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| The Simplest Case: One-Way Treatment Structure in a Completely Randomized Design Structure with Homogeneous Errors | |
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| Model Definitions and Assumptions | |
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| Parameter Estimation | |
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| Inferences on Linear Combinations-Tests and Confidence Intervals | |
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| Example-Tasks and Pulse Rate | |
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| Simultaneous Tests on Several Linear Combinations | |
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| Example-Tasks and Pulse Rate (Continued) | |
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| Testing the Equality of all Means | |
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| Example-Tasks and Pulse Rate (Continued) | |
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| General Method for Comparing Two Models-The Principle of Conditional Error | |
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| Example-Tasks and Pulse Rate (Continued) | |
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| Computer Analyses | |
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| One-Way Treatment Structure in a Completely Randomized Design Structure with Heterogeneous Errors | |
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| Model Definitions and Assumptions | |
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| Parameter Estimation | |
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| Tests for Homogeneity of Variances | |
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| Example-Drugs and Errors | |
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| Inferences on Linear Combinations | |
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| Example-Drugs and Errors (Continued) | |
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| General Satterthwaite Approximation for Degrees of Freedom | |
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| Comparing All Means | |
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| Simultaneous Inference Procedures and Multiple Comparisons | |
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| Error Rates | |
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| Recommendations | |
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| Least Significant Difference | |
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| Fisher's LSD Procedure | |
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| Bonferroni's Method | |
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| Scheff�'s Procedure | |
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| Tukey-Kramer Method | |
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| Simulation Methods | |
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| �id�k Procedure | |
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| Example-Pairwise Comparisons | |
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| Dunnett's Procedure | |
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| Example-Comparing with a Control | |
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| Multivariate | |
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| Example-Linearly Independent Comparisons | |
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| Sequential Rejective Methods | |
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| Example-Linearly Dependent Comparisons | |
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| Multiple Range Tests | |
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| Waller-Duncan Procedure | |
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| Example-Multiple Range for Pairwise Comparisons | |
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| A Caution | |
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| Basics for Designing Experiments | |
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| Introducing Basic Ideas | |
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| Structures of a Designed Experiment | |
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| Examples of Different Designed Experiments | |
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| Multilevel Designs: Split-Plots, Strip-Plots, Repeated Measures, and Combinations | |
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| Identifying Sizes of Experimental Units-Four Basic Design Structures | |
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| Hierarchical Design: A Multilevel Design Structure | |
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| Split-Plot Design Structures: Two-Level Design Structures | |
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| Strip-Plot Design Structures: A Nonhierarchical Multilevel Design | |
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| Repeated Measures Designs | |
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| Designs Involving Nested Factors | |
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| Matrix Form of the Model | |
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| Basic Notation | |
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| Least Squares Estimation | |
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| Estimability and Connected Designs | |
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| Testing Hypotheses about Linear Model Parameters | |
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| Population Marginal Means | |
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| Balanced Two-Way Treatment Structures | |
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| Model Definition and Assumptions | |
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| Parameter Estimation | |
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| Interactions and Their Importance | |
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| Main Effects | |
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| Computer Analyses | |
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| Case Study: Complete Analyses of Balanced Two-Way Experiments | |
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| Contrasts of Main Effect Means | |
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| Contrasts of Interaction Effects | |
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| Paint-Paving Example | |
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| Analyzing Quantitative Treatment Factors | |
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| Multiple Comparisons | |
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| Using the Means Model to Analyze Balanced Two-Way Treatment Structures with Unequal Subclass Numbers | |
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| Model Definitions and Assumptions | |
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| Parameter Estimation | |
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| Testing whether All Means Are Equal | |
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| Interaction and Main Effect Hypotheses | |
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| Population Marginal Means | |
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| Simultaneous Inferences and Multiple Comparisons | |
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| Using the Effects Model to Analyze Balanced Two-Way Treatment Structures with Unequal Subclass Numbers | |
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| Model Definition | |
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| Parameter Estimates and Type I Analysis | |
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| Using Estimable Functions in SAS | |
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| Types I-IV Hypotheses | |
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| Using Types I-IV Estimable Functions in SAS-GLM | |
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| Population Marginal Means and Least Squares Means | |
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| Computer Analyses | |
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| Analyzing Large Balanced Two-Way Experiments Having Unequal Subclass Numbers | |
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| Feasibility Problems | |
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| Method of Unweighted Means | |
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| Simultaneous Inference and Multiple Comparisons | |
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| An Example of the Method of Unweighted Means | |
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| Computer Analyses | |
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| Case Study: Balanced Two-Way Treatment Structure with Unequal Subclass Numbers | |
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| Fat-Surfactant Example | |
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| Using the Means Model to Analyze Two-Way Treatment Structures with Missing Treatment Combinations | |
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| Parameter Estimation | |
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| |
| Hypothesis Testing and Confidence Intervals | |
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| |
| Computer Analyses | |
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| Using the Effects Model to Analyze Two-Way Treatment Structures with Missing Treatment Combinations | |
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| Type I and II Hypotheses | |
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| Type III Hypotheses | |
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| |
| Type IV Hypotheses | |
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| |
| Population Marginal Means and Least Squares Means | |
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| |
| Case Study: Two-Way Treatment Structure with Missing Treatment Combinations | |
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| Case Study | |
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| Analyzing Three-Way and Higher-Order Treatment Structures | |
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| General Strategy | |
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| Balanced and Unbalanced Experiments | |
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| Type I and II Analyses | |
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| Case Study: Three-Way Treatment Structure with Many Missing Treatment Combinations | |
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| Nutrition Scores Example | |
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| |
| An SAS-GLM Analysis | |
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| A Complete Analysis | |
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| |
| Random Effects Models and Variance Components | |
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| Introduction | |
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| |
| General Random Effects Model in Matrix Notation | |
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| |
| Computing Expected Mean Squares | |
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| |
| Methods for Estimating Variance Components | |
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| |
| Method of Moments | |
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| |
| Maximum Likelihood Estimators | |
| |
| |
| Restricted or Residual Maximum Likelihood Estimation | |
| |
| |
| MIVQUE Method | |
| |
| |
| Estimating Variance Components Using JMP<SUP>“</SUP> | |
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| |
| Methods for Making Inferences about Variance Components | |
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| |
| Testing Hypotheses | |
| |
| |
| Constructing Confidence Intervals | |
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| |
| Simulation Study | |
| |
| |
| Case Study: Analysis of a Random Effects Model | |
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| |
| Data Set | |
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| |
| Estimation | |
| |
| |
| Model Building | |
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| |
| Reduced Model | |
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| |
| Confidence Intervals | |
| |
| |
| Computations Using JMP<SUP>“</SUP> | |
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| |
| Analysis of Mixed Models | |
| |
| |
| Introduction to Mixed Models | |
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| |
| Analysis of the Random Effects Part of the Mixed Model | |
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| |
| Analysis of the Fixed Effects Part of the Model | |
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| |
| Best Linear Unbiased Prediction | |
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| |
| Mixed Model Equations | |
| |
| |
| Case Studies of a Mixed Model | |
| |
| |
| Unbalanced Two-Way Mixed Model | |
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| |
| JMP<SUP>“</SUP>Analysis of the Unbalanced Two-Way Data Set | |
| |
| |
| Methods for Analyzing Split-Plot Type Designs | |
| |
| |
| Introduction | |
| |
| |
| Model Definition and Parameter Estimation | |
| |
| |
| Standard Errors for Comparisons among Means | |
| |
| |
| A General Method for Computing Standard Errors of Differences of Means | |
| |
| |
| Comparison via General Contrasts | |
| |
| |
| Additional Examples | |
| |
| |
| Sample Size and Power Considerations | |
| |
| |
| Computations Using JMP<SUP>“</SUP> | |
| |
| |
| Methods for Analyzing Strip-Plot Type Designs | |
| |
| |
| Description of the Strip-Plot Design and Model | |
| |
| |
| Techniques for Making Inferences | |
| |
| |
| Example: Nitrogen by Irrigation | |
| |
| |
| Example: Strip-Plot with Split-Plot 1 | |
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| |
| Example: Strip-Plot with Split-Plot 2 | |
| |
| |
| Strip-Plot with Split-Plot 3 | |
| |
| |
| Split-Plot with Strip-Plot 4 | |
| |
| |
| Strip-Strip-Plot Design with Analysis via JMP<SUP>“</SUP>7 | |
| |
| |
| Methods for Analyzing Repeated Measures Experiments | |
| |
| |
| Model Specifications and Ideal Conditions | |
| |
| |
| The Split-Plot in Time Analyses | |
| |
| |
| Data Analyses Using the SAS-MIXED Procedure | |
| |
| |
| Analysis of Repeated Measures Experiments When the Ideal Conditions Are Not Satisfied | |
| |
| |
| Introduction | |
| |
| |
| MANOVA Methods | |
| |
| |
| p-Value Adjustment Methods | |
| |
| |
| Mixed Model Methods | |
| |
| |
| Case Studies: Complex Examples Having Repeated Measures | |
| |
| |
| Complex Comfort Experiment | |
| |
| |
| Family Attitudes Experiment | |
| |
| |
| Multilocation Experiment | |
| |
| |
| Analysis of Crossover Designs | |
| |
| |
| Definitions, Assumptions, and Models | |
| |
| |
| Two Period/Two Treatment Designs | |
| |
| |
| Crossover Designs with More Than Two Periods | |
| |
| |
| Crossover Designs with More Than Two Treatments | |
| |
| |
| Analysis of Nested Designs | |
| |
| |
| Definitions, Assumptions, and Models | |
| |
| |
| Parameter Estimation | |
| |
| |
| Testing Hypotheses and Confidence Interval Construction | |
| |
| |
| Analysis Using JMP<SUP>“</sup> | |
| |
| |
| Appendix | |
| |
| |
| Index | |
| |
| |
| Concluding Remarks, Exercises, and References appear at the end of each chapter | |