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