2nd Edition

# Analysis of Messy Data Volume 1 Designed Experiments, Second Edition

**Also available as eBook on:**

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.

**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.*

### Biography

George A. Milliken, Dallas E. Johnson

"…Every chapter has been systematically re-written for greater clarity, and added explanatory material has been inserted throughout. Many new diagrams and redrawn diagrams have been provided; those that show how to lay out the experimental designs are just superb and extraordinarily clear. The reference list has increased … . This revision is highly recommended to those who plan and analyze experiments of the type described."

—International Statistical Review(2009), 77, 2