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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 | |