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More About This Textbook
Overview
This market leader offers a readable introduction to the statistical analysis of multivariate observations. Gives readers the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Starts with a formulation of the population models, delineates the corresponding sample results, and liberally illustrates everything with examples. Offers an abundance of examples and exercises based on real data. Appropriate for experimental scientists in a variety of disciplines.
Editorial Reviews
From The Critics
Johnson (U. of WisconsinMadison) and Wichern (Texas A&M U.) present the newest edition of this college text on the statistical methods for describing and analyzing multivariate data, designed for students who have taken two or more statistics courses. The fifth edition includes the addition of several exercises and data sets, new graphics, and expanded discussion of the dimensionality of multivariate data, growth curves and classification and regression trees, revision of the algebraic development of correspondence analysis, and a new section on data mining. the accompanying CDROM contains the full data sets used in the book , saved as ASCII files. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
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Meet the Author
Dean W. Wichern is Professor Emeritus at the Mays School of Business at Texas A&M University. He holds membership in the American Statistical Association, Royal Statistical Society, International Institute of Forecasters, and Institute for Operations Research and the Management Sciences. He is the author for four textbooks and was Associate Editor of Journal of Business and Economic Statistics from 19831991.
Professor Richard A. Johnson is Professor in the Department of Statistics at the University of Wisconsin. He is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association and he is amember of the Royal Statistical Society and International Statistical Institute. He is the author of six textbooks and over 120 technical publications and is the founding Editor of Statistics and Probability Letters (1981).
Table of Contents
DRAFT
(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.)
I. GETTING STARTED.
1. Aspects of Multivariate Analysis.
Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments.
2. Matrix Algebra and Random Vectors.
Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A SquareRoot Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts.
3. Sample Geometry and Random Sampling.
The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables.
4. The Multivariate Normal Distribution.
The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. LargeSample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality.
II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS.
5. Inferences About a Mean Vector.
The Plausibility of …m0 as a Value for a Normal Population Mean. Hotelling's T ^{2} and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the pDimensional Ellipsoids.
6. Comparisons of Several Multivariate Means.
Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (OneWay MANOVA). Simultaneous Confidence Intervals for Treatment Effects. TwoWay Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models.
7. Multivariate Linear Regression Models.
The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model.
III. ANALYSIS OF A COVARIANCE STRUCTURE.
8. Principal Components.
Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. LargeSample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation.
9. Factor Analysis and Inference for Structured Covariance Matrices.
The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation.
10. Canonical Correlation Analysis
Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences.
IV. CLASSIFICATION AND GROUPING TECHNIQUES.
11. Discrimination and Classification.
Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function…ñSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments.
12. Clustering, Distance Methods and Ordination.
Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations.
Appendix.
Standard Normal Probabilities. Student's tDistribution Percentage Points. …c2 Distribution Percentage Points. FDistribution Percentage Points. FDistribution Percentage Points (…a = .10). FDistribution Percentage Points (…a = .05). FDistribution Percentage Points (…a = .01).
Data Index.
Subject Index.
Preface
INTENDED AUDIENCE
This book originally grew out of our lecture notes for an "Applied Multivariate Analysis" course offered jointly by the Statistics Department and the School of Business at the University of WisconsinMadison. Applied Multivariate Statistical Analysis, Fifth Edition, is concerned with statistical methods for describing and analyzing multivariate data. Data analysis, while interesting with one variable, becomes truly fascinating and challenging when several variables are involved. Researchers in the biological, physical, and social sciences frequently collect measurements on several variables. Modern computer packages readily provide the numerical results to rather complex statistical analyses. We have "tried to provide readers with the supporting knowledge necessary for making proper interpretations, selecting appropriate techniques, and understanding their strengths and weaknesses. We hope our discussions will meet the needs of experimental scientists, in a wide variety of subject matter areas, as a readable introduction to the statistical analysis of multivariate observations.
LEVEL
Our aim is to present the concepts and methods of multivariate analysis at a level that is readily understandable by readers who have taken two or more statistics courses. We emphasize the applications of multivariate methods and, consequently, have attempted to make the mathematics as palatable as possible. We avoid the use of calculus. On the other hand, the concepts of a matrix and of matrix manipulations are important. We do not assume the reader is familiar with matrix algebra. Rather, we introduce matrices as they appear naturally in ourdiscussions, and we then show how they simplify the presentation of multivariate models and techniques.
The introductory account of matrix algebra, in Chapter 2, highlights the more important matrix algebra results as they apply to multivariate analysis. The Chapter 2 supplement provides a summary of matrix algebra results for those with little or no previous exposure to the subject. This supplementary material helps make the book selfcontained and is used to complete proofs. The proofs may be ignored on the first reading. In this way we hope to make the book accessible to a wide audience.
In our attempt to make the study of multivariate analysis appealing to a large audience of both practitioners and theoreticians, we have had to sacrifice a consistency of level. Some sections are harder than others. In particular, we have summarized a voluminous amount of material on regression in Chapter 7. The resulting presentation is rather succinct and difficult the first time through. We hope instructors will be able to compensate for the unevenness in level by judiciously choosing those sections, and subsections, appropriate for their students and by toning them down if necessary.
ORGANIZATION AND APPROACH
The methodological "tools" of multivariate analysis are contained in Chapters 5 through 12. These chapters represent the heart of the book, but they cannot be assimilated without much of the material in the introductory Chapters 1 through 4. Even those readers with a good knowledge of matrix algebra or those willing to accept the mathematical results on faith should, at the very least, peruse Chapter 3, "Sample Geometry," and Chapter 4, "Multivariate Normal Distribution."
Our approach in the methodological chapters is to keep the discussion direct and uncluttered. Typically, we start with a formulation of the population models, delineate the corresponding sample results, and liberally illustrate everything with examples. The examples are of two types: those that are simple and whose calculations can be easily done by hand, and those that rely on realworld data and computer software. These will provide an opportunity to (1) duplicate our analyses, (2) carry out the analyses dictated by exercises, or (3) analyze the data using methods other than the ones we have used or suggested.
The division of the methodological chapters (5 through 12) into three units allows instructors some flexibility in tailoring a course to their needs. Possible sequences for a onesemester (two quarter) course are indicated schematically.
Each instructor will undoubtedly omit certain sections from some chapters to cover a broader collection of topics than is indicated by these two choices.
For most students, we would suggest a quick pass through the first four chapters (concentrating primarily on the material in Chapter 1; Sections 2.1, 2.212.3, 2.5, 2.6, and 3.6; and the "assessing normality" material in Chapter 4) followed by a selection of methodological topics. For example, one might discuss the comparison of mean vectors, principal components, factor analysis, discriminant analysis and clustering. The discussions could feature the many "worked out" examples included in these sections of the text. Instructors may rely on diagrams and verbal descriptions to teach the corresponding theoretical developments. If the students have uniformly strong mathematical backgrounds, much of the book can successfully be covered in one term.
We have found individual dataanalysis projects useful for integrating material from several of the methods chapters. Here, our rather complete treatments of multivariate analysis of variance (MANOVA), regression analysis, factor analysis, canonical correlation, discriminant analysis, and so forth are helpful, even though they may not be specifically covered in lectures.
CHANGES TO THE FIFTH EDITION
New material. Users of the previous editions will notice that we have added several exercises and data sets, some new graphics, and have expanded the discussion of the dimensionality of multivariate data, growth curves and classification and regression trees (CART). In addition, the algebraic development of correspondence analysis has been redone and a new section on data mining has been added to Chapter 12. We put the data mining material in Chapter 12 since much of data mining, as it is now applied in business, has a classification and/or grouping objective. As always, we have tried to improve the exposition in several places.
Data CD. Recognizing the importance of modern statistical packages in the analysis of multivariate data, we have added numerous realdata sets. The full data sets used in the book are saved as ASCII files on the CDROM that is packaged with each copy of the book. This format will allow easy interface with existing statistical software packages and provide more convenient handson data analysis opportunities.
Instructors Solutions Manual. An Instructors Solutions Manual (ISBN 0130925551) containing complete solutions to most of the exercises in the book is available free upon adoption from Prentice Hall.