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Mathematics

 

Review Essays of Academic, Professional & Technical Books in the Humanities & Sciences

 

Using Multivariate Statistics (5th Edition) by Barbara G. Tabachnick, Linda S. Fidell (Allyn & Bacon) provides advanced students with a timely and comprehensive introduction to today’s most commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge of higher level mathematics.

This long-awaited revision reflects extensive updates throughout, especially in the areas of Data Screening (Chapter 4) Multiple Regression (Chapter 5) and Logistic Regression (Chapter 12). A brand new chapter (Chapter 15) on Multilevel Linear Modeling explains techniques for dealing with hierarchical data sets. Also included are syntax and output for accomplishing many analyses through the most recent releases of SAS and SPSS.

As in past editions, each technique chapter:

• discusses tests for assumptions of analysis (and procedures for dealing with their violation)
• presents a small example, hand-worked for the most basic analysis
• describes varieties of analysis
• discusses important issues (such as effect size)
• provides an example with a real data set from tests of assumptions to write-up of a results section
• compares features of relevant programs

Obesity threatened, and we've had to consider putting the book on a diet. We've added only one chapter this time around, Multilevel Linear Modeling (Chapter 15), and some spiffy new techniques for dealing with missing data (in Chapter 4). Otherwise, we've mostly streamlined and said good­bye to some old friends. We've forsaken the Time-Series Analysis chapter in the text, but you'll be able to download it from the publisher's web site at www.ablongman.com/tabachnick5e. Another sadly forsaken old friend is SYSTAT. We still love the program, however, for its right-to-the-point analyses and terrific graphics, and are pleased that most of the graphics have been incorporated into SPSS. Although absent from demonstrations, features of SYSTAT, and any other programs we've cut, still appear in the last sections of Chapters 5 through 16, and in online Chapter 18, where pro­grams are compared. We've changed the order of some chapters: canonical correlation seemed rather difficult to appear as early as it did, and survival analysis seemed to want to snuggle up to logistic regression. Actually, the order doesn't seem to matter much; perusal of syllabi on the Web convinces us that professors feel free to present chapters in any order they choose—and that's fine with us.

Multilevel linear modeling (MLM) seems to have taken the world by storm; how did we ever live without it? Real life is hierarchical—students come to us within classrooms, teachers work within different schools, patients share wards and nursing staff, and audiences attend different per­formances. We hardly ever get to break these groups apart for research purposes, so we have to deal with intact groups and all their shared experiences. MLM lets us do this without violating all of the statistical assumptions we learned to know and hate. Now that SAS and SPSS can deal with these models, we're ready to tackle the real world.

SAS and SPSS also now offer reasonable ways to impute missing data through multiple-imputation techniques and fully assess missing data patterns, respectively. We expanded Chapter 4 to demonstrate these enhancements. SPSS and SAS keep adding goodies, which we'll try to show off. As before, we adapt our syntax from Windows menus whenever possible, and all of our data sets are available on the book's web page (www.ablongman.com/tabachnick5e). We've also paid more attention to effect sizes and, especially, confidence intervals around effect sizes. Michael Simpson of the Australian National University has kindly given us permission to include some nifty SPSS and SAS syntax and data files in our web page downloads. Jim Steiger and Rachel Fouladi have gra­ciously given us permission to include their DOS program that finds confidence intervals around R2.

One thing we'll never change is our practical bent, focusing on the benefits and limitations of applications of a technique to a data set—when, why, and how to do it. The math is wonderful, and we suggest (but don't insist) that students follow along through section four of each chapter using readily available software for matrix manipulations or spreadsheets. But we still feel that under­standing the math is not enough to insure appropriate analysis of data. And our readers assure us that they really are able to apply the techniques without a great deal of attention to the math of section four. Our small-sample examples remain silly; alas, our belly dancing days are over. As for our most recent reviewers, kindly provided by our publisher, we had the three bears checking out beds: too hard, too soft, and just right. So we've not changed the tone or level of difficulty.

Multivariate Statistical Methods: A Primer, Third Edition by Bryan F. J. Manly (Chapman & Hall/CRC) This is a thoroughly revised, updated edition of a best-selling introductory textbook and primer. The third edition retains the author's trademark concise and clear style and its focus on examples in the biological and environmental sciences. Topics new to this edition include confirmatory factor analysis, handling missing values, and the emerging techniques of data mining and neural networks. While not linking the book to any specific software package, the book now includes an appendix comparing and contrasting various statistical software packages, such as Stata, Statistica, SAS, and Genstat.

Multivariate Statistical Methods: A Primer introduces multivariate methods to non-mathematicians and provides a general overview without overwhelming the novice with comprehensive details. This third edition is a thoroughly revised and updated version of a best-selling introductory textbook and primer. It retains the author's trademark clear, concise style and focuses on examples in the biological and environmental sciences. Topics new to this edition include confirmatory factor analysis, the use of mixture models for cluster analysis, and the emerging techniques of data mining and neural networks. While not linked to any specific software package, the book now includes an appendix comparing and contrasting various statistical software packages, such as Stata, Statistica, SAS, and Genstat. The author also notes which software was used for a particular example, when appropriate.

Features:

  • Includes references to major statistical software packages

  • Appeals to a broad range of quantitative scientists and statisticians

  • Presents new topics including confirmatory factor analysis, the use

  • of mixture models for cluster analysis, neural networks, and data

  • mining

  • Provides all the data used in the book on a companion website

In his efforts to produce a book that is as short as possible and that enables readers to begin to use multivariate methods in an intelligent manner, the author has produced a succinct and handy reference. With updated information on multivariate analyses, new examples using the latest software, and updated references, this. book provides a timely introduction to useful tools for statistical analysis.

The purpose of this book is to introduce multivariate statistical methods to non-mathematicians. It is not intended to be a comprehensive textbook. Rather, the intention is to keep the details to a minimum while serving as a practical guide that illustrates the possibilities of multivariate statistical analysis. In other words, it is a book to "get you going" in a particular area of statistical methods.

It is assumed that readers have a working knowledge of elementary statistics, including tests of significance using normal-, t-, chi-squared, and F-distributions; analysis of variance; and linear regression. The material cov­ered in a typical first-year university course in statistics should be quite adequate in this respect. Some facility with algebra is also required to follow the equations in certain parts of the text. Understanding the theory of mul­tivariate methods requires some matrix algebra. However, the amount needed is not great if some details are accepted on faith. Matrix algebra is summarized in Chapter 2, and anyone that masters this chapter will have a reasonable competency in this area.

One of the reasons why multivariate methods are being used so often these days is the ready availability of computer packages to do the calculations. Indeed, access to suitable computer software is essential if the methods are to be used. However, the details of the use of computer packages are not stressed in this book because there are so many of these packages available. It would be impossible to discuss them all, and it would be too restrictive to concentrate on one or two of them. The approach taken here is to mention which package was used for a particular example when this is appropriate. In addition, the Appendix gives information about some of the packages in terms of what analyses are available and how easy the programs are to use for someone who is relatively inexperienced at carrying out multivariate analyses.

To some extent, the chapters can be read independently of each other. The first five are preliminary reading, focusing mainly on general aspects of multivariate data rather than specific techniques. Chapter 1 introduces data for several examples that are used to illustrate the application of analytical methods throughout the book. Chapter 2 covers matrix algebra, and Chapter 3 discusses various graphical techniques. Chapter 4 discusses tests of signif­icance, and Chapter 5 addresses the measurement of relative "distances"

between objects based on variables measured on those objects. These chap­ters should be reviewed before Chapters 6 to 12, which cover the most important multivariate procedures in current use. The final Chapter 13 contains some general comments about the analysis of multivariate data.

The chapters in this third edition of the book are the same as those in the second edition. The changes that have been made for the new edition are the updating of references, some new examples, some examples carried out using newer computer software, and changes in the text to reflect new ideas about multivariate analyses.

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