The Essence of Multivariate Thinking: Basic Themes and Methods

265 Pages·2005·12.183 MB·English

by  Lisa L. Harlow

THE ESSENCE OF
MULTIVARIATE THINKING
Basic Themes and Methods
Multivariate Applications Series
Sponsored by the Society of Multivariate Experimental Psychology, the goal of this series is
to apply complex statistical methods to significant social or behavioral issues, in such a way
so as to be accessible to a nontechnical-oriented readership (e.g., nonmethodological re-
searchers, teachers, students, government personnel, practitioners, and other professionals).
Applications from a variety of disciplines, such as psychology, public health, sociology,
education, and business, are welcome. Books can be single- or multiple-authored, or edited
volumes that: (1) demonstrate the application of a variety of multivariate methods to a
single, major area of research; (2) describe a multivariate procedure or framework that
could be applied to a number of research areas; or (3) present a variety of perspectives on
a controversial topic of interest to applied multivariate researchers.
There are currently nine books in the series:
• What if there were no significance tests? co-edited by Lisa L. Harlow, Stanley A.
Mulaik, and James H. Steiger (1997).
• Structural Equation Modeling with LISREL, PRELIS, and SIMPLIS: Basic Concepts,
Applications, and Programming written by Barbara M. Byrne (1998).
• Multivariate Applications in Substance Use Research: New Methods for New Ques-
tions, co-edited by: Jennifer S. Rose, Laurie Chassin, Clark C. Presson, and Steven J.
Sherman (2000).
• Item Response Theory for Psychologists, co-authored by Susan E. Embretson and
Steven P. Reise (2000).
• Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Pro-
gramming, written by Barbara M. Byrne (2001).
• Conducting Meta-Analysis Using SAS, written by Winfred Arthur, Jr., Winston Ben-
nett, Jr., and Allen I. Huffcutt (2001).
• Modeling Intraindividual Variability with Repeated Measures Data: Methods and
Applications, co-edited by D. S. Moskowitz and Scott L. Hershberger (2002).
• Multilevel Modeling: Methodological Advances, Issues, and Applications, co-edited
by Steven P. Reise and Naihua Duan (2003).
• The Essence of Multivariate Thinking: Basic Themes and Methods by Lisa Harlow
(2005).
Anyone wishing to submit a book proposal should send the following: (1) author/title,
(2) timeline including completion date, (3) brief overview of the book's focus, including
table of contents, and ideally a sample chapter (or more), (4) a brief description of competing
publications, and (5) targeted audiences.
For more information please contact the series editor, Lisa Harlow, at: Department of
Psychology, University of Rhode Island, 10 Chafee Road, Suite 8, Kingston, RI 02881-0808;
Phone: [phone]; Fax: [phone]; or e-mail: [email protected]. Information
may also be obtained from members of the advisory board: Leona Aiken (Arizona State
University), Gwyneth Boodoo (Educational Testing Service), Barbara M. Byrne (University
of Ottawa), Patrick Curran (University of North Carolina), Scott E. Maxwell (University of
Notre Dame), David Rindskopf (City University of New York), Liora Schmelkin (Hofstra
University) and Stephen West (Arizona State University).
THE ESSENCE OF
MULTIVARIATE THINKING
Basic Themes and Methods
Lisa L. Harlow
University of Rhode Island
LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS
2005 Mahwah, New Jersey London
Senior Editor: Debra Riegert
Editorial Assistant: Kerry Breen
Cover Design: Kathryn Houghtaling Lacey and Lisa L. Harlow
Textbook Production Manager: Paul Smolenski
Full-Service Compositor: TechBooks
Text and Cover Printer: Hamilton Printing Company
This book was typeset in 10/12 pt. Times, Italic, Bold, and Bold Italic. The heads were typeset in
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Copyright © 2005 by Lawrence Erlbaum Associates, Inc.
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other means, without prior written permission of the publisher.
Lawrence Erlbaum Associates, Inc., Publishers
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Library of Congress Cataloging-in-Publication Data
Harlow, Lisa Lavoie, 1951-
The essence of multivariate thinking : basic themes and methods / Lisa L. Harlow.
p. cm.—(Multivariate applications book series)
Includes bibliographical references and index.
ISBN 0-8058-3729-9 (hardback : alk. paper)—ISBN 0-8058-3730-2 (pbk. : alk. paper)
1. Multivariate analysis. 2. Psychology—Mathematical models. I. Title. II. Series.
QA278.H349 2005
519.5'35—dc22 2004028095
Books published by Lawrence Erlbaum Associates are printed on
acid-free paper, and their bindings are chosen for strength and
durability.
Printed in the United States of America
10 9 8 7 6 5 4 3 21
Disclaimer:
This eBook does not include the ancillary media that was
packaged with the original printed version of the book.
In memory of
Jacob Cohen
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Contents
List of Figures and Tables xv
Preface xxi
I: OVERVIEW
1 Introduction 3
What is Multivariate Thinking? 3
Benefits 4
Drawbacks 6
Context for Multivariate Thinking 7
2 Multivariate Themes 10
Overriding Theme of Multiplicity 10
Theory 11
Hypotheses 11
Empirical Studies 12
Measurement 12
Multiple Time Points 13
Multiple Controls 13
Multiple Samples 14
Practical Implications 15
Multiple Statistical Methods 15
Summary of Multiplicity Theme 17
Central Themes 17
Variance 18
Covariance 18
Ratio of (Co-)Variances 18
Linear Combinations 19
Components 19
Factors 20
Summary of Central Themes 20
Interpretation Themes 21
Macro-Assessment 21
vii
viii CONTENTS
Significance Test 21
Effect Sizes 22
Micro-Assessment 23
Means 23
Weights 24
Summary of Interpretation Themes 25
Summary of Multivariate Themes 25
3 Background Themes 28
Preliminary Considerations before Multivariate Analyses 28
Data 28
Measurement Scales 29
Roles of Variables 30
Incomplete Information 31
Missing Data . 32
Descriptive Statistics 33
Inferential Statistics 34
Roles of Variables and Choice of Methods 35
Summary of Background Themes 36
Questions to Help Apply Themes to Multivariate Methods 37
II: INTERMEDIATE MULTIVARIATE METHODS WITH
1 CONTINUOUS OUTCOME
4 Multiple Regression 43
Themes Applied to Multiple Regression (MR)
What Is MR and How Is It Similar to and Different from
Other Methods? 43
When Is MR Used and What Research Questions Can It Address? 44
What Are the Main Multiplicity Themes for MR? 45
What Are the Main Background Themes Applied to MR? 45
What Is the Statistical Model That Is Tested with MR? 46
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to MR? 47
What Are the Main Themes Needed to Interpret Results
at a Macro-Level? 47
What Are the Main Themes Needed to Interpret Results
at a Micro-Level? 49
Significance t-Tests for Variables 49
Weights 49
Squared Semipartial Correlations 50
What Are Some Other Considerations or Next Steps After
Applying MR? 50
CONTENTS ix
What Is an Example of Applying MR to a Research Question? 51
Descriptive Statistics 51
Reliability Coefficients and Correlations 52
Standard Multiple Regression (DV: STAGEB) 52
Hierarchical Multiple Regression (DV: STAGEB) 54
Stepwise Multiple Regression (DV: STAGEB) 56
Summary 61
5 Analysis of Covariance 63
Themes Applied to Analysis of Covariance (ANCOVA)
What Is ANCOVA and How Is It Similar to and Different
from Other Methods? 63
When is ANCOVA Used and What Research Questions
Can it Address? 65
What Are the Main Multiplicity Themes for ANCOVA? 66
What Are the Main Background Themes Applied to ANCOVA? 67
What Is the Statistical Model That Is Tested with ANCOVA? 68
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to ANCOVA? 69
What Are the Main Themes Needed to Interpret ANCOVA Results
at a Macro-Level? 69
Significance Test 70
Effect Size 70
What Are the Main Themes Needed to Interpret ANCOVA results
at a Micro-Level? 70
What Are Some Other Considerations or Next Steps After
Applying ANCOVA? 71
What Is an Example of Applying ANCOVA to a Research Question? 71
Descriptive Statistics 72
Correlations 73
Test of Homogeneity of Regressions 74
ANOVA and Follow-up Tukey Tests 74
ANCOVA and Follow-up Tukey Tests 77
Summary 80
III: MATRICES
6 Matrices and Multivariate Methods 85
Themes Applied to Matrices
What Are Matrices and How Are They Similar to and Different
from Other Tools? 85
What Kinds of Matrices Are Commonly Used with
Multivariate Methods? 86