**Edited by Connie M. Borror**

Methods of Multivariate Analysis, 2nd ed..

by Alvin C. Rencher

Multivariate Statistical Process Control with Industrial Applications

by Robert L. Mason and John C. Young

Statistical Thinking: Improving Business Performance

by Roger Hoerl and Ronald D. Snee

*Connie M. Borror*, Department of Decision Sciences, Drexel University, Philadelphia, PA 19104

**Methods of Multivariate Analysis, 2nd ed.** by Alvin C. Rencher. John Wiley & Sons, Inc., New York, NY. 2002. xxii+708 pp. $105.00

THE second edition of *Methods of Multivariate Analysis* offers some new material and new exercises. The new material consists of a chapter on cluster analysis and a chapter on graphical procedures (multidimensional scaling, correspondence analysis, and biplots). The exercises offer a variety of applications and derivations for students of different disciplines and background.

The material is well written and presented in a manner that is conducive to understanding the subject matter at many different levels. The author provides enough derivations and proofs throughout the book to support the methods, but they are not necessary for the reader to comprehend and apply the methods. The prerequisites needed are matrix algebra and some basic statistics. The second chapter provides the necessary background in matrix algebra to understand the remaining material in the text. As the title suggests, this book emphasizes methods and applications rather than detailed proofs.

There are fifteen chapters and three appendices:

Chapter 1. Introduction

Chapter 2. Matrix Algebra

Chapter 3. Characterization and Displaying Multivariate Data

Chapter 4. The Multivariate Normal Distribution

Chapter 4. Principal Components Analysis

Chapter 5. Exploratory Factor Analysis

Chapter 6. Con.rmatory Factor Analysis

Chapter 7. Multidimensional Scaling

Chapter 8. Cluster Analysis

Chapter 5. Tests on One or Two Mean Vectors

Chapter 6. Multivariate Analysis of Variance

Chapter 7. Tests on Covariance Matrices

Chapter 8. Discriminant Analysis: Description of Group Separation

Chapter 9. Classification Analysis: Allocation of Observations to Groups

Chapter 10. Multivariate Regression

Chapter 11. Canonical Correlation

Chapter 12. Principal Component Analysis

Chapter 13. Factor Analysis

Chapter 14. Cluster Analysis

Chapter 15. Graphical Procedures

Appendix A. Tables

Appendix B. Answers and Hints to Problems

Appendix C. Data Sets and SAS Files

The electronic copies of the data sets and SAS files are available on the Wiley website (at www.wiley.com) and not packaged with the book. Instructions on how to access these files are given in Appendix C, and I found them easy to download. The SAS files are complete and include the commands and statements needed to carry out the appropriate analysis. Students and instructors alike should find this to be very useful for implementing the procedures.

The second edition of this text is an excellent resource for multivariate statistical methods and their applications. It provides something for everyone who is interested in applying multivariate methods in science and engineering. The author has once again done an outstanding job of presenting the material and supplementing it with practical problems and examples.

*Charles W. Champ*, Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460.

**Multivariate Statistical Process Control with Industrial Applications** by *Robert L. Mason and John C. Young*. ASA-SIAM, Philadelphia, PA 19104. xiii+263 pp. List: $70.00, Member: $49.00

AS pointed out by the authors, ''there are many industrial settings where process performance is based on the behavior of a set of interrelated variables...Since the variables do not behave independently of one another, they must be examined together as a group and not separately.'' This is why multivariate statistical quality control (SQC) procedures are needed. The ''major intent'' of this text ''is to present to the practitioner a modern and comprehensive overview on how to establish and operate an applied multivariate control procedure based on our conceptual view of Hotelling's *T*^{2} chart.''

According to the authors, ''the intended audience for this book are professionals or students involved with multivariate quality control.'' They assume that the reader has a background in ''univariate statistical estimation and control procedures (such as Shewhart charts) and is familiar with certain probability functions, such the normal, chi-square, *t*, and *F* distributions.'' It is also helpful if the reader has some exposure to regression analysis. The authors point out that knowledge of matrix algebra is essential in studying any multivarite statistical method. For the reader who may not have this background, they have attempted to ''downplay'' the use of matrix algebra while providing a minimal coverage of this topic as it applies to the *T*^{2} statistic.

Virtually all multivariate statistical methods require a significant amount of computation when applying the methods. The *T*^{2} is no exception. To remove the drudgery of computation, the authors suggest the use of a statistical software package produced by InControl Technologies, Inc. The computational examples in the text concerning the *T*^{2} procedures use this package. A free demonstration version of QualStat^{TM} is provided with the text.

There are eleven chapters in the book:

Chapter 1. Introduction to theThere are also a preface, an appendix with distribution tables, a bibliography, and an index.T^{2}Chart Chapter 2. Basic Concepts About theT^{2}Statistic Chapter 3. Checking Assumptions for Using theT^{2}Statistic Chapter 4. Construction of Historical Data Set Chapter 5. Charting theT^{2}Statistic in Phase I Chapter 6. Charting theT^{2}Statistic in Phase II Chapter 7. Interpretation ofT^{2}Signals for Two Variables Chapter 8. Interpretation ofT^{2}Signals for the General Case Chapter 9. Improving the Sensitivity of theT^{2}Statistic Chapter 10. Autocorrelation inT^{2}Control Charts Chapter 11. TheT^{2}Statistic and Batch Processes

This text is one of a very small number devoted to multivariate statistical process control. The authors only study the Hotelling's *T*^{2} chart as it is used in detecting a change in the mean vector of a multivariate quality measurement, but they do so in detail. They bring together literature that is available on this topic and present it in a clear and concise manner. Illustrative examples are given, although there are no chapter exercises. This text should be considered as supplementary reading in a course on statistical quality control. Practitioners interested in applying multivariate quality control procedures also will find this text by Mason and Young readable and quite useful.

*Cathy A. Lawson*, General Dynamics Decision Systems, Scottsdale, AZ 85257.

**Statistical Thinking: Improving Business Performance** by *Roger Hoerl and Ronald D. Snee*. Duxbury Press/ITP, Pacific Grove, CA 93950-5098. 2002. 526 pp. $95.95

SIX Sigma is a topic that continues to receive a lot of attention in literature that references Quality Management practices. However, for all of the discussion about Six Sigma, there are remarkably few sources that actually explain the concept of statistical thinking and provide a practical roadmap for companies wishing to implement a robust continuous improvement process. This book does just that.

*Statistical Thinking* is written for the engineer or manager who wants to implement some practical yet powerful tools to help achieve improvements in quality and cycle time in a manufacturing and/or business process. This is not a book aimed at experienced statisticians. While the authors do provide an overview of a good number of statistical topics, they address these topics at a very introductory level. This book is more focused on the process of improvement and the use of statistical thinking to cultivate a culture of robust and disciplined problem solving and prevention. The case studies and examples in the book are drawn from a variety of industries, which assists the authors in making the point that these tools and methods are applicable in just about any organization.

In Chapter 1, the authors set the stage for the rest of the book by providing good reasons why businesses need to improve their processes. The concept of statistical thinking is introduced in this chapter and carried forward in the subsequent chapters. In Chapter 2, statistical thinking is the main topic and is illustrated by two very good but very different case studies. The first case study shows how a structured data-driven approach to understanding the causal relationship between process variables can favorably impact a company's bottom line. The second case study illustrates the effective use of data in solving a problem and driving improvement for a soccer team. Chapter 3 rounds out the first section of the book by providing an overview of business processes. In this chapter, the authors show how virtually anything can be considered a process and introduce some tools that can help the practitioner define that process to assist in identifying where it can be improved.

The discussion in Chapter 4 focuses on specific tools, methods, and strategies for improvement. In this chapter, the approach to process improvement is contrasted with problem solving. The authors provide a nice distinction between the two approaches. In problem solving, the right amount of emphasis is placed on properly defining the problem before jumping to conclusions about its solution, a practice that many teams fail to understand. The only way in which this chapter could be improved would be by the inclusion of options to consider when the problem has not been satisfactorily resolved. Chapter 5 contains a discussion of specific tools that are used during process improvement or problem solving and a good overview of data collection and sampling issues. This is a topic not usually addressed in statistics books, which generally focus on how to analyze the data after it has been collected. The discussion in this chapter nicely fills the gap in that subject.

There are three short chapters, not numbered, which are devoted to the use of common software packages for analyzing data. Microsoft Excel, MINITAB, and JMP are profiled in these chapters. The authors provide a brief overview of these software tools and show some examples of how they can be used. In keeping with the spirit of practical discussions provided throughout this book, this is another nice addition for the reader.

In Chapters 6 and 7, the authors deal with building and using models. A handy checklist of steps to follow when building a model is given in Chapter 6. Chapter 7 includes experimentation tools such as factorial experiments. Two case studies are provided which show how the experiments are used to impact a process's performance. In Chapters 8 and 9, the authors address statistical inference. A great deal of emphasis is placed on graphical tools which can be very helpful in trying to understand what the data can mean. Many practitioners can get by without a great deal of statistical training if they can adequately represent their data in a graphical format. Chapter 9 is the most theoretical chapter in the book, covering topics such as central limit theorem, sampling distributions, and data transformations. The authors' approach to these topics is as straightforward and practical as the rest of the book, and the reader should be able to come away from this chapter with some basic understanding of these topics.

Chapter 10 serves as the conclusion to the text by providing a roadmap for implementation and sustaining improvement. Additional case studies are provided which further illustrate the application of the concepts. The authors go on to provide 10 appendices which address a variety of topics from forming an effective team to process re-design. These appendices are each like a short paper which provides practical advice on a specific topic. Many of the topics addressed in these appendices are not found in a typical statistical text and further serve to make this book a good resource for practitioners.

In conclusion, I believe that this book is well written, that the topics are adequately covered, and that a variety of interesting and diverse case studies are included. It is not a book for the Master Black Belt or experienced statistician; however, it is a book that the Master Black Belt or experienced statistician could use to help bridge the gap between themselves and the managers and engineers in their company. would recommend this text to anyone wishing to implement a quality improvement program in their company.

**Duxbury Press/ITP**, 4511 Forest Lodge Road, Pacific Grove, CA 93950-5098; (800) 423-0563; www.duxbury.com.

**John Wiley & Sons**, 4605 Third Ave., New York, NY 10128; (800) 352-3566; http://www.wiley.com