Milliken / Johnson Analysis of Messy Data Volume 1

Designed Experiments, Second Edition
2. Auflage 2009
ISBN: 978-1-4200-1015-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 674 Seiten

A bestseller for nearly 25 years, Analysis of Messy Data, Volume 1: Designed Experiments helps applied statisticians and researchers analyze the kinds of data sets encountered in the real world. Written by two long-time researchers and professors, this second edition has been fully updated to reflect the many developments that have occurred since the original publication.
New to the Second Edition

- Several modern suggestions for multiple comparison procedures

- Additional examples of split-plot designs and repeated measures designs

- The use of SAS-GLM to analyze an effects model

- The use of SAS-MIXED to analyze data in random effects experiments, mixed model experiments, and repeated measures experiments

The book explores various techniques for multiple comparison procedures, random effects models, mixed models, split-plot experiments, and repeated measures designs. The authors implement the techniques using several statistical software packages and emphasize the distinction between design structure and the structure of treatments. They introduce each topic with examples, follow up with a theoretical discussion, and conclude with a case study. Bringing a classic work up to date, this edition will continue to show readers how to effectively analyze real-world, nonstandard data sets.

Zielgruppe

Applied statisticians and researchers involved with experiment design and data analysis, particularly in the pharmaceutical industry, agriculture, and the life sciences; Graduate students in a variety of disciplines taking a course in linear model theory or experiment design

Autoren/Hrsg.

Milliken, George A.

Johnson, Dallas E.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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

Estimating Variance Components Using JMP®
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

Computations Using JMP®
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

JMP® 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®
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

Strip-Strip-Plot Design with Analysis via JMP®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®
Appendix
Index
Concluding Remarks, Exercises, and References appear at the end of each chapter.