Student Solutions Manual for Introduction to the Design & Analysis of Experiments

Description

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 σ²ε

            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

• 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.

This manual contains worked-out solutions for all the odd-numbered exercises in the text.