2nd Edition

Analysis of Messy Data Volume 1 Designed Experiments, Second Edition

    688 Pages 100 B/W Illustrations
    by Chapman & Hall

    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


    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


    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


    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


    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


    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.


    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