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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 Experiments1.1 Introduction1.2 The Use of Designed Experiments in Process Studies1.3 Fundamental Aspects of Designed Experiments1.4 Documentation Form for a Designed Experiment1.5 SummaryReferencesExercises 2. Investigating a Single Factor: Completely Randomized Experiments2.1 Introduction and Graphical Analysis of Sample Data2.2 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 Model2.3 Methods for Multiple Comparisons 2.3.1 Tukey's Method for Multiple Comparisons 2.3.2 Scheffe's Method for Multiple Comparisons2.4 Potential Consequences of Violating Analysis of Variance Assumptions2.5 The Use of P-values in Testing Statistical Hypotheses2.6 SummaryReferencesExercisesAppendix 2: Introduction to and Computer Instructions for Using Minitab, Release 15 3. Investigating a Single Factor: Randomized Complete and Incomplete Block and Latin Square Designs3.1 Introduction3.2 Analysis of Variance for Blocked Data: Partitioning the Total Variation in the Data3.3 Assumptions and Validity of Analysis of Variance for Randomized Complete Block Designs3.4 Tukey and Scheffe's Procedures for a Randomized Complete Block Design3.5 Balanced Incomplete Block Designs3.6 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 Designs3.7 SummaryReferencesExercisesAppendix 3: Minitab Instructions 4. Factorial Experiments: Completely Randomized Designs4.1 Introduction4.2 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 Squares4.3 No Replication in Factorial Experiments4.4 Fixed, Random, and Mixed Models: Expected Mean Squares4.5 SummaryReferencesExercisesAppendix 4: Minitab Instructions 5. Factorial Experiments: Randomized Block and Latin Square Designs5.1 Introduction5.2 Factorial Experiments in Randomized Complete Blocks5.3 Factorial Experiments in Latin Square Designs5.4 SummaryReferencesExercisesAppendix 5: Minitab Instructions 6. Nested Factorial Experiments and Repeated Measures Designs6.1 Introduction6.2 Nested Factorial Experiments6.3 Repeated Measures Designs6.4 SummaryReferencesExercisesAppendix 6: Minitab Instructions 7. 2f and 3f Factorial Experiments7.1 Introduction7.2 2f Factorial Experiments7.3 3f Factorial Experiments7.4 SummaryReferencesExercisesAppendix 7: Minitab Instructions 8. Confounding in 2f and 3f Factorial Experiments8.1 Introduction8.2 The Concept of Confounding8.3 Choosing Effects to Confound in 2f Factorial Experiments: Defining Contrasts8.4 2f Factorial Experiments in Four Blocks8.5 Confounding in 3f Factorial Experiments8.6 SummaryReferencesExercisesAppendix 8: Minitab Instructions 9. Fractional Factorial Experiments9.1 Introduction9.2 One-Half Fractions of 2f Factorial Experiments9.3 One-Fourth Fractions of 2f Factorial Experiments9.4 Fractions of 3f Factorial Experiments9.5 A Comparison of Fractions of 2f Experiments with Fractions of 3f Experiments9.6 SummaryReferencesExercisesAppendix 9: Minitab Instructions 10. Regression Analysis: The General Linear Model10.1 Introduction10.2 Uses of Regression Equations10.3 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 Variation10.4 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 Prediction10.5 Incorporating Qualitative Predictor Variables in the General Linear Model10.6 Curvilinear Regression Models10.7 Analysis of Residuals and the Problem of Collinearity 10.7.1 The Analysis of Residuals 10.7.2 The Problem of Collinearity10.8 Criteria for Selecting the Best Set of Predictor Variables 10.8.1 Variable Selection Techniques10.9 SummaryReferencesExercisesAppendix 10A: Minitab InstructionsAppendix 10B: A Brief Review of Matrix Algebra 11. Response Surface Designs for First- and Second-Order Models11.1 Introduction11.2 Response Surface Designs for Fitting First-Order Models11.3 Response Surface Designs for Fitting Second-Order Models11.4 SummaryReferencesExercisesAppendix 11: Minitab InstructionsAnswers to Selected Odd-Numbered ExercisesIndex
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