by Charles R. Hicks and Kenneth V. Turner

Edition: 5TH 99Copyright: 1999

Publisher: Oxford University Press

Published: 1999

International: No

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This text is a solid revision and redesign of Charles Hicks' comprehensive fourth edition of Fundamental Concepts in the Design of Experiments. It covers the essentials of experimental design used by applied researchers in solving problems in the field. It is appropriate for a variety of experimental methods courses found in engineering and statistics departments. Students learn to use applied statistics for planning, running, and analyzing as an experiment. Students learn to use applied statistics for planning, running, and analyzing an experiment. The text includes 350+ problems taken from the author's actual industrial consulting experiences to give students valuable practice with real data and problem solving. About 60 new problems have been added for this edition. SAS (Statistical Analysis System) computer programs are incorporated to facilitate analysis. There is extensive coverage of the analysis of residuals, the concepts of resolution in fractional replications, the Plackett-Burman designs, and Taguchi techniques. The new edition will place a greater emphasis on computer use, include additional problems, and add computer outputs from statistical packages like Minitab, SPSS, and JMP.

The book is written for anyone engaged in experimental work who has a good background in statistical inference. It will be most profitable reading to those witha background in statistical methods including analysis of variance. This text is suitable for senior undergraduate/graduate level students in mathematics, statistics, or engineering. It is appropriate for a variety of experimental methods courses found in engineering and statistics deparmtents -- majors in this course are usually in applied statistics; non-majors, in industrial and electrical engineering, or education and life sciences.

**Hicks, Charles R. : Purdue University**

**Turner, Kenneth V. Jr. : Anderson University**

Preface

**1. The Experiment, the Design, and the Analysis**

1.1. Introduction to Experimental Design

1.2. The Experiment

1.3. The Design

1.4. The Analysis

1.5. Examples

1.6. Summary in Outline

1.7. Further Reading

Problems

**2. Review of Statistical Inference**

2.1. Introduction

2.2. Estimation

2.3. Tests of Hypothesis

2.4. The Operating Characteristic Curve

2.5. How Large a Sample?

2.6. Application to Tests on Variances

2.7. Application to Tests on Means

2.8. Assessing Normality

2.9. Applications to Tests on Proportions

2.10. Analysis of Experiments with SAS

2.11. Further Reading

Problems

**3. Single-Factor Experiments with No Restrictions on Randomization**

3.1. Introduction

3.2. Analysis of Variance Rationale

3.3. After ANOVA--What?

3.4. Tests on Means

3.5. Confidence Limits on Means

3.6. Components of Variance

3.7. Checking the Model

3.8. SAS Programs for ANOVA and Tests after ANOVA

3.9. Summary

3.10. Further Reading

Problems

**4. Single-Factor Experiments: Randomized Block and Latin Square Designs**

4.1. Introduction

4.2. Randomized Complete Block Design

4.3. ANOVA Rationale

4.4. Missing Values

4.5. Latin Squares

4.6. Interpretations

4.7. Assessing the Model

4.8. Graeco-Latin Squares

4.9. Extensions

4.10. SAS Programs for Randomized Blocks and Latin Squares

4.11. Summary

4.12. Further Reading

Problems

**5. Factorial Experiments**

5.1. Introduction

5.2. Factorial Experiments: An Example

5.3. Interpretations

5.4. The Model and Its Assessment

5.5. ANOVA Rationale

5.6. One Observation Per Treatment

5.7. SAS Programs for Factorial Experiments

5.8. Summary

5.9. Further Reading

Problems

**6. Fixed, Random, and Mixed Models**

6.1. Introduction

6.2. Single-Factor Models

6.3. Two-Factor Models

6.4. EMS Rules

6.5. EMS Derivations

6.6. The Pseudo-F Test

6.7. Expected Mean Squares Via Statistical Computing Packages

6.8. Remarks

6.9. Repeatability and Reproducibility for a Measurement System

6.10. SAS Problems for Random and Mixed Models

6.11. Further Reading

Problems

**7. Nested and Nested-Factorial Experiments**

7.1. Introduction

7.2. Nested Experiments

7.3. ANOVA Rationale

7.4. Nested-Factorial Experiments

7.5. Repeated-Measures Design and Nested-Factorial Experiments

7.6. SAS Programs for Nested and Nested-Factorial Experiments

7.7. Summary

Further Reading

Problems

**8. Experiments of Two or More Factors: Restrictions on Randomization**

8.1. Introduction

8.2. Factorial Experiment in a Randomized Block Design

8.3. Factorial Experiment in a Latin Square Design

8.4. Remarks

8.5. SAS Programs

8.6. Summary

Problems

**9. 2f Factorial Experiments.**

9.1. Introduction

9.2. 2 Squared Factorial

9.3. 2 Cubed Factorial

9.4. 2f Remarks

9.5. The Yates Method

9.6. Analysis of 2f Factorials When n=1

9.7 Some Commments about Computer Use.

9.8. Summary

9.9. Further Reading

Problems

**10. 3f Factorial Experiments**

10.1. Introduction

10.2. 3 Squared Factorial

10.3. 3 Cubed Factorial

10.4. Computer Programs

10.5. Summary

Problems

**11. Factorial Experiment: Split-Plot Design**

11.1. Introduction

11.2. A Split-Plot Design

11.3. A Split-Split-Plot Design

11.4. Using SAS to Analyze a Split-Plot Experiment

11.5. Summary

11.6. Further Reading

Problems

**12. Factorial Experiment: Confounding in Blocks**

12.1. Introduction

12.2. Confounding Systems

12.3. Block Confounding, No Replication

12.4. Block Confounding with Replication

12.5. Confounding in 3F Factorials

12.6. SAS Progrms

12.7. Summary

12.8. Further Reading

Problems

**13. Fractional Replication**

13.1. Introduction

13.2. Aliases

13.3. 2f Fractional Replications

13.4. Plackett-Burman Designs

13.5. Design Resolution

13.6. 3f-k Fractional Factorials

13.7. SAS Programs

13.8. Summary

13.9. Further Reading

Problems

**14. The Taguchi Approach to the Design of Experiments**

14.1. Introduction

14.2. The L4 (2 Cubed) Orthogonal Array

14.3. Outer Arrays

14.4. Signal-To-Noise Ratio

14.5. The L8 (2 7) Orthogonal Array

14.6. The L16 (2 15) Orthogonal Array

14.7. The L9 (3 4) Orthogonal Array

14.8. Some Other Taguchi Designs

14.9. Summary

14.10. Further Reading

Problems

**15. Regression**

15.1. Introduction

15.2. Linear Regression

15.3. Curvilinear Regression

15.4. Orthogonal Polynomials

15.5. Multiple Regression

15.6. Summary

15.7. Further Reading

Problems

**16. Miscellaneous Topics**

16.1. Introduction

16.2. Covariance Analysis

16.3. Response Surface Experimentation

16.4. Evolutionary Operation (EVOP)

16.5. Analysis of Attribute Data

16.6. Randomized Incomplete Blocks: Restriction On Experimentation

16.7. Youden Squares

16.8. Further Reading

Problems

Summary and Special Problems

Glossary of Terms

References

Statistical Tables

Table A. Areas Under the Normal Curve

Table B. Student's t Distribution

Table C. Cumulative Chi-Square Distribution

Table D. Cumulative F Distribution

Table E.1. Upper 5% of Studentized Range q

Table E.2. Upper 1% of Studentized Range q

Table F. Coefficients of Orthogonal Polynomials

Answers to Selected Problems

Index

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Summary

This text is a solid revision and redesign of Charles Hicks' comprehensive fourth edition of Fundamental Concepts in the Design of Experiments. It covers the essentials of experimental design used by applied researchers in solving problems in the field. It is appropriate for a variety of experimental methods courses found in engineering and statistics departments. Students learn to use applied statistics for planning, running, and analyzing as an experiment. Students learn to use applied statistics for planning, running, and analyzing an experiment. The text includes 350+ problems taken from the author's actual industrial consulting experiences to give students valuable practice with real data and problem solving. About 60 new problems have been added for this edition. SAS (Statistical Analysis System) computer programs are incorporated to facilitate analysis. There is extensive coverage of the analysis of residuals, the concepts of resolution in fractional replications, the Plackett-Burman designs, and Taguchi techniques. The new edition will place a greater emphasis on computer use, include additional problems, and add computer outputs from statistical packages like Minitab, SPSS, and JMP.

The book is written for anyone engaged in experimental work who has a good background in statistical inference. It will be most profitable reading to those witha background in statistical methods including analysis of variance. This text is suitable for senior undergraduate/graduate level students in mathematics, statistics, or engineering. It is appropriate for a variety of experimental methods courses found in engineering and statistics deparmtents -- majors in this course are usually in applied statistics; non-majors, in industrial and electrical engineering, or education and life sciences.

Author Bio

**Hicks, Charles R. : Purdue University**

**Turner, Kenneth V. Jr. : Anderson University**

Table of Contents

Preface

**1. The Experiment, the Design, and the Analysis**

1.1. Introduction to Experimental Design

1.2. The Experiment

1.3. The Design

1.4. The Analysis

1.5. Examples

1.6. Summary in Outline

1.7. Further Reading

Problems

**2. Review of Statistical Inference**

2.1. Introduction

2.2. Estimation

2.3. Tests of Hypothesis

2.4. The Operating Characteristic Curve

2.5. How Large a Sample?

2.6. Application to Tests on Variances

2.7. Application to Tests on Means

2.8. Assessing Normality

2.9. Applications to Tests on Proportions

2.10. Analysis of Experiments with SAS

2.11. Further Reading

Problems

**3. Single-Factor Experiments with No Restrictions on Randomization**

3.1. Introduction

3.2. Analysis of Variance Rationale

3.3. After ANOVA--What?

3.4. Tests on Means

3.5. Confidence Limits on Means

3.6. Components of Variance

3.7. Checking the Model

3.8. SAS Programs for ANOVA and Tests after ANOVA

3.9. Summary

3.10. Further Reading

Problems

**4. Single-Factor Experiments: Randomized Block and Latin Square Designs**

4.1. Introduction

4.2. Randomized Complete Block Design

4.3. ANOVA Rationale

4.4. Missing Values

4.5. Latin Squares

4.6. Interpretations

4.7. Assessing the Model

4.8. Graeco-Latin Squares

4.9. Extensions

4.10. SAS Programs for Randomized Blocks and Latin Squares

4.11. Summary

4.12. Further Reading

Problems

**5. Factorial Experiments**

5.1. Introduction

5.2. Factorial Experiments: An Example

5.3. Interpretations

5.4. The Model and Its Assessment

5.5. ANOVA Rationale

5.6. One Observation Per Treatment

5.7. SAS Programs for Factorial Experiments

5.8. Summary

5.9. Further Reading

Problems

**6. Fixed, Random, and Mixed Models**

6.1. Introduction

6.2. Single-Factor Models

6.3. Two-Factor Models

6.4. EMS Rules

6.5. EMS Derivations

6.6. The Pseudo-F Test

6.7. Expected Mean Squares Via Statistical Computing Packages

6.8. Remarks

6.9. Repeatability and Reproducibility for a Measurement System

6.10. SAS Problems for Random and Mixed Models

6.11. Further Reading

Problems

**7. Nested and Nested-Factorial Experiments**

7.1. Introduction

7.2. Nested Experiments

7.3. ANOVA Rationale

7.4. Nested-Factorial Experiments

7.5. Repeated-Measures Design and Nested-Factorial Experiments

7.6. SAS Programs for Nested and Nested-Factorial Experiments

7.7. Summary

Further Reading

Problems

**8. Experiments of Two or More Factors: Restrictions on Randomization**

8.1. Introduction

8.2. Factorial Experiment in a Randomized Block Design

8.3. Factorial Experiment in a Latin Square Design

8.4. Remarks

8.5. SAS Programs

8.6. Summary

Problems

**9. 2f Factorial Experiments.**

9.1. Introduction

9.2. 2 Squared Factorial

9.3. 2 Cubed Factorial

9.4. 2f Remarks

9.5. The Yates Method

9.6. Analysis of 2f Factorials When n=1

9.7 Some Commments about Computer Use.

9.8. Summary

9.9. Further Reading

Problems

**10. 3f Factorial Experiments**

10.1. Introduction

10.2. 3 Squared Factorial

10.3. 3 Cubed Factorial

10.4. Computer Programs

10.5. Summary

Problems

**11. Factorial Experiment: Split-Plot Design**

11.1. Introduction

11.2. A Split-Plot Design

11.3. A Split-Split-Plot Design

11.4. Using SAS to Analyze a Split-Plot Experiment

11.5. Summary

11.6. Further Reading

Problems

**12. Factorial Experiment: Confounding in Blocks**

12.1. Introduction

12.2. Confounding Systems

12.3. Block Confounding, No Replication

12.4. Block Confounding with Replication

12.5. Confounding in 3F Factorials

12.6. SAS Progrms

12.7. Summary

12.8. Further Reading

Problems

**13. Fractional Replication**

13.1. Introduction

13.2. Aliases

13.3. 2f Fractional Replications

13.4. Plackett-Burman Designs

13.5. Design Resolution

13.6. 3f-k Fractional Factorials

13.7. SAS Programs

13.8. Summary

13.9. Further Reading

Problems

**14. The Taguchi Approach to the Design of Experiments**

14.1. Introduction

14.2. The L4 (2 Cubed) Orthogonal Array

14.3. Outer Arrays

14.4. Signal-To-Noise Ratio

14.5. The L8 (2 7) Orthogonal Array

14.6. The L16 (2 15) Orthogonal Array

14.7. The L9 (3 4) Orthogonal Array

14.8. Some Other Taguchi Designs

14.9. Summary

14.10. Further Reading

Problems

**15. Regression**

15.1. Introduction

15.2. Linear Regression

15.3. Curvilinear Regression

15.4. Orthogonal Polynomials

15.5. Multiple Regression

15.6. Summary

15.7. Further Reading

Problems

**16. Miscellaneous Topics**

16.1. Introduction

16.2. Covariance Analysis

16.3. Response Surface Experimentation

16.4. Evolutionary Operation (EVOP)

16.5. Analysis of Attribute Data

16.6. Randomized Incomplete Blocks: Restriction On Experimentation

16.7. Youden Squares

16.8. Further Reading

Problems

Summary and Special Problems

Glossary of Terms

References

Statistical Tables

Table A. Areas Under the Normal Curve

Table B. Student's t Distribution

Table C. Cumulative Chi-Square Distribution

Table D. Cumulative F Distribution

Table E.1. Upper 5% of Studentized Range q

Table E.2. Upper 1% of Studentized Range q

Table F. Coefficients of Orthogonal Polynomials

Answers to Selected Problems

Index

Publisher Info

Publisher: Oxford University Press

Published: 1999

International: No

Published: 1999

International: No

The book is written for anyone engaged in experimental work who has a good background in statistical inference. It will be most profitable reading to those witha background in statistical methods including analysis of variance. This text is suitable for senior undergraduate/graduate level students in mathematics, statistics, or engineering. It is appropriate for a variety of experimental methods courses found in engineering and statistics deparmtents -- majors in this course are usually in applied statistics; non-majors, in industrial and electrical engineering, or education and life sciences.

**Hicks, Charles R. : Purdue University**

**Turner, Kenneth V. Jr. : Anderson University**

Preface

**1. The Experiment, the Design, and the Analysis**

1.1. Introduction to Experimental Design

1.2. The Experiment

1.3. The Design

1.4. The Analysis

1.5. Examples

1.6. Summary in Outline

1.7. Further Reading

Problems

**2. Review of Statistical Inference**

2.1. Introduction

2.2. Estimation

2.3. Tests of Hypothesis

2.4. The Operating Characteristic Curve

2.5. How Large a Sample?

2.6. Application to Tests on Variances

2.7. Application to Tests on Means

2.8. Assessing Normality

2.9. Applications to Tests on Proportions

2.10. Analysis of Experiments with SAS

2.11. Further Reading

Problems

**3. Single-Factor Experiments with No Restrictions on Randomization**

3.1. Introduction

3.2. Analysis of Variance Rationale

3.3. After ANOVA--What?

3.4. Tests on Means

3.5. Confidence Limits on Means

3.6. Components of Variance

3.7. Checking the Model

3.8. SAS Programs for ANOVA and Tests after ANOVA

3.9. Summary

3.10. Further Reading

Problems

**4. Single-Factor Experiments: Randomized Block and Latin Square Designs**

4.1. Introduction

4.2. Randomized Complete Block Design

4.3. ANOVA Rationale

4.4. Missing Values

4.5. Latin Squares

4.6. Interpretations

4.7. Assessing the Model

4.8. Graeco-Latin Squares

4.9. Extensions

4.10. SAS Programs for Randomized Blocks and Latin Squares

4.11. Summary

4.12. Further Reading

Problems

**5. Factorial Experiments**

5.1. Introduction

5.2. Factorial Experiments: An Example

5.3. Interpretations

5.4. The Model and Its Assessment

5.5. ANOVA Rationale

5.6. One Observation Per Treatment

5.7. SAS Programs for Factorial Experiments

5.8. Summary

5.9. Further Reading

Problems

**6. Fixed, Random, and Mixed Models**

6.1. Introduction

6.2. Single-Factor Models

6.3. Two-Factor Models

6.4. EMS Rules

6.5. EMS Derivations

6.6. The Pseudo-F Test

6.7. Expected Mean Squares Via Statistical Computing Packages

6.8. Remarks

6.9. Repeatability and Reproducibility for a Measurement System

6.10. SAS Problems for Random and Mixed Models

6.11. Further Reading

Problems

**7. Nested and Nested-Factorial Experiments**

7.1. Introduction

7.2. Nested Experiments

7.3. ANOVA Rationale

7.4. Nested-Factorial Experiments

7.5. Repeated-Measures Design and Nested-Factorial Experiments

7.6. SAS Programs for Nested and Nested-Factorial Experiments

7.7. Summary

Further Reading

Problems

**8. Experiments of Two or More Factors: Restrictions on Randomization**

8.1. Introduction

8.2. Factorial Experiment in a Randomized Block Design

8.3. Factorial Experiment in a Latin Square Design

8.4. Remarks

8.5. SAS Programs

8.6. Summary

Problems

**9. 2f Factorial Experiments.**

9.1. Introduction

9.2. 2 Squared Factorial

9.3. 2 Cubed Factorial

9.4. 2f Remarks

9.5. The Yates Method

9.6. Analysis of 2f Factorials When n=1

9.7 Some Commments about Computer Use.

9.8. Summary

9.9. Further Reading

Problems

**10. 3f Factorial Experiments**

10.1. Introduction

10.2. 3 Squared Factorial

10.3. 3 Cubed Factorial

10.4. Computer Programs

10.5. Summary

Problems

**11. Factorial Experiment: Split-Plot Design**

11.1. Introduction

11.2. A Split-Plot Design

11.3. A Split-Split-Plot Design

11.4. Using SAS to Analyze a Split-Plot Experiment

11.5. Summary

11.6. Further Reading

Problems

**12. Factorial Experiment: Confounding in Blocks**

12.1. Introduction

12.2. Confounding Systems

12.3. Block Confounding, No Replication

12.4. Block Confounding with Replication

12.5. Confounding in 3F Factorials

12.6. SAS Progrms

12.7. Summary

12.8. Further Reading

Problems

**13. Fractional Replication**

13.1. Introduction

13.2. Aliases

13.3. 2f Fractional Replications

13.4. Plackett-Burman Designs

13.5. Design Resolution

13.6. 3f-k Fractional Factorials

13.7. SAS Programs

13.8. Summary

13.9. Further Reading

Problems

**14. The Taguchi Approach to the Design of Experiments**

14.1. Introduction

14.2. The L4 (2 Cubed) Orthogonal Array

14.3. Outer Arrays

14.4. Signal-To-Noise Ratio

14.5. The L8 (2 7) Orthogonal Array

14.6. The L16 (2 15) Orthogonal Array

14.7. The L9 (3 4) Orthogonal Array

14.8. Some Other Taguchi Designs

14.9. Summary

14.10. Further Reading

Problems

**15. Regression**

15.1. Introduction

15.2. Linear Regression

15.3. Curvilinear Regression

15.4. Orthogonal Polynomials

15.5. Multiple Regression

15.6. Summary

15.7. Further Reading

Problems

**16. Miscellaneous Topics**

16.1. Introduction

16.2. Covariance Analysis

16.3. Response Surface Experimentation

16.4. Evolutionary Operation (EVOP)

16.5. Analysis of Attribute Data

16.6. Randomized Incomplete Blocks: Restriction On Experimentation

16.7. Youden Squares

16.8. Further Reading

Problems

Summary and Special Problems

Glossary of Terms

References

Statistical Tables

Table A. Areas Under the Normal Curve

Table B. Student's t Distribution

Table C. Cumulative Chi-Square Distribution

Table D. Cumulative F Distribution

Table E.1. Upper 5% of Studentized Range q

Table E.2. Upper 1% of Studentized Range q

Table F. Coefficients of Orthogonal Polynomials

Answers to Selected Problems

Index