**Edited by Connie M. Borror**

Analysis of Messy Data Volume III: Analysis
of Covariance.

by G. A. Milliken and D. E. Johnson

Elementary Statistics

by R. Larson and B. Farber

Experiments with Mixtures, 3rd ed.

by John Cornell

*The following brief editor's reviews are of new editions,
collections of papers, or other books that may be of interest
to some readers. *

*Lisa M. Hughes*, Florida A&M University, Tallahassee,
FL 32301

**Analysis of Messy
Data Volume III: Analysis of Covariance** by *G. A.
Milliken and D. E. Johnson*. Chapman & Hall/CRC Press,
Boca Raton, FL, 2001. 605 pp. $69.95

THIS book provides a comprehensive presentation of various ways to analyze data using the analysis of covariance method. It is primarily intended for practitioners who need to analyze data with covariate information. The entire text can be viewed as a model building cookbook that will provide practitioners with the necessary tools for performing analysis and appropriately interpreting results. For each topic covered, several examples are provided based on the authors personal consulting experiences. Accordingly, this text is presented from a practical view-point. Hence, emphasis is placed on practical implementation of the various methods rather than extensive presentations of underlying theory. The authors illustrate each computation using either SAS or JMP statistical software. Statistical background information and theoretical developments are presented as needed.

The text is arranged into eighteen different chapters, each containing introduction, reference, and exercise sections.The chapter titles are:

Chapter 1. Introduction to the Analysis of Covariance

Chapter 2. One-Way Analysis of Covariance

Chapter 3. Examples: One-Way Analysis of Covariance

Chapter 4. Multiple Covariates in a One-Way Treatment Structure in a Completely Randomized Design Structure

Chapter 5. Two-Way Treatment Structure and Analysis of Covariance in a Completely Randomized Design Structure

Chapter 6. Beta-Hat Models

Chapter 7. Variable Selection in the Analysis Selection of Covariance Model

Chapter 8. Comparing Models for Several Treatments

Chapter 9. Two Treatments in a Randomized Complete Block Design Structure

Chapter 10. More than Two Treatments in a Blocked Design Structure

Chapter 11. Covariates Measured on the Block in RCB and Incomplete Block Design Structures

Chapter 12. Random Effects Models with Covariates

Chapter 13. Mixed Models

Chapter 14. Analysis of Covariance Models with Heterogeneous Errors

Chapter 15. Analysis of Covariance for Split-Plot and Strip-Plot Design Structures

Chapter 16. Analysis of Covariance for Repeated Measures Designs

Chapter 17. Analysis of Covariance for Nonreplicated Experiments

Chapter 18. Special Applications of Analysis of Co-variance

Chapter 6 presents the beta-hat model and its analysis procedures for comparing models. The procedure for performing variable selection within the analysis of covariance model is presented in Chapter 7. Chapter 9 covers models with two treatments in a complete block design structure and a covariate measure within each block. Models with more than two treatments are addressed in Chapter 10. This discussion includes blocking between and within for randomized complete block (RCB) designs and incomplete designs. Chapter 11 addresses RCB and incomplete designs where the covariate is measured on the block. Chapter 12 presents the covariance model and estimation techniques for balanced and unbalanced one-and two-way treatment structures.

The latter part of the book (Chapters
13 18) provides discussion of covariance models for more advanced
topics. Chapter 13 describes the covariance model and estimation
techniques with examples using the SAS procedure MIXED. Chapter
14 describes testing unequal variances using techniques such
as Levene's Test, Hartley's *F*-Max Test, Bartlett's
Test and likelihood ratio tests. In this chapter, the authors
discuss how to develop and estimate unequal slope models,
and how to compare models with parallel and nonparallel lines.
Chapter 15 presents analysis of split-plot designs including
models for the co-variate(s) measured on the whole plot, or
the sub-plot, or both. By way of example, the authors explain
how covariance models for split plots and strip plots can
be reduced to mixed models and analyzed using PROC MIXED.
Chapter 17 extends the results contained in *Analysis of
Messy Data, Volume II: Nonreplicated Experiments* (Milliken
and Johnson (1989) and presents a method for increasing the
quality of the model using null and non-null partitions. In
chapter 18, the authors address topics such as using the covariate
to form blocks, covariates in crossover designs, nonparametric
analysis of covariance, non-linear modeling of covariates,
and mixed modeling for detection of outliers.

In this third addition to the *Analysis
of Messy Data* volume set, the authors have once again
provided a text that thoroughly explores a topic and also
interjects their own approaches to modeling and analysis.
This text would be an excellent reference for practitioners
dealing with covariates. The inclusion of numerous practical
examples concerning the analysis of covariance, along with
corresponding software implementation procedures, makes this
book quite useful in the data analysis arena.

Milliken, G. A. and Johnson, D. E. (1989). *Analysis of
Messy Data Volume 2: Nonreplicated Experiments*, Van Nostrand
Reinhold, New York, NY.

*Lloyd S. Nelson*, Statistical Consultant, Londonderry,
NH 03053-3647.

**Elementary Statistics**
by *R. Larson and B. Farber.* Prentice-Hall, Upper Saddle
River, NJ, 2000. xxix + 651 pp. $91.00.

NO introductory statistics book I
have ever read comes close to matching this book in either
its artistic presentation or its completeness. The chapter
headings are: (1) Introduction, (2) Descriptive Statistics,
(3) Probability, (4) Discrete Probability Distributions, (5)
Normal Probability Distributions, (6) Con dence Intervals,
(7) Hypothesis Testing with One Sample, (8) Hypothesis Testing
with Two Samples, (9) Correlation and Regression, (10) Chi
Square and the *F*-Distribution, and (11) Non-parametric
Tests. Ten tables of precentage points of conventional statistics
are provided.

Throughout the book the student is given the opportunity to try out the technique being discussed and is provided with excellent advice. The more than 1700 exercises are related to realistic problems. Answers are given for odd-numbered exercises. There are more than 200 data sets. Those with more than twenty values are available both on a disk which accompanies the book and on the Internet. The included disk contains selected examples in ASCII, Minitab, and Excel formats. A conscientious student will come away with a first-rate background in basic statistics and ready for a course in the design of experiments.

There is also available a set of
videotapes by Jim Condor (ISBN 0-13-040085-8) that provides
short lectures and worked examples. A number of resources
are available for the instructor, including an *Instructor's
Solution Manual* giving complete solutions to all the exercises.
Furthermore, there are available three "Companion Technology
Manuals": The TI-83 Manual, The Minitab Manual, and The Excel
Manual. This last includes *Phstat*, a statistics add-in
for Microsoft Excel that assists in statistical analysis.

There are, however, a few problems
with the text that should be noted. The first involves the
authors statement that a *c*-confidence interval contains
the population proportion *p* with probability *c*.
This is misleading, because it is true only for the random
interval and not for a specific interval. In their guidelines
for constructing this interval, Step 1 is to "identify the
sample statistics, *n* and *x*. By definition, a
statistic is a random variable, so *n* is not a statistic.
Despite the extensive attention paid to the construction and
use of histograms, no mention is made of setting up a histogram
in which it is appropriate to use class intervals of unequal
length (see Nelson (1988)).

Overall, though, this is a well written textbook. The figures and diagrams are superb. Every effort has been made to provide the reader with both interesting and useful examples. Because of its many excellent features, this book would be an excellent choice for either a class or for individual study.

Nelson, L. S. (1988). "Notes on the Histogram II: Unequal
Class Intervals". *Journal of Quality Technology* 20,
pp. 273–275.

*Heidi Goldfarb,*, Dial Corporation, Scotts-dale, Arizona,
85254.

**Experiments with Mixtures,
3rd ed.** by *John Cornell*. John Wiley & Sons,
Inc. New York, NY. 2002. 608 pp. $115.00.

THE third edition of this authoritative text on mixture experiments is a much-welcomed update. In the twelve years since the second edition was published, there has been significant activity in the mixture design arena, much of which has been by the author himself. The amount of activity is apparent by looking at the bibliography and noting all of the post-1990 entries. The references alone make this update a valuable resource.

Most of the additions include helpful
worked-out examples of the new material. There have been only
minor additions to chapters 1-4, which deal with the de nition
and design of pure mixture experiments. Chapter 1 introduces
the problem of mixture designs and gives the reader an updated
historical perspective. In Chapter 2, the author defines the
mixture space and shows many of the standard designs used.
An alternative design approach, turning *q* mixture components
into *q* - 1 independent variables, is the subject of
Chapter 3. Dealing with constraints on the mixture components
in the form of lower and/or upper bounds is covered in Chapter
4.

Chapter 5 is dedicated to the analysis of mixture designs. The inclusion of output from modern software packages is a nice addition to this chapter. Chapter 6 deals with other mixture forms such as ratio models, Cox's effects models, and a new section dealing with slack variable models. All of these alternate models are well supported with numerical examples. Mixture experiments with process variables and mixture amount experiments are thoroughly covered in Chapter 7. A valuable new section in this chapter addresses some very important miscellaneous issues in the area of designs with mixture components and process variables. Specifically, this new section addresses some of the finer points of working with reduced models and making predictions.

The most significant additions to the book are in Chapter 8, the "Additional Topics" chapter. This chapter contains a variety of topics, including blocking, optimal designs, and collinearity issues for highly constrained regions. In this latest edition, four sections dealing with multiple response models have been added. Biplots, overlay plots, and desirability functions are all described and demonstrated as ways to handle such situations. These sections are particularly valuable to practitioners who regularly deal with such problems. The two fully worked-out examples help illustrate the concepts presented.

Chapter 9 provides a concise review of matrix algebra, least squares, and ANOVA. An additional section on the PRESS statistic and studentized residuals has been added in this new edition. Chapter 10 provides the reader with some interesting sample data sets, partially worked-out solutions, and guidance for further steps in the analysis procedure. It remains unchanged from the previous edition.

This book is an excellent reference for any industrial statistician or statistical consultant who encounters mixture design problems. It is extremely readable, and the core chapters are very accessible to those with even modest statistical backgrounds. The numerous worked-out examples are excellent in demonstrating the concepts and allowing readers to try to replicate the analyses on their own. It is also a suitable textbook for a short course or graduate level course on mixture designs.

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