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Analysis of Messy Data Volume 1 Designed Experiments (Milliken)

 Author(s)  George A. Milliken, Dallas E. Johnson
 Title  Analysis of Messy Data Volume 1: Designed Experiments
 Year  1992
 Publisher  Chapman & Hall/CRC
 ISBN  0-412-99081-4

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®



Concluding Remarks, Exercises, and References appear at the end of each chapter.

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