Fundamental Concepts in the Design of Experiments

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