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Presents the principles of statistical design and analysis for comparative scientific studies. The text emphasizes the research design process-the total effort in a study that includes development of the research hypothesis, the choice of treatment designed to address the research hypothesis, and the experiment design choice to facilitate data collection.
The principles are exemplified and demonstrated using a real case study introduced in Chapter 1.
New material includes coverage of Resolvable Block Designs, the Simultaneous Confidence Interval, the Generalized Linear Model, and the Taguchi Method.
Expanded discussion of advanced methodology for analysis choices, such as those for variance component estematia, mixed model software for split plots, and choices for covariance matrices for repeated measure.
Focus on research design provides a structural viewpoint for the researcher.
Large array of real data sets from a broad spectrum of scientific and technological fields, including life and agriculture sciences, engineering, industrial, and chemical research.
Excellent examples often based on actual research studies, are organized in an action-oriented style.
Consistent emphasis on data analysis of the design.
Interpretation is provided for each analysis.
Introduces a new modern approach to Simultaneous Statistical Inference.
Author Bio
Kuehl, Robert O. : University of Arizona
1. RESEARCH DESIGN PRINCIPLES.
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.
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 for the F Test?
Appendix: Expected Values.
Appendix: Expected Mean Squares.
Appendix: Computer Generation of Random Permutations.
Appendix: Computer Random Sample of Observational Units.
3. TREATMENT COMPARISONS.
Treatment Comparisons Answer Research Questions.
Planning Comparisons Among Treatments.
Response Curves for Quantitative Treatment Factors.
Multiple Comparisons Affect Error Rates.
Multiple Comparisons with the Best Treatment.
Comparison of All Treatments to a Control.
Pairwise Comparison 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.
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.
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 Blocks 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.
2n Factorials to Evaluate Many Factors.
Incomplete Block Designs for 2n Factorials.
A General Method to Create Incomplete Blocks.
Incomplete Block Designs for 3n Factorials.
Concluding Remarks.
Appendix: Incomplete Block Design Plans for 2n Factorials.
12. FRACTIONAL FACTORIAL DESIGNS.
Reduce Experiment Size with Fractional Treatment Designs.
The Half Fraction of the 2n Factorial.
Design Resolution Related to Aliases.
Analysis of Half Replicate 2n-1 Designs.
The Quarter Fractions of 2n Factorials.
Construction of 2n-p Designs with Resolution III and IV.
Concluding Remarks.
Appendix: Fractional Factorial Design Plans.
13. RESPONSE SURFACE DESIGNS.
Describe Responses with Equations and Graphs.
Identify Important Factors with 2n Factorials.
Designs to Estimate Second-Order Response Surfaces.
Quadratic Response Surface Estimation.
Response Surface Exploration.
Designs for Mixtures of Ingredients.
Analysis of Mixture Experiments.
Appendix: Least Squares Estimation to 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-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.
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 Designs.
The Analysis of Covariance for Blocked Experiment Designs.
Practical Consequences of Covariance Analysis.
REFERENCES.
APPENDIX TABLES.
ANSWERS TO SELECTED EXERCISES.
INDEX.
Presents the principles of statistical design and analysis for comparative scientific studies. The text emphasizes the research design process-the total effort in a study that includes development of the research hypothesis, the choice of treatment designed to address the research hypothesis, and the experiment design choice to facilitate data collection.
The principles are exemplified and demonstrated using a real case study introduced in Chapter 1.
New material includes coverage of Resolvable Block Designs, the Simultaneous Confidence Interval, the Generalized Linear Model, and the Taguchi Method.
Expanded discussion of advanced methodology for analysis choices, such as those for variance component estematia, mixed model software for split plots, and choices for covariance matrices for repeated measure.
Focus on research design provides a structural viewpoint for the researcher.
Large array of real data sets from a broad spectrum of scientific and technological fields, including life and agriculture sciences, engineering, industrial, and chemical research.
Excellent examples often based on actual research studies, are organized in an action-oriented style.
Consistent emphasis on data analysis of the design.
Interpretation is provided for each analysis.
Introduces a new modern approach to Simultaneous Statistical Inference.
Author Bio
Kuehl, Robert O. : University of Arizona
Table of Contents
1. RESEARCH DESIGN PRINCIPLES.
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.
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 for the F Test?
Appendix: Expected Values.
Appendix: Expected Mean Squares.
Appendix: Computer Generation of Random Permutations.
Appendix: Computer Random Sample of Observational Units.
3. TREATMENT COMPARISONS.
Treatment Comparisons Answer Research Questions.
Planning Comparisons Among Treatments.
Response Curves for Quantitative Treatment Factors.
Multiple Comparisons Affect Error Rates.
Multiple Comparisons with the Best Treatment.
Comparison of All Treatments to a Control.
Pairwise Comparison 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.
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.
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 Blocks 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.
2n Factorials to Evaluate Many Factors.
Incomplete Block Designs for 2n Factorials.
A General Method to Create Incomplete Blocks.
Incomplete Block Designs for 3n Factorials.
Concluding Remarks.
Appendix: Incomplete Block Design Plans for 2n Factorials.
12. FRACTIONAL FACTORIAL DESIGNS.
Reduce Experiment Size with Fractional Treatment Designs.
The Half Fraction of the 2n Factorial.
Design Resolution Related to Aliases.
Analysis of Half Replicate 2n-1 Designs.
The Quarter Fractions of 2n Factorials.
Construction of 2n-p Designs with Resolution III and IV.
Concluding Remarks.
Appendix: Fractional Factorial Design Plans.
13. RESPONSE SURFACE DESIGNS.
Describe Responses with Equations and Graphs.
Identify Important Factors with 2n Factorials.
Designs to Estimate Second-Order Response Surfaces.
Quadratic Response Surface Estimation.
Response Surface Exploration.
Designs for Mixtures of Ingredients.
Analysis of Mixture Experiments.
Appendix: Least Squares Estimation to 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-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.
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 Designs.
The Analysis of Covariance for Blocked Experiment Designs.
Practical Consequences of Covariance Analysis.
REFERENCES.
APPENDIX TABLES.
ANSWERS TO SELECTED EXERCISES.
INDEX.