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Applied MANOVA andDiscriminant Analysis
Second Edition
CARL J. HUBERTY
The University of GeorgiaDepartment of Educational PsychologyAthens, Georgia
STEPHEN OLEJNIK
The University of GeorgiaDepartment of Educational PsychologyAthens, Georgia
A JOHN WILEY & SONS, INC. PUBLICATION
InnodataFile Attachment9780471789468.jpg
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Applied MANOVA andDiscriminant Analysis
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WILEY SERIES IN PROBABILITY AND STATISTICS
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J. Balding, Noel A. C. Cressie, Nicholas I. Fisher,Iain M. Johnstone, J. B. Kadane, Geert Molenberghs, Louise M. Ryan,David W. Scott, Adrian F. M. Smith, Jozef L. TeugelsEditors Emeriti: Vic Barnett, J. Stuart Hunter, David G. Kendall
A complete list of the titles in this series appears at the end of this volume.
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Applied MANOVA andDiscriminant Analysis
Second Edition
CARL J. HUBERTY
The University of GeorgiaDepartment of Educational PsychologyAthens, Georgia
STEPHEN OLEJNIK
The University of GeorgiaDepartment of Educational PsychologyAthens, Georgia
A JOHN WILEY & SONS, INC. PUBLICATION
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This book is printed on acid-free paper.
Copyright 2006 by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any formor by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except aspermitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the priorwritten permission of the Publisher, or authorization through payment of the appropriate percopy fee to theCopyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, JohnWiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008,E-Mail: [email protected].
For ordering and customer service, call 1-800-CALL-WILEY.
Library of Congress Cataloging-in-Publication Data:
Huberty, Carl J., 1934-Applied MANOVA and discriminant analysis.2nd ed./Carl J. Huberty, Stephen Olejnik.
p. cmRev. ed. of: Applied discriminant analysis. c1994.Includes bibliographical references and index.ISBN-13: 978-0-471-46815-8 (acid-free paper)ISBN-10: 0-471-46815-0 (acid-free paper)
1. Discriminant analysis. 2. Multivariate analysis. I. Olejnik, Stephen. II. Huberty, Carl J., 1934-Applied discriminant analysis. III. Title.
QA278.65.H83 2006519.535dc22
2005054231
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
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To our wives, Sandy and Sherrie
In memory of Clem (father), Rosalie (mother), andKen (brother) Huberty
Harry (father), Ann (mother), andTony (brother) Olejnik
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Brief Contents
PART I: INTRODUCTION 1
Chapter 1 Discriminant Analysis in Research 3
Chapter 2 Preliminaries 15
PART II: ONE-FACTOR MANOVA/DDA 33
Chapter 3 Group Separation 35
Chapter 4 Assessing MANOVA Effects 61
Chapter 5 Describing MANOVA Effects 81
Chapter 6 Deleting and Ordering Variables 103
Chapter 7 Reporting DDA Results 117
PART III: COMPLEX MANOVA 129
Chapter 8 Factorial MANOVA 131
Chapter 9 Analysis of Covariance 163
Chapter 10 Repeated-Measures Analysis 193
Chapter 11 Mixed-Model Analysis 227
PART IV: GROUP-MEMBERSHIP PREDICTION 253
Chapter 12 Classification Basics 255
Chapter 13 Multivariate Normal Rules 269
vii
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viii BRIEF CONTENTS
Chapter 14 Classification Results 285
Chapter 15 Hit Rate Estimation 295
Chapter 16 Effectiveness of Classification Rules 315
Chapter 17 Deleting and Ordering Predictors 335
Chapter 18 Two-Group Classification 349
Chapter 19 Nonnormal Rules 361
Chapter 20 Reporting PDA Results 375
Chapter 21 PDA-Related Analyses 385
PART V: ISSUES AND PROBLEMS 391
Chapter 22 Issues in PDA and DDA 393
Chapter 23 Problems in PDA and DDA 401
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Contents
List of Figures xix
List of Tables xxi
Preface to Second Edition xxv
Acknowledgments xxvii
Preface to First Edition xxix
Notation xxxi
I INTRODUCTION 1
1 Discriminant Analysis in Research 3
1.1 A Little History, 31.2 Overview, 51.3 Descriptive Discriminant Analysis, 51.4 Predictive Discriminant Analysis, 71.5 Design in Discriminant Analysis, 9
1.5.1 Grouping Variables, 91.5.2 Response Variables, 9Exercises, 13
2 Preliminaries 15
2.1 Introduction, 152.2 Research Context, 152.3 Data, Analysis Units, Variables, and Constructs, 162.4 Summarizing Data, 182.5 Matrix Operations, 21
2.5.1 SSCP Matrix, 22
ix
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x CONTENTS
2.5.2 Determinant, 232.5.3 Inverse, 242.5.4 Eigenanalysis, 25
2.6 Distance, 262.7 Linear Composite, 282.8 Probability, 282.9 Statistical Testing, 292.10 Judgment in Data Analysis, 302.11 Summary, 31
Further Reading, 31Exercises, 32
II ONE-FACTOR MANOVA/DDA 33
3 Group Separation 35
3.1 Introduction, 353.2 Two-Group Analyses, 35
3.2.1 Univariate Analysis, 353.2.2 Multivariate Analysis, 39
3.3 Test for Covariance Matrix Equality, 413.4 Yao Test, 433.5 Multiple-Group AnalysesSingle Factor, 44
3.5.1 Univariate Analysis, 443.5.2 Multivariate Analysis, 47
3.6 Computer Application, 523.7 Summary, 56
Exercises, 57
4 Assessing MANOVA Effects 61
4.1 Introduction, 614.2 Strength of Association, 62
4.2.1 Univariate, 624.2.2 Multivariate, 624.2.3 Bias, 65
4.3 Computer Application I, 664.4 Group Contrasts, 67
4.4.1 Univariate, 674.4.2 Multivariate, 68
4.5 Computer Application II, 724.6 Covariance Matrix Heterogeneity, 744.7 Sample Size, 74
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CONTENTS xi
4.8 Summary, 75Technical Notes, 76Exercises, 77
5 Describing MANOVA Effects 81
5.1 Introduction, 815.2 Omnibus Effects, 82
5.2.1 An Eigenanalysis, 825.2.2 Linear Discriminant Functions, 83
5.3 Computer Application I, 855.4 Standardized LDF Weights, 875.5 LDF Space Dimension, 88
5.5.1 Statistical Tests, 895.5.2 Proportion of Variance, 915.5.3 LDF Plots, 91
5.6 Computer Application II, 935.7 Computer Application III, 945.8 Contrast Effects, 965.9 Computer Application IV, 965.10 Summary, 98
Technical Note, 99Further Reading, 100Exercises, 100
6 Deleting and Ordering Variables 103
6.1 Introduction, 1036.2 Variable Deletion, 103
6.2.1 Purposes of Deletion, 1036.2.2 McCabe Analysis, 1046.2.3 Computer Application, 105
6.3 Variable Ordering, 1066.3.1 Meaning of Importance, 1066.3.2 Computer Application I, 1086.3.3 Variable Ranking, 110
6.4 Contrast Analyses, 1106.5 Computer Application II, 1116.6 Comments, 113
Further Reading, 114Exercises, 115
7 Reporting DDA Results 117
7.1 Introduction, 1177.2 Example of Reporting DDA Results, 117
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xii CONTENTS
7.3 Computer Package Information, 1227.4 Reporting Terms, 1237.5 MANOVA/DDA Applications, 1247.6 Concerns, 1247.7 Overview, 126
Further Reading, 127Exercises, 127
III FACTORIAL MANOVA, MANCOVA, AND REPEATEDMEASURES 129
8 Factorial MANOVA 131
8.1 Introduction, 1318.2 Research Context, 1318.3 Univariate Analysis, 1348.4 Multivariate Analysis, 136
8.4.1 Omnibus Tests, 1368.4.2 Distribution Assumptions, 138
8.5 Computer Application I, 1398.6 Computer Application II, 1468.7 Nonorthogonal Design, 1508.8 Outcome Variable Ordering and Deletion, 1518.9 Summary, 152
Technical Notes, 152Exercises, 159
9 Analysis of Covariance 163
9.1 Introduction, 1639.2 Research Context, 1649.3 Univariate ANCOVA, 166
9.3.1 Testing for Equality of Regression Slopes, 1669.3.2 Omnibus Test of Adjusted Means, 168
9.4 Multivariate ANCOVA (MANCOVA), 1709.4.1 Matrix Calculations, 1709.4.2 Testing for Equal Slopes, 171
9.5 Computer Application I, 1739.6 Comparing Adjusted MeansOmnibus Test, 1749.7 Computer Application II, 1759.8 Contrast Analysis, 1809.9 Computer Application III, 180
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CONTENTS xiii
9.10 Summary, 184Technical Note, 184Exercises, 190
10 Repeated-Measures Analysis 193
10.1 Introduction, 19310.2 Research Context, 19510.3 Univariate Analyses, 196
10.3.1 Omnibus Test, 19610.3.2 Contrast Analysis, 197
10.4 Multivariate Analysis, 19910.5 Computer Application I, 20210.6 Univariate and Multivariate Analyses, 20410.7 Testing for Sphericity, 20710.8 Computer Application II, 21010.9 Contrast Analysis, 21210.10 Computer Application III, 21410.11 Summary, 216
Technical Notes, 217Exercises, 223
11 Mixed-Model Analysis 227
11.1 Introduction, 22711.2 Research Context, 22811.3 Univariate Analysis, 22911.4 Multivariate Analysis, 231
11.4.1 Group-by-Time Interaction, 23211.4.2 Repeated-Measures Variable Main Effect, 235
11.5 Computer Application I, 23711.6 Contrast Analysis, 24011.7 Computer Application II, 24311.8 Summary, 246
Technical Note, 247Exercises, 249
IV GROUP MEMBERSHIP PREDICTION 253
12 Classificatio
