Comparaciones multiples

ISBN-13: 978-0-13-187715--3 ISBN-l0: 0-13-18771S-1

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Applied Multivariate Statistical Analysis
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SIXTH EDITION

Applied Multivariate Statistical Analysis
RICHARD A. JOHNSON
University of Wisconsin-Madison

DEAN W. WICHERN
Texas A&M University

PEARSON
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,brary of Congress Cataloging-in-Publication Data

>hnson, Richard A. Statistical analysisiRichard A. Johnson.-61h ed. Dean W. Winchern p.em. Includes index. ISBN 0-13-187715-1 1. Statistical Analysis
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To the memory of my mother and my father.

R. A. J.
To Dorothy, Michael, and An drew.
D. W. W.

© 2007 Pearson Education, Inc. Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ 07458

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ISBN-13: 978-0-13-187715-3 0- 13 - 187715'- 1 ISBN-l0:
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Contents
PREFACE

xv
1

1

ASPECTS OF MULTlVARIATE ANALYSIS

1.1 1.2
1.3

Introduction 1 Applications of Multivariate Techniques 3 The Organization of Data 5
Arrays,5 Descriptive Statistics, 6 Graphical Techniques, 11

1.4Data Displays and Pictorial Representations 19
Linking Multiple Two-Dimensional Scatter Plots, 20 Graphs of Growth Curves, 24 Stars, 26 Chernoff Faces, 27

1.5

1.6

Distance 30 Final Comments 37 Exercises 37 References 47
49

2

MATRIX ALGEBRA AND RANDOM VECTORS

2.1 2.2

Introduction 49 Some Basics of Matrix and Vector Algebra 49
Vectors, 49 Matrices, 54

2.3 2.4 2.5 2.6Positive Definite Matrices 60 A Square-Root Matrix 65 Random Vectors and Matrices 66 Mean Vectors and Covariance Matrices

68

Partitioning the Covariance Matrix, 73 The Mean Vector and Covariance Matrix for Linear Combinations of Random Variables, 75 Partitioning the Sample Mean Vector and Covariance Matrix, 77

2.7

Matrix Inequalities and Maximization 78
vii

viii

Contents

Contentsix

Supplement 2A: Vectors and Matrices: Basic Concepts 82
Vectors, 82 Matrices, 87

5

INFERENCES ABOUT A MEAN VECTOR

210

Exercises 103 References 110
3
SAMPLE GEOMETRY AND RANDOM SAMPLING

5.1 5.2 5.3 111 5.4

Introduction 210 The Plausibility of Po as a Value for a Normal Population Mean 210 HotelIing's T2 and Likelihood Ratio Tests 216
General Likelihood Ratio Method,219

3.1 3.2 3.3 3.4

Introduction 111 The Geometry of the Sample 111 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix 119 Generalized Variance 123
Situations in which the Generalized Sample Variance Is Zero, 129 Generalized Variance Determined by I R I and Its Geometrical Interpretation, 134 Another Generalization of Variance, 137

Confidence Regions and...