Table of Contents
The Simplest Case: One-Way Treatment Structure in a Completely Randomized Design Structure with Homogeneous Errors
Model Definitions and Assumptions
Parameter Estimation
Inferences on Linear Combinations—Tests and Confidence Intervals
Example—Tasks and Pulse Rate
Simultaneous Tests on Several Linear Combinations
Example—Tasks and Pulse Rate (Continued)
Testing the Equality of all Means
Example—Tasks and Pulse Rate (Continued)
General Method for Comparing Two Models—The Principle of Conditional Error
Example—Tasks and Pulse Rate (Continued)
Computer Analyses
One-Way Treatment Structure in a Completely Randomized Design Structure with Heterogeneous Errors
Model Definitions and Assumptions
Parameter Estimation
Tests for Homogeneity of Variances
Example—Drugs and Errors
Inferences on Linear Combinations
Example—Drugs and Errors (Continued)
General Satterthwaite Approximation for Degrees of Freedom
Comparing All Means
Simultaneous Inference Procedures and Multiple Comparisons
Error Rates
Recommendations
Least Significant Difference
Fisher’s LSD Procedure
Bonferroni’s Method
Scheffé’s Procedure
Tukey–Kramer Method
Simulation Methods
Šidák Procedure
Example—Pairwise Comparisons
Dunnett’s Procedure
Example—Comparing with a Control
Multivariate t
Example—Linearly Independent Comparisons
Sequential Rejective Methods
Example—Linearly Dependent Comparisons
Multiple Range Tests
Waller–Duncan Procedure
Example—Multiple Range for Pairwise Comparisons
A Caution
Basics for Designing Experiments
Introducing Basic Ideas
Structures of a Designed Experiment
Examples of Different Designed Experiments
Multilevel Designs: Split-Plots, Strip-Plots, Repeated Measures, and Combinations
Identifying Sizes of Experimental Units—Four Basic Design Structures
Hierarchical Design: A Multilevel Design Structure
Split-Plot Design Structures: Two-Level Design Structures
Strip-Plot Design Structures: A Nonhierarchical Multilevel Design
Repeated Measures Designs
Designs Involving Nested Factors
Matrix Form of the Model
Basic Notation
Least Squares Estimation
Estimability and Connected Designs
Testing Hypotheses about Linear Model Parameters
Population Marginal Means
Balanced Two-Way Treatment Structures
Model Definition and Assumptions
Parameter Estimation
Interactions and Their Importance
Main Effects
Computer Analyses
Case Study: Complete Analyses of Balanced Two-Way Experiments
Contrasts of Main Effect Means
Contrasts of Interaction Effects
Paint–Paving Example
Analyzing Quantitative Treatment Factors
Multiple Comparisons
Using the Means Model to Analyze Balanced Two-Way Treatment Structures with Unequal Subclass Numbers
Model Definitions and Assumptions
Parameter Estimation
Testing whether All Means Are Equal
Interaction and Main Effect Hypotheses
Population Marginal Means
Simultaneous Inferences and Multiple Comparisons
Using the Effects Model to Analyze Balanced Two-Way Treatment Structures with Unequal Subclass Numbers
Model Definition
Parameter Estimates and Type I Analysis
Using Estimable Functions in SAS
Types I–IV Hypotheses
Using Types I–IV Estimable Functions in SAS-GLM
Population Marginal Means and Least Squares Means
Computer Analyses
Analyzing Large Balanced Two-Way Experiments Having Unequal Subclass Numbers
Feasibility Problems
Method of Unweighted Means
Simultaneous Inference and Multiple Comparisons
An Example of the Method of Unweighted Means
Computer Analyses
Case Study: Balanced Two-Way Treatment Structure with Unequal Subclass Numbers
Fat–Surfactant Example
Using the Means Model to Analyze Two-Way Treatment Structures with Missing Treatment Combinations
Parameter Estimation
Hypothesis Testing and Confidence Intervals
Computer Analyses
Using the Effects Model to Analyze Two-Way Treatment Structures with Missing Treatment Combinations
Type I and II Hypotheses
Type III Hypotheses
Type IV Hypotheses
Population Marginal Means and Least Squares Means
Case Study: Two-Way Treatment Structure with Missing Treatment Combinations
Case Study
Analyzing Three-Way and Higher-Order Treatment Structures
General Strategy
Balanced and Unbalanced Experiments
Type I and II Analyses
Case Study: Three-Way Treatment Structure with Many Missing Treatment Combinations
Nutrition Scores Example
An SAS-GLM Analysis
A Complete Analysis
Random Effects Models and Variance Components
Introduction
General Random Effects Model in Matrix Notation
Computing Expected Mean Squares
Methods for Estimating Variance Components
Method of Moments
Maximum Likelihood Estimators
Restricted or Residual Maximum Likelihood Estimation
MIVQUE Method
Methods for Making Inferences about Variance Components
Testing Hypotheses
Constructing Confidence Intervals
Simulation Study
Case Study: Analysis of a Random Effects Model
Data Set
Estimation
Model Building
Reduced Model
Confidence Intervals
Analysis of Mixed Models
Introduction to Mixed Models
Analysis of the Random Effects Part of the Mixed Model
Analysis of the Fixed Effects Part of the Model
Best Linear Unbiased Prediction
Mixed Model Equations
Case Studies of a Mixed Model
Unbalanced Two-Way Mixed Model
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
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
Example: Strip-Plot with Split-Plot 2
Strip-Plot with Split-Plot 3
Split-Plot with Strip-Plot 4
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®
Appendix
Index
Concluding Remarks, Exercises, and References appear at the end of each chapter.