Fundamental Concepts in the Design of Experiments

"An excellent presentation of the basic concepts of experimental design. It uses many numerical examples with 'real' data. It is clearly written and at the appropriate level for my students."--Noel Artiles-Leon, University of Puerto Rico

• 1. The Experiment, the Design, and the Analysis; 1.1 Introduction; 1.2 The Experiment; 1.3 The Design; 1.4 The Analysis; 1.5 Examples; 1.6 Summary in Outline; Further Reading; Problems; 2. Review of Statistical Inference; 2.1 Introduction; 2.2 Estimation; 2.3 Tests of hypothesis; 2.4 The Operating Characterisitc 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; 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 of 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; 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; 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; Further Reading; Summary; 6. Fixed, Random, and Mixed Models; 6.1 Introduction; 6.2 Single-Factor Models; 6.3 Two-Factor Models; 6.4 EMS Rule; 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; 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 and Randomization; 8.1 Introductin; 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; Further Reading; Problems; 9.2 2 Squared Factorial; 9.3 2 Cubed Factorial; 9.4 2f Factorial; 9.5 The Yates Method; 9.6 Analysis of 2f Factorials When n=1; 9.8 Summary; 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; Further Reading; 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; Further Reading; Problems; 12. Factorial Experiment -- Confounding in Blocks; 12.1 Introduction; 12.2 Confounding Systems; 12.3 Block Confounding -- No Replication; 12.4 Blcok Confounding with Replication; 12.5 Confounding in 3F Factorials; 12.6 SAS Progrms; 12.7 Summary; Further Reading; Problems; 13. Fractional Replication; 13.1 Introduction; 13.2 Aliases; 13.3 2f Fractional Replication; 13.4 Plackett-Burman Designs; 14. 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; Futher Reading; Problems; 15. Regression; 15.1 Introduction; 15.2 Linear Regression; 15.3 Curvilinear Regression; 15.4 Orthogronal Polynomials; 15.5 Multiple Regression; 15.6 Summary; Further Reading; Summary; 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; 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 Percent of Studentized Range q; Table E.2 Upper 1 Percent of Studentized Range q; Table F Coefficients of Orthogonal Polynomials; ANSWERS TO SELECTED PROBLEMS; INDEX