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.
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 Scheffe'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 Scheffe'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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