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| Acknowledgments | |
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| Introduction | |
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| About This Book | |
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| Statistical Topics and SAS Procedures | |
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| Regression | |
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| Introduction | |
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| The REG Procedure | |
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| Using the REG Procedure to Fit a Model with One Independent Variable | |
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| The P, CLM, and CLI Options: Predicted Values and Confidence Limits | |
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| A Model with Several Independent Variables | |
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| The SS1 and SS2 Options: Two Types of Sums of Squares | |
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| Tests of Subsets and Linear Combinations of Coefficients | |
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| Fitting Restricted Models: The RESTRICT Statement and NOINT Option | |
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| Exact Linear Dependency | |
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| The GLM Procedure | |
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| Using the GLM Procedure to Fit a Linear Regression Model | |
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| Using the CONTRAST Statement to Test Hypotheses about Regression Parameters | |
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| Using the ESTIMATE Statement to Estimate Linear Combinations of Parameters | |
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| Statistical Background | |
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| Terminology and Notation | |
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| Partitioning the Sums of Squares | |
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| Hypothesis Tests and Confidence Intervals | |
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| Using the Generalized Inverse | |
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| Analysis of Variance for Balanced Data | |
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| Introduction | |
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| One- and Two-Sample Tests and Statistics | |
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| One-Sample Statistics | |
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| Two Related Samples | |
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| Two Independent Samples | |
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| The Comparison of Several Means: Analysis of Variance | |
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| Terminology and Notation | |
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| Crossed Classification and Interaction Sum of Squares | |
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| Nested Effects and Nested Sum of Squares | |
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| Using the ANOVA and GLM Procedures | |
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| Multiple Comparisons and Preplanned Comparisons | |
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| The Analysis of One-Way Classification of Data | |
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| Computing the ANOVA Table | |
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| Computing Means, Multiple Comparisons of Means, and Confidence Intervals | |
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| Planned Comparisons for One-Way Classification: The CONTRAST Statement | |
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| Linear Combinations of Model Parameters | |
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| Testing Several Contrasts Simultaneously | |
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| Orthogonal Contrasts | |
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| Estimating Linear Combinations of Parameters: The Estimate Statement | |
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| Randomized-Blocks Designs | |
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| Analysis of Variance for Randomized-Blocks Design | |
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| Additional Multiple Comparison Methods | |
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| Dunnett's Test to Compare Each Treatment to a Control | |
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| A Latin Square Design with Two Response Variables | |
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| A Two-Way Factorial Experiment | |
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| ANOVA for a Two-Way Factorial Experiment | |
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| Multiple Comparisons for a Factorial Experiment | |
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| Multiple Comparisons of METHOD Means by VARIETY | |
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| Planned Comparisons in a Two-Way Factorial Experiment | |
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| Simple Effect Comparisons | |
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| Main Effect Comparisons | |
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| Simultaneous Contrasts in Two-Way Classifications | |
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| Comparing Levels of One Factor within Subgroups of Levels of Another Factor | |
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| An Easier Way to Set Up CONTRAST and ESTIMATE Statements | |
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| Analyzing Data with Random Effects | |
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| Introduction | |
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| Nested Classifications | |
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| Analysis of Variance for Nested Classifications | |
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| Computing Variances of Means from Nested Classifications and Deriving Optimum Sampling Plans | |
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| Analysis of Variance for Nested Classifications: Using Expected Mean Squares to Obtain Valid Tests of Hypotheses | |
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| Variance Component Estimation for Nested Classifications: Analysis Using PROC MIXED | |
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| Additional Analysis of Nested Classifications Using PROC MIXED: Overall Mean and Best Linear Unbiased Prediction | |
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| Blocked Designs with Random Blocks | |
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| Random-Blocks Analysis Using PROC MIXED | |
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| Differences between GLM and MIXED Randomized-Complete-Blocks Analysis: Fixed versus Random Blocks | |
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| Treatment Means | |
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| Treatment Differences | |
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| The Two-Way Mixed Model | |
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| Analysis of Variance for the Two-Way Mixed Model: Working with Expected Mean Squares to Obtain Valid Tests | |
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| Standard Errors for the Two-Way Mixed Model: GLM versus MIXED | |
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| More on Expected Mean Squares: Determining Quadratic Forms and Null Hypotheses for Fixed Effects | |
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| A Classification with Both Crossed and Nested Effects | |
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| Analysis of Variance for Crossed-Nested Classification | |
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| Using Expected Mean Squares to Set Up Several Tests of Hypotheses for Crossed-Nested Classification | |
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| Satterthwaite's Formula for Approximate Degrees of Freedom | |
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| PROC MIXED Analysis of Crossed-Nested Classification | |
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| Split-Plot Experiments | |
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| A Standard Split-Plot Experiment | |
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| Analysis of Variance Using PROC GLM | |
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| Analysis with PROC MIXED | |
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| Unbalanced Data Analysis: Basic Methods | |
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| Introduction | |
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| Applied Concepts of Analyzing Unbalanced Data | |
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| ANOVA for Unbalanced Data | |
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| Using the CONTRAST and Estimate Statements with Unbalanced Data | |
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| The LSMEANS Statement | |
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| More on Comparing Means: Other Hypotheses and Types of Sums of Squares | |
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| Issues Associated with Empty Cells | |
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| The Effect of Empty Cells on Types of Sums of Squares | |
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| The Effect of Empty Cells on CONTRAST, ESTIMATE, and LSMEANS Results | |
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| Some Problems with Unbalanced Mixed-Model Data | |
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| Using the GLM Procedure to Analyze Unbalanced Mixed-Model Data | |
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| Approximate F-Statistics from ANOVA Mean Squares with Unbalanced Mixed-Model Data | |
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| Using the CONTRAST, ESTIMATE, and LSMEANS Statements in GLM with Unbalanced Mixed-Model Data | |
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| Using the MIXED Procedure to Analyze Unbalanced Mixed-Model Data | |
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| Using the GLM and MIXED Procedures to Analyze Mixed-Model Data with Empty Cells | |
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| Summary and Conclusions about Using the GLM and MIXED Procedures to Analyze Unbalanced Mixed-Model Data | |
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| Understanding Linear Models Concepts | |
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| Introduction | |
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| The Dummy-Variable Model | |
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| The Simplest Case: A One-Way Classification | |
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| Parameter Estimates for a One-Way Classification | |
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| Using PROC GLM for Analysis of Variance | |
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| Estimable Functions in a One-Way Classification | |
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| Two-Way Classification: Unbalanced Data | |
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| General Considerations | |
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| Sums of Squares Computed by PROC GLM | |
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| Interpreting Sums of Squares in Reduction Notation | |
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| Interpreting Sums of Squares in [mu]-Model Notation | |
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| An Example of Unbalanced Two-Way Classification | |
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| The MEANS, LSMEANS, CONTRAST, and ESTIMATE Statements in a Two-Way Layout | |
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| Estimable Functions for a Two-Way Classification | |
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| The General Form of Estimable Functions | |
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| Interpreting Sums of Squares Using Estimable Functions | |
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| Estimating Estimable Functions | |
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| Interpreting LSMEANS, CONTRAST, and ESTIMATE Results Using Estimable Functions | |
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| Empty Cells | |
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| Mixed-Model Issues | |
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| Proper Error Terms | |
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| More on Expected Mean Squares | |
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| An Issue of Model Formulation Related to Expected Mean Squares | |
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| ANOVA Issues for Unbalanced Mixed Models | |
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| Using Expected Mean Squares to Construct Approximate F-Tests for Fixed Effects | |
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| GLS and Likelihood Methodology Mixed Model | |
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| An Overview of Generalized Least Squares Methodology | |
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| Some Practical Issues about Generalized Least Squares Methodology | |
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| Analysis of Covariance | |
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| Introduction | |
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| A One-Way Structure | |
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| Covariance Model | |
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| Means and Least-Squares Means | |
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| Contrasts | |
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| Multiple Covariates | |
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| Unequal Slopes | |
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| Testing the Heterogeneity of Slopes | |
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| Estimating Different Slopes | |
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| Testing Treatment Differences with Unequal Slopes | |
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| A Two-Way Structure without Interaction | |
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| A Two-Way Structure with Interaction | |
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| Orthogonal Polynomials and Covariance Methods | |
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| A 2 x 3 Example | |
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| Use of the IML ORPOL Function to Obtain Orthogonal Polynomial Contrast Coefficients | |
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| Use of Analysis of Covariance to Compute ANOVA and Fit Regression | |
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| Repeated-Measures Analysis | |
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| Introduction | |
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| The Univariate ANOVA Method for Analyzing Repeated Measures | |
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| Using GLM to Perform Univariate ANOVA of Repeated-Measures Data | |
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| The CONTRAST, ESTIMATE, and LSMEANS Statements in Univariate ANOVA of Repeated-Measures Data | |
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| Multivariate and Univariate Methods Based on Contrasts of the Repeated Measures | |
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| Univariate ANOVA of Repeated Measures at Each Time | |
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| Using the REPEATED Statement in PROC GLM to Perform Multivariate Analysis of Repeated-Measures Data | |
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| Univariate ANOVA of Contrasts of Repeated Measures | |
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| Mixed-Model Analysis of Repeated Measures | |
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| The Fixed-Effects Model and Related Considerations | |
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| Selecting an Appropriate Covariance Model | |
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| Reassessing the Covariance Structure with a Means Model Accounting for Baseline Measurement | |
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| Information Criteria to Compare Covariance Models | |
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| PROC MIXED Analysis of FEV1 Data | |
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| Inference on the Treatment and Time Effects of FEV1 Data Using PROC MIXED | |
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| Comparisons of DRUG*HOUR Means | |
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| Comparisons Using Regression | |
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| Multivariate Linear Models | |
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| Introduction | |
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| A One-Way Multivariate Analysis of Variance | |
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| Hotelling's T[superscript 2] Test | |
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| A Two-Factor Factorial | |
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| Multivariate Analysis of Covariance | |
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| Contrasts in Multivariate Analyses | |
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| Statistical Background | |
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| Generalized Linear Models | |
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| Introduction | |
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| The Logistic and Probit Regression Models | |
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| Logistic Regression: The Challenger Shuttle O-Ring Data Example | |
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| Using the Inverse Link to Get the Predicted Probability | |
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| Alternative Logistic Regression Analysis Using 0-1 Data | |
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| An Alternative Link: Probit Regression | |
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| Binomial Models for Analysis of Variance and Analysis of Covariance | |
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| Logistic ANOVA | |
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| The Analysis-of-Variance Model with a Probit Link | |
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| Logistic Analysis of Covariance | |
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| Count Data and Overdispersion | |
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| An Insect Count Example | |
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| Model Checking | |
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| Correction for Overdispersion | |
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| Fitting a Negative Binomial Model | |
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| Using PROC GENMOD to Fit the Negative Binomial with a Log Link | |
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| Fitting the Negative Binomial with a Canonical Link | |
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| Advanced Application: A User-Supplied Program to Fit the Negative Binomial with a Canonical Link | |
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| Generalized Linear Models with Repeated Measures--Generalized Estimating Equations | |
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| A Poisson Repeated-Measures Example | |
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| Using PROC GENMOD to Compute a GEE Analysis of Repeated Measures | |
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| Background Theory | |
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| The Generalized Linear Model Defined | |
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| How the GzLM's Parameters Are Estimated | |
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| Standard Errors and Test Statistics | |
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| Quasi-Likelihood | |
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| Repeated Measures and Generalized Estimating Equations | |
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| Examples of Special Applications | |
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| Introduction | |
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| Confounding in a Factorial Experiment | |
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| Confounding with Blocks | |
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| A Fractional Factorial Example | |
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| A Balanced Incomplete-Blocks Design | |
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| A Crossover Design with Residual Effects | |
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| Models for Experiments with Qualitative and Quantitative Variables | |
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| A Lack-of-Fit Analysis | |
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| An Unbalanced Nested Structure | |
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| An Analysis of Multi-Location Data | |
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| An Analysis Assuming No LocationxTreatment Interaction | |
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| A Fixed-Location Analysis with an Interaction | |
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| A Random-Location Analysis | |
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| Further Analysis of a LocationxTreatment Interaction Using a Location Index | |
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| Absorbing Nesting Effects | |
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| References | |
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| Index | |