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Applied Multivariate Statistical Analysis

by: Johnson, Richard Arnold; Wichern, Dean W.

Applied Multivariate Statistical Analysis

by: Johnson, Richard Arnold; Wichern, Dean W.

ISBN 13:
9780138341947
ISBN 10:
013834194X
Edition: 4th
Format: Hardcover
Copyright: 02/01/1998
Publisher: Prentice Hall
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Summary

This market leading text is appropriate for courses that teach statistical methods for describing and analyzing multivariate data in depts. of statistics, math, marketing, and in the biological, physical, and social sciences. The 4th edition makes more extensive use of SAS and SPSS output with an emphasis on interpretation. Features include additional exercises, data sets, and graphics to illustrate points. Various techniques such as MANOVA and Discriminate Analysis, Correspondence Analysis, and Biplots are integrated more thoroughly.

PREFACE

xiii

PART I Getting Started

(223)

1 ASPECTS OF MULTIVARIATE ANALYSIS

(48)

1.1 Introduction

(2)

1.2 Applications of Multivariate Techniques

(2)

1.3 The Organization of Data

(14)

1.4 Data Displays and Pictorial Representations

(9)

1.5 Distance

(8)

1.6 Final Comments

(1)

Exercises

(11)

References

(2)

2 MATRIX ALGEBRA AND RANDOM VECTORS

(67)

2.1 Introduction

(1)

2.2 Some Basics of Matrix and Vector Algebra

(12)

2.3 Positive Definite Matrices

(6)

2.4 A Square-Root Matrix

(1)

2.5 Random Vectors and Matrices

(1)

2.6 Mean Vectors and Covariance Matrices

(12)

2.7 Matrix Inequalities and Maximization

(5)

Supplement 2A Vectors and Matrices: Basic Concepts

(21)

Exercises

107

(8)

References

115

(1)

3 SAMPLE GEOMETRY AND RANDOM SAMPLING

116

(41)

3.1 Introduction

116

(1)

3.2 The Geometry of the Sample

117

(7)

3.3 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix

124

(5)

3.4 Generalized Variance

129

(16)

3.5 Sample Mean, Covariance, and Correlation as Matrix Operations

145

(3)

3.6 Sample Values of Linear Combinations of Variables

148

(5)

Exercises

153

(3)

References

156

(1)

4 THE MULTIVARIATE NORMAL DISTRIBUTION

157

(67)

4.1 Introduction

157

(1)

4.2 The Multivariate Normal Density and Its Properties

158

(19)

4.3 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation

177

(7)

4.4 The Sampling Distribution of X and S

184

(1)

4.5 Large-Sample Behavior of X and S

185

(3)

4.6 Assessing the Assumption of Normality

188

(12)

4.7 Detecting Outliers and Data Cleaning

200

(4)

4.8 Transformations to Near Normality

204

(10)

Exercises

214

(8)

References

222

(2)

PART II Inferences About Multivariate Means and Linear Models

224

(234)

5 INFERENCES ABOUT A MEAN VECTOR

224

(66)

5.1 Introduction

224

(1)

5.2 The Plausibility of XXX(0) as a Value for a Normal Population Mean

224

(7)

5.3 Hotelling's T(2) and Likelihood Ratio Tests

231

(4)

5.4 Confidence Regions and Simultaneous Comparisons of Component Means

235

(17)

5.5 Large Sample Inferences about a Population Mean Vector

252

(5)

5.6 Multivariate Quality Control Charts

257

(11)

5.7 Inferences about Mean Vectors When Some Observations Are Missing

268

(5)

5.8 Difficulties Due To Time Dependence in Multivariate Observations

273

(3)

Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids

276

(3)

Exercises

279

(9)

References

288

(2)

6 COMPARISONS OF SEVERAL MULTIVARIATE MEANS

290

(87)

6.1 Introduction

290

(1)

6.2 Paired Comparisons and a Repeated Measures Design

291

(11)

6.3 Comparing Mean Vectors from Two Populations

302

(12)

6.4 Comparing Several Multivariate Population Means (One-Way MANOVA)

314

(15)

6.5 Simultaneous Confidence Intervals for Treatment Effects

329

(2)

6.6 Two-Way Multivariate Analysis of Variance

331

(12)

6.7 Profile Analysis

343

(7)

6.8 Repeated Measures Designs and Growth Curves

350

(5)

6.9 Perspectives and a Strategy for Analyzing Multivariate Models

355

(3)

Exercises

358

(17)

References

375

(2)

7 MULTIVARIATE LINEAR REGRESSION MODELS

377

(81)

7.1 Introduction

377

(1)

7.2 The Classical Linear Regression Model

377

(4)

7.3 Least Squares Estimation

381

(9)

7.4 Inferences About the Regression Model

390

(10)

7.5 Inferences from the Estimated Regression Function

400

(4)

7.6 Model Checking and Other Aspects of Regression

404

(6)

7.7 Multivariate Multiple Regression

410

(17)

7.8 The Concept of Linear Regression

427

(11)

7.9 Comparing the Two Formulations of the Regression Model

438

(3)

7.10 Multiple Regression Models with Time Dependent Errors

441

(5)

Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Multiple Regression Model

446

(2)

Exercises

448

(8)

References

456

(2)

PART III Analysis of Covariance Structure

458

(171)

8 PRINCIPAL COMPONENTS

458

(56)

8.1 Introduction

458

(1)

8.2 Population Principal Components

458

(13)

8.3 Summarizing Sample Variation by Principal Components

471

(13)

8.4 Graphing the Principal Components

484

(3)

8.5 Large Sample Inferences

487

(3)

8.6 Monitoring Quality with Principal Components

490

(8)

Supplement 8A The Geometry of the Sample Principal Component Approximation

498

(5)

Exercises

503

(9)

References

512

(2)

9 FACTOR ANALYSIS AND INFERENCE FOR STRUCTURED COVARIANCE MATRICES

514

(73)

9.1 Introduction

514

(1)

9.2 The Orthogonal Factor Model

515

(6)

9.3 Methods of Estimation

521

(19)

9.4 Factor Rotation

540

(10)

9.5 Factor Scores

550

(7)

9.6 Perspectives and a Strategy for Factor Analysis

557

(8)

9.7 Structural Equation Models

565

(7)

Supplement 9A Some Computational Details for Maximum Likelihood Estimation

572

(3)

Exercises

575

(10)

References

585

(2)

10 CANONICAL CORRELATION ANALYSIS

587

(42)

10.1 Introduction

587

(1)

10.2 Canonical Variates and Canonical Correlations

587

(8)

10.3 Interpreting the Population Canonical Variables

595

(6)

10.4 The Sample Canonical Variates and Sample Canonical Correlations

601

(9)

10.5 Additional Sample Descriptive Measures

610

(5)

10.6 Large Sample Inferences

615

(4)

Exercises

619

(8)

References

627

(2)

PART IV Classification and Grouping Techniques

629

(171)

11 DISCRIMINATION AND CLASSIFICATION

629

(97)

11.1 Introduction

629

(1)

11.2 Separation and Classification for Two Populations

630

(9)

11.3 Classification with Two Multivariate Normal Populations

639

(10)

11.4 Evaluating Classification Functions

649

(12)

11.5 Fisher's Discriminant Function--Separation of Populations

661

(4)

11.6 Classification with Several Populations

665

(18)

11.7 Fisher's Method for Discriminating among Several Populations

683

(14)

11.8 Final Comments

697

(6)

Exercises

703

(20)

References

723

(3)

12 CLUSTERING, DISTANCE METHODS AND ORDINATION

726

(74)

12.1 Introduction

726

(2)

12.2 Similarity Measures

728

(10)

12.3 Hierarchical Clustering Methods

738

(16)

12.4 Nonhierarchical Clustering Methods

754

(6)

12.5 Multidimensional Scaling

760

(10)

12.6 Correspondence Analysis

770

(9)

12.7 Biplots for Viewing Sampling Units and Variables

779

(3)

12.8 Procrustes Analysis: A Method for Comparing Configurations

782

(8)

Exercises

790

(8)

References

798

(2)

APPENDIX

800

(11)

Table 1 Standard Normal Probabilities

801

(1)

Table 2 Student's t-Distribution Percentage Points

802

(1)

Table 3 Alpha(2) Distribution Percentage Points

803

(1)

Table 4 F-Distribution Percentage Points (Alpha = .10)

804

(2)

Table 5 F-Distribution Percentage Points (Alpha = .05)

806

(2)

Table 6 F-Distribution Percentage Points (Alpha = .01)

808

(3)

DATA INDEX

811

(1)

SUBJECT INDEX

812

Amazon no longer offers textbook rentals. We do!

Applied Multivariate Statistical Analysis

Applied Multivariate Statistical Analysis

9780138341947

013834194X

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Applied Multivariate Statistical Analysis

Applied Multivariate Statistical Analysis

9780138341947

013834194X

Summary

Table of Contents

Supplemental Materials

Write a Review

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