomplete Block Designs
3.6 Latin Square Designs
3.6.1 Analysis of Variance for Latin Square Designs: Partitioning the Total Variation in the Data
3.6.2 Assumptions and Validity of the Analysis of Variance for Latin Square Designs
3.7 Summary
References
Exercises
Appendix 3: Minitab Instructions
4. Factorial Experiments: Completely Randomized Designs
4.1 Introduction
4.2 Inference Objectives in Factorial Experiments: Main Effects and Interaction Effects
4.2.1 Complete Randomization in Factorial Experiments
4.2.2 Graphical Analysis
4.2.3 Analysis of Variance Procedure: Partitioning the Total Sum of Squares
4.3 No Replication in Factorial Experiments
4.4 Fixed, Random, and Mixed Models: Expected Mean Squares
4.5 Summary
References
Exercises
Appendix 4: Minitab Instructions
5. Factorial Experiments: Randomized Block and Latin Square Designs
5.1 Introduction
5.2 Factorial Experiments in Randomized Complete Blocks
5.3 Factorial Experiments in Latin Square Designs
5.4 Summary
References
Exercises
Appendix 5: Minitab Instructions
6. Nested Factorial Experiments and Repeated Measures Designs
6.1 Introduction
6.2 Nested Factorial Experiments
6.3 Repeated Measures Designs
6.4 Summary
References
Exercises
Appendix 6: Minitab Instructions
7. 2f and 3f Factorial Experiments
7.1 Introduction
7.2 2f Factorial Experiments
7.3 3f Factorial Experiments
7.4 Summary
References
Exercises
Appendix 7: Minitab Instructions
8. Confounding in 2f and 3f Factorial Experiments
8.1 Introduction
8.2 The Concept of Confounding
8.3 Choosing Effects to Confound in 2f Factorial Experiments: Defining Contrasts
8.4 2f Factorial Experiments in Four Blocks
8.5 Confounding in 3f Factorial Experiments
8.6 Summary
References
Exercises
Appendix 8: Minitab Instructions
9. Fractional Factorial Experiments
9.1 Introduction
9.2 One-Half Fractions of 2f Factorial Experiments
9.3 One-Fourth Fractions of 2f Factorial Experiments
9.4 Fractions of 3f Factorial Experiments
9.5 A Comparison of Fractions of 2f Experiments with Fractions of 3f Experiments
9.6 Summary
References
Exercises
Appendix 9: Minitab Instructions
10. Regression Analysis: The General Linear Model
10.1 Introduction
10.2 Uses of Regression Equations
10.3 Estimating the Parameters of the General Linear Regression Model
10.3.1 The General Linear Regression Model
10.3.2 The Method of Least Squares
10.3.3 Estimating the Error Variance s2e
10.3.4 The Coefficient of Determination: Partitioning the Total Variation
10.4 How Good Is the Model? Statistical Inference for the General Linear Regression Model
10.4.1 Statistical Inferences on the Overall Model: An Analysis of Variance Approach
10.4.2 Evaluating the Contribution of an Individual Predictor Variable
10.4.3 Using the Least Squares Equation for Estimation and Prediction
10.5 Incorporating Qualitative Predictor Variables in the General Linear Model
10.6 Curvilinear Regression Models
10.7 Analysis of Residuals and the Problem of Collinearity
10.7.1 The Analysis of Residuals
10.7.2 The Problem of Collinearity
10.8 Criteria for Selecting the Best Set of Predictor Variables
10.8.1 Variable Selection Techniques
10.9 Summary
References
Exercises
Appendix 10A: Minitab Instructions
Appendix 10B: A Brief Review of Matrix Algebra
11. Response Surface Designs for First- and Second-Order Models
11.1 Introduction
11.2 Response Surface Designs for Fitting First-Order Models
11.3 Response Surface Designs for Fitting Second-Order Models
11.4 Summary
References
Exercises
Appendix 11: Minitab Instructions
Answers to Selected Odd-Numbered Exercises
Index
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