Design of Experiments

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1. RESEARCH DESIGN PRINCIPLES The Legacy of Sir Ronald A. Fisher / Planning for Research / Experiments, Treatments, and Experimental Units / Research Hypotheses Generate Treatment Designs / Local Control of Experimental Errors / Replication for Valid Experiments / How Many Replications? / Randomization for Valid Inferences / Relative Efficiency of Experiment Designs / From Principles to Practice: A Case Study 2. GETTING STARTED WITH COMPLETELY RANDOMIZED DESIGNS Assembling the Research Design / How to Randomize / Preparation of Data Files for the Analysis / A Statistical Model for the Experiment / Estimation of the Model Parameters with Least Squares / Sums of Squares to Identify Important Sources of Variation / A Treatment Effects Model / Degrees of Freedom / Summaries in the Analysis of Variance Table / Tests of Hypotheses About Linear Models / Significance Testing and Tests of Hypotheses / Standard Errors and Confidence Intervals for Treatment Means / Unequal Replication of the Treatments / How Many Replications of the F Test? / Appendix: Expected Values / Appendix: Expected Mean Squares 3. TREATMENT COMPARISONS Treatment Comparisons Answer Research Questions / Planning Comparisons Among Treatments / Response Curves for Quantitative Treatment Factors / Multiple Comparisons Affect Error Rates / Simultaneous Statistical Inference / Multiple Comparisons with the Best Treatment / Comparison of All Treatments with a Control / Pairwise Comparisons of All Treatments / Summary Comments on Multiple Comparisons / Appendix: Linear Functions of Random Variables 4. DIAGNOSING AGREEMENT BETWEEN THE DATA AND THE MODEL Valid Analysis Depends on Valid Assumptions / Effects of Departures from Assumptions / Residuals Are the Basis of Diagnostic Tools / Looking for Outliers with the Residuals / Variance-Stabilizing Transformations for Data with Known Distributions / Power Transformations to Stabilize Variances / Generalizing the Linear Model / Model Evaluation with Residual-Fitted Spread Plots / Appendix: Data for Example 4.1 5. EXPERIMENTS TO STUDY VARIANCES Random Effects Models for Variances / A Statistical Model for Variance Components / Point Estimates of Variance Components / Interval Estimates for Variance Components / Courses of Action with Negative Variance Estimates / Intraclass Correlation Measures Similarity in a Group / Unequal Numbers of Observations in the Groups / How Many Observations to Study Variances? / Random Subsamples to Procure Data for the Experiment / Using Variance Estimates to Allocate Sampling Efforts / Unequal Numbers of Replications and Subsamples / Appendix: Coefficient Calculations for Expected Mean Squares in Table 5.9 6. FACTORIAL TREATMENT DESIGNS Efficient Experiments with Factorial Treatment Designs / Three Types of Treatment Factor Effects / The Statistical Model for Two Treatment Factors / The Analysis for Two Factors / Using Response Curves for Quantitative Treatment Factors / Three Treatment Factors / Estimation of Error Variance with One Replication / How Many Replications to Test Factor Effects? / Unequal Replication of Treatments / Appendix: Least Squares for Factorial Treatment Designs 7. FACTORIAL TREATMENT DESIGNS: RANDOM AND MIXED MODELS Random Effects for Factorial Treatment Designs / Mixed Models / Nested Factor Designs: A Variation on the Theme / Nested and Crossed Factors Designs / How Many Replications? / Expected Mean Square Rules 8. COMPLETE BLOCK DESIGNS Blocking to Increase Precision / Randomized Complete Block Designs Use One Blocking Criterion / Latin Square Designs Use Two Blocking Criteria / Factorial Experiments in Complete Block Designs / Missing Data in Blocked Designs / Experiments Performed Several Times / Appendix: Selected Latin Squares 9. INCOMPLETE BLOCK DESIGNS: AN INTRODUCTION Incomplete Blocks of Treatments to Reduce Block Size / Balanced Incomplete Block (BIB) Designs / How to Randomize Incomplete Block Designs / Analysis of BIB Designs / Row-Column Designs for Two Blocking Criteria / Reduce Experiment Size with Partially Balanced (PBIB) Designs / Efficiency of Incomplete Block Designs / Appendix: Selected Balanced Incomplete Block Designs / Appendix: Selected Incomplete Latin Square Designs / Appendix: Least Squares Estimates for BIB Designs 10. INCOMPLETE BLOCK DESIGNS: RESOLVABLE AND CYCLIC DESIGNS Resolvable Designs to Help Manage the Experiment / Resolvable Row-Column Designs for Two Blocking Criteria / Cyclic Designs Simplify Design Construction / Choosing Incomplete Block Designs / Appendix: Plans for Cyclic Designs / Appendix: Generating Arrays for a Designs 11. INCOMPLETE BLOCK DESIGNS: FACTORIAL TREATMENT DESIGNS Taking Greater Advantage of Factorial Treatment Designs / 2 to the nth Power Factorials to Evaluate Many Factors / Incomplete Block Designs for 2 to the nth Power Factorials / A General Method to Create Incomplete Blocks / Incomplete Blocks for 3 to the nth Power Factorials / Concluding Remarks / Appendix: Incomplete Block Design Plans for 2 to the nth Power Factorials 12. FRACTIONAL FACTORIAL DESIGNS Reduce Experiment Size with Fractional Treatment Designs / The Half Fraction of the 2 to the nth Power Factorial / Design Resolution Related to Aliases / Analysis of Half Replicate 2^n - 1 Designs / The Quarter Fractions of 2 to the nth Power Factorials / Construction of 2^(n - p) Designs with Resolution III and IV / Genichi Taguchi and Quality Improvement / Concluding Remarks / Appendix: Fractional Factorial Design Plans 13. RESPONSE SURFACE DESIGNS Describe Responses with Equations and Graphs / Identify Important Factors with 2 to the nth Power Factorials / Designs to Estimate Second-Order Response Surfaces / Quadratic Responses Surface Estimation / Response Surface Exploration / Designs for Mixtures of Ingredients / Analysis of Mixture Experiments / Appendix: Least Squares Estimation of Regression Models / Appendix: Location of Coordinates for the Stationary Point / Appendix: Canonical Form of the Quadratic Equation 14. SPLIT-PLOT DESIGNS Plots of Different Size in the Same Experiment / Two Experimental Errors for Two Plot Sizes / The Analysis for Split-Plot Designs / Standard Errors for Treatment Factor Means / Features of the Split-Plot Design / Relative Efficiency of Subplot and Whole-Plot Comparisons / The Split-Split-Plot Design for Three Treatment Factors / The Split-Block Design / Additional Information About Split-Plot Designs 15. REPEATED MEASURES DESIGNS Studies of Time Trends / Relationships Among Repeated Measurements / A Test for the Huynh-Feldt Assumption / A Univariate Analysis of Variance for Repeated Measures / Analysis When Univariate Analysis Assumptions Do Not Hold / Other Experiments with Repeated Measures Properties / Other Models for Correlation Among Repeated Measures / Appendix: The Mauchly Test for Sphericity / Appendix: Degrees of Freedom Adjustments for Repeated Measures Analysis of Variance 16. CROSSOVER DESIGNS Administer All Treatments to Each Experimental Unit / Analysis of Crossover Designs / Balanced Designs for Crossover Studies / Crossover Designs for Two Treatments / Appendix: Coding Data Files for Crossover Studies / Appendix: Treatment Sum of Squares for Balanced Designs 17. ANALYSIS OF COVARIANCE Local Control with a Measured Covariate / Analysis of Covariance for Completely Randomized Block Designs / The Analysis of Covariance for Blocked Experiment Designs / Practical Consequences of Covariance Analysis / REFERENCES / APPENDIX TABLES / ANSWERS TO SELECTED EXERCISES / INDEX

1. RESEARCH DESIGN PRINCIPLES The Legacy of Sir Ronald A. Fisher / Planning for Research / Experiments, Treatments, and Experimental Units / Research Hypotheses Generate Treatment Designs / Local Control of Experimental Errors / Replication for Valid Experiments / How Many Replications? / Randomization for Valid Inferences / Relative Efficiency of Experiment Designs / From Principles to Practice: A Case Study 2. GETTING STARTED WITH COMPLETELY RANDOMIZED DESIGNS Assembling the Research Design / How to Randomize / Preparation of Data Files for the Analysis / A Statistical Model for the Experiment / Estimation of the Model Parameters with Least Squares / Sums of Squares to Identify Important Sources of Variation / A Treatment Effects Model / Degrees of Freedom / Summaries in the Analysis of Variance Table / Tests of Hypotheses About Linear Models / Significance Testing and Tests of Hypotheses / Standard Errors and Confidence Intervals for Treatment Means / Unequal Replication of the Treatments / How Many Replications of the F Test? / Appendix: Expected Values / Appendix: Expected Mean Squares 3. TREATMENT COMPARISONS Treatment Comparisons Answer Research Questions / Planning Comparisons Among Treatments / Response Curves for Quantitative Treatment Factors / Multiple Comparisons Affect Error Rates / Simultaneous Statistical Inference / Multiple Comparisons with the Best Treatment / Comparison of All Treatments with a Control / Pairwise Comparisons of All Treatments / Summary Comments on Multiple Comparisons / Appendix: Linear Functions of Random Variables 4. DIAGNOSING AGREEMENT BETWEEN THE DATA AND THE MODEL Valid Analysis Depends on Valid Assumptions / Effects of Departures from Assumptions / Residuals Are the Basis of Diagnostic Tools / Looking for Outliers with the Residuals / Variance-Stabilizing Transformations for Data with Known Distributions / Power Transformations to Stabilize Variances / Generalizing the Linear Model / Model Evaluation with Residual-Fitted Spread Plots / Appendix: Data for Example 4.1 5. EXPERIMENTS TO STUDY VARIANCES Random Effects Models for Variances / A Statistical Model for Variance Components / Point Estimates of Variance Components / Interval Estimates for Variance Components / Courses of Action with Negative Variance Estimates / Intraclass Correlation Measures Similarity in a Group / Unequal Numbers of Observations in the Groups / How Many Observations to Study Variances? / Random Subsamples to Procure Data for the Experiment / Using Variance Estimates to Allocate Sampling Efforts / Unequal Numbers of Replications and Subsamples / Appendix: Coefficient Calculations for Expected Mean Squares in Table 5.9 6. FACTORIAL TREATMENT DESIGNS Efficient Experiments with Factorial Treatment Designs / Three Types of Treatment Factor Effects / The Statistical Model for Two Treatment Factors / The Analysis for Two Factors / Using Response Curves for Quantitative Treatment Factors / Three Treatment Factors / Estimation of Error Variance with One Replication / How Many Replications to Test Factor Effects? / Unequal Replication of Treatments / Appendix: Least Squares for Factorial Treatment Designs 7. FACTORIAL TREATMENT DESIGNS: RANDOM AND MIXED MODELS Random Effects for Factorial Treatment Designs / Mixed Models / Nested Factor Designs: A Variation on the Theme / Nested and Crossed Factors Designs / How Many Replications? / Expected Mean Square Rules 8. COMPLETE BLOCK DESIGNS Blocking to Increase Precision / Randomized Complete Block Designs Use One Blocking Criterion / Latin Square Designs Use Two Blocking Criteria / Factorial Experiments in Complete Block Designs / Missing Data in Blocked Designs / Experiments Performed Several Times / Appendix: Selected Latin Squares 9. INCOMPLETE BLOCK DESIGNS: AN INTRODUCTION Incomplete Blocks of Treatments to Reduce Block Size / Balanced Incomplete Block (BIB) Designs / How to Randomize Incomplete Block Designs / Analysis of BIB Designs / Row-Column Designs for Two Blocking Criteria / Reduce Experiment Size with Partially Balanced (PBIB) Designs / Efficiency of Incomplete Block Designs / Appendix: Selected Balanced Incomplete Block Designs / Appendix: Selected Incomplete Latin Square Designs / Appendix: Least Squares Estimates for BIB Designs 10. INCOMPLETE BLOCK DESIGNS: RESOLVABLE AND CYCLIC DESIGNS Resolvable Designs to Help Manage the Experiment / Resolvable Row-Column Designs for Two Blocking Criteria / Cyclic Designs Simplify Design Construction / Choosing Incomplete Block Designs / Appendix: Plans for Cyclic Designs / Appendix: Generating Arrays for a Designs 11. INCOMPLETE BLOCK DESIGNS: FACTORIAL TREATMENT DESIGNS Taking Greater Advantage of Factorial Treatment Designs / 2 to the nth Power Factorials to Evaluate Many Factors / Incomplete Block Designs for 2 to the nth Power Factorials / A General Method to Create Incomplete Blocks / Incomplete Blocks for 3 to the nth Power Factorials / Concluding Remarks / Appendix: Incomplete Block Design Plans for 2 to the nth Power Factorials 12. FRACTIONAL FACTORIAL DESIGNS Reduce Experiment Size with Fractional Treatment Designs / The Half Fraction of the 2 to the nth Power Factorial / Design Resolution Related to Aliases / Analysis of Half Replicate 2^n - 1 Designs / The Quarter Fractions of 2 to the nth Power Factorials / Construction of 2^(n - p) Designs with Resolution III and IV / Genichi Taguchi and Quality Improvement / Concluding Remarks / Appendix: Fractional Factorial Design Plans 13. RESPONSE SURFACE DESIGNS Describe Responses with Equations and Graphs / Identify Important Factors with 2 to the nth Power Factorials / Designs to Estimate Second-Order Response Surfaces / Quadratic Responses Surface Estimation / Response Surface Exploration / Designs for Mixtures of Ingredients / Analysis of Mixture Experiments / Appendix: Least Squares Estimation of Regression Models / Appendix: Location of Coordinates for the Stationary Point / Appendix: Canonical Form of the Quadratic Equation 14. SPLIT-PLOT DESIGNS Plots of Different Size in the Same Experiment / Two Experimental Errors for Two Plot Sizes / The Analysis for Split-Plot Designs / Standard Errors for Treatment Factor Means / Features of the Split-Plot Design / Relative Efficiency of Subplot and Whole-Plot Comparisons / The Split-Split-Plot Design for Three Treatment Factors / The Split-Block Design / Additional Information About Split-Plot Designs 15. REPEATED MEASURES DESIGNS Studies of Time Trends / Relationships Among Repeated Measurements / A Test for the Huynh-Feldt Assumption / A Univariate Analysis of Variance for Repeated Measures / Analysis When Univariate Analysis Assumptions Do Not Hold / Other Experiments with Repeated Measures Properties / Other Models for Correlation Among Repeated Measures / Appendix: The Mauchly Test for Sphericity / Appendix: Degrees of Freedom Adjustments for Repeated Measures Analysis of Variance 16. CROSSOVER DESIGNS Administer All Treatments to Each Experimental Unit / Analysis of Crossover Designs / Balanced Designs for Crossover Studies / Crossover Designs for Two Treatments / Appendix: Coding Data Files for Crossover Studies / Appendix: Treatment Sum of Squares for Balanced Designs 17. ANALYSIS OF COVARIANCE Local Control with a Measured Covariate / Analysis of Covariance for Completely Randomized Block Designs / The Analysis of Covariance for Blocked Experiment Designs / Practical Consequences of Covariance Analysis / REFERENCES / APPENDIX TABLES / ANSWERS TO SELECTED EXERCISES / INDEX

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