APPLIED MULTIVARIATE STATISTICSFOR THE SOCIAL SCIENCESNow in its 6th edition, the authoritative textbook Applied Multivariate Statistics forthe Social Sciences, continues to provide advanced students with a practical and conceptual understanding of statistical procedures through examples and data-sets fromactual research studies. With the added expertise of co-author Keenan Pituch (University of Texas-Austin), this 6th edition retains many key features of the previous editions, including its breadth and depth of coverage, a review chapter on matrix algebra,applied coverage of MANOVA, and emphasis on statistical power. In this new edition,the authors continue to provide practical guidelines for checking the data, assessingassumptions, interpreting, and reporting the results to help students analyze data fromtheir own research confidently and professionally.Features new to this edition include: NEW chapter on Logistic Regression (Ch. 11) that helps readers understand anduse this very flexible and widely used procedure NEW chapter on Multivariate Multilevel Modeling (Ch. 14) that helps readersunderstand the benefits of this “newer” procedure and how it can be used in conventional and multilevel settings NEW Example Results Section write-ups that illustrate how results should be presented in research papers and journal articles NEW coverage of missing data (Ch. 1) to help students understand and addressproblems associated with incomplete data Completely re-written chapters on Exploratory Factor Analysis (Ch. 9), Hierarchical Linear Modeling (Ch. 13), and Structural Equation Modeling (Ch. 16) withincreased focus on understanding models and interpreting results NEW analysis summaries, inclusion of more syntax explanations, and reductionin the number of SPSS/SAS dialogue boxes to guide students through data analysis in a more streamlined and direct approach Updated syntax to reflect newest versions of IBM SPSS (21) /SAS (9.3)

A free online resources site with data setsand syntax from the text, additional data sets, and instructor’s resources (includingPowerPoint lecture slides for select chapters, a conversion guide for 5th editionadopters, and answers to exercises).Ideal for advanced graduate-level courses in education, psychology, and other socialsciences in which multivariate statistics, advanced statistics, or quantitative techniquescourses are taught, this book also appeals to practicing researchers as a valuable reference. Pre-requisites include a course on factorial ANOVA and covariance; however, aworking knowledge of matrix algebra is not assumed.Keenan Pituch is Associate Professor in the Quantitative Methods Area of the Department of Educational Psychology at the University of Texas at Austin.James P. Stevens is Professor Emeritus at the University of Cincinnati.

APPLIED MULTIVARIATESTATISTICS FOR THESOCIAL SCIENCESAnalyses with SAS andIBM‘s SPSSSixth editionKeenan A. Pituch and James P. Stevens

Sixth edition published 2016by Routledge711 Third Avenue, New York, NY 10017and by Routledge2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RNRoutledge is an imprint of the Taylor & Francis Group, an informa business 2016 Taylor & FrancisThe right of Keenan A. Pituch and James P. Stevens to be identified as authors of this work hasbeen asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and PatentsAct 1988.All rights reserved. No part of this book may be reprinted or reproduced or utilised in any formor by any electronic, mechanical, or other means, now known or hereafter invented, includingphotocopying and recording, or in any information storage or retrieval system, without permissionin writing from the publishers.Trademark notice: Product or corporate names may be trademarks or registered trademarks, and areused only for identification and explanation without intent to infringe.Fifth edition published by Routledge 2009Library of Congress Cataloging-in-Publication DataPituch, Keenan A.â Applied multivariate statistics for the social sciences / Keenan A. Pituch and JamesP. Stevens –– 6th edition.â â pages cmâ Previous edition by James P. Stevens.â Includes index.â ‡1.â ‡ Multivariate analysis.â 2.â ‡ Social sciences––Statistical methods.â I.â ‡ Stevens, James (JamesPaul)â II.â ‡ Title.â QA278.S74 2015â 519.5'350243––dc23â 2015017536ISBN 13: 978-0-415-83666-1(pbk)ISBN 13: 978-0-415-83665-4(hbk)ISBN 13: 978-1-315-81491-9(ebk)Typeset in Times New Romanby Apex CoVantage, LLCCommissioning Editor: Debra RiegertTextbook Development Manager: Rebecca PearceProject Manager: Sheri SipkaProduction Editor: Alf SymonsCover Design: Nigel TurnerCompanion Website Manager: Natalya DyerCopyeditor: Apex CoVantage, LLC

Keenan would like to dedicate this:To his Wife: Elizabeth andTo his Children: Joseph and AlexisJim would like to dedicate this:To his Grandsons: Henry and Killian andTo his Granddaughter: Fallon

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CONTENTSPreface 1.2.xvIntroduction 1.1 Introduction 1.2 Type IÂ Error, Type II Error, and Power 1.3 Multiple Statistical Tests and the Probabilityof Spurious Results 1.4 Statistical Significance Versus Practical Importance 1.5 Outliers 1.6 Missing Data 1.7 Unit or Participant Nonresponse 1.8 Research Examples for Some AnalysesConsidered in This Text 1.9 The SAS and SPSS Statistical Packages 1.10 SAS and SPSS Syntax 1.11 SAS and SPSS Syntax and Data Sets on the Internet 1.12 Some Issues Unique to Multivariate Analysis 1.13 Data Collection and Integrity 1.14 Internal and External Validity 1.15 Conflict of Interest 1.16 Summary 1.17 Exercises Matrix Algebra 2.1 Introduction 2.2 Addition, Subtraction, and Multiplication of aMatrix by a Scalar 2.3 Obtaining the Matrix of Variances and Covariances 2.4 Determinant of a Matrix 2.5 Inverse of a Matrix 2.6 SPSS Matrix Procedure 1136101218313235353636373940404144444750525558

viii↜æ å ↜æ å Contents2. IML Procedure Summary Exercises Multiple Regression for Prediction 3.1 Introduction 3.2 Simple Regression 3.3 Multiple Regression for Two Predictors: Matrix Formulation 3.4 Mathematical Maximization Nature ofLeast Squares Regression 3.5 Breakdown of Sum of Squares and F Test forMultiple Correlation 3.6 Relationship of Simple Correlations to Multiple Correlation 3.7 Multicollinearity 3.8 Model Selection 3.9 Two Computer Examples 3.10 Checking Assumptions for the Regression Model 3.11 Model Validation 3.12 Importance of the Order of the Predictors 3.13 Other Important Issues 3.14 Outliers and Influential Data Points 3.15 Further Discussion of the Two Computer Examples 3.16 Sample Size Determination for a Reliable Prediction Equation 3.17 Other Types of Regression Analysis 3.18 Multivariate Regression 3.19 Summary 3.20 Exercises 4128129Two-Group Multivariate Analysis of Variance 4.1 Introduction 4.2 Four Statistical Reasons for Preferring a Multivariate Analysis 4.3 The Multivariate Test Statistic as a Generalization ofthe Univariate t Test 4.4 Numerical Calculations for a Two-Group Problem 4.5 Three Post Hoc Procedures 4.6 SAS and SPSS Control Lines for Sample Problemand Selected Output 4.7 Multivariate Significance but No Univariate Significance 4.8 Multivariate Regression Analysis for the Sample Problem 4.9 Power Analysis 4.10 Ways of Improving Power 4.11 A Priori Power Estimation for a Two-Group MANOVA 4.12 Summary 4.13 Exercises 142142143K-Group MANOVA: A Priori and Post Hoc Procedures 5.1 Introduction 175175144146150152156156161163165169170 Regression Analysis for a Sample Problem Traditional Multivariate Analysis of Variance Multivariate Analysis of Variance for Sample Data Post Hoc Procedures The Tukey Procedure Planned Comparisons Test Statistics for Planned Comparisons Multivariate Planned Comparisons on SPSS MANOVA Correlated Contrasts Studies Using Multivariate Planned Comparisons Other Multivariate Test Statistics How Many Dependent Variables for a MANOVA? Power Analysis—A Priori Determination of Sample Size Summary Exercises ↜æ å ↜æ å ptions in MANOVA 6.1 Introduction 6.2 ANOVA and MANOVA Assumptions6.3 Independence Assumption6.4 What Should Be Done With Correlated Observations? 6.5 Normality Assumption 6.6 Multivariate Normality 6.7 Assessing the Normality Assumption 6.8 Homogeneity of Variance Assumption 6.9 Homogeneity of the Covariance Matrices 6.10 Summary 6.11 Complete Three-Group MANOVA Example 6.12 Example Results Section for One-Way MANOVA 6.13 Analysis Summary Appendix 6.1 Analyzing Correlated Observations Appendix 6.2 Multivariate Test Statistics for UnequalCovariance Matrices 6.14 Exercises rial ANOVA and MANOVA 7.1 Introduction 7.2 Advantages of a Two-Way Design 7.3 Univariate Factorial Analysis 7.4 Factorial Multivariate Analysis of Variance 7.5 Weighting of the Cell Means 7.6 Analysis Procedures for Two-Way MANOVA 7.7 Factorial MANOVA With SeniorWISE Data 7.8 Example Results Section for Factorial MANOVA WithSeniorWise Data 7.9 Three-Way MANOVA 265265266268277280280281259262290292ix

x↜æ å ↜æ å Contents7.10 Factorial Descriptive Discriminant Analysis 7.11 Summary 7.12 Exercises 2942982998.Analysis of Covariance 3018.1 Introduction 3018.2 Purposes of ANCOVA 3028.3 Adjustment of Posttest Means and Reduction of Error Variance 3038.4 Choice of Covariates 3078.5 Assumptions in Analysis of Covariance 3088.6 Use of ANCOVA With Intact Groups 3118.7 Alternative Analyses for Pretest–Posttest Designs 3128.8 Error Reduction and Adjustment of Posttest Means forSeveral Covariates 3148.9 MANCOVA—Several Dependent Variables and315Several Covariates 8.10 Testing the Assumption of HomogeneousHyperplanes on SPSS 3168.11 Effect Size Measures for Group Comparisons inMANCOVA/ANCOVA 3178.12 Two Computer Examples 3188.13 Note on Post Hoc Procedures 3298.14 Note on the Use of MVMM 3308.15 Example Results Section for MANCOVA 3308.16 Summary 3328.17 Analysis Summary 3338.18 Exercises 3359.Exploratory Factor Analysis 3399.1 Introduction 3399.2 The Principal Components Method 3409.3 Criteria for Determining How Many Factors to RetainUsing Principal Components Extraction 3429.4 Increasing Interpretability of Factors by Rotation 3449.5 What Coefficients Should Be Used for Interpretation? 3469.6 Sample Size and Reliable Factors 3479.7 Some Simple Factor Analyses Using PrincipalComponents Extraction 3479.8 The Communality Issue 3599.9 The Factor Analysis Model 3609.10 Assumptions for Common Factor Analysis 3629.11 Determining How Many Factors Are Present With364Principal Axis Factoring 9.12 Exploratory Factor Analysis Example With Principal AxisFactoring 3659.13 Factor Scores 373

Contents10.11.↜æ å ↜æ å SPSS in Factor Analysis Using SAS in Factor Analysis Exploratory and Confirmatory Factor Analysis Example Results Section for EFA of Reactions-toTests Scale 9.18 Summary 9.19 Exercises 376378382Discriminant Analysis 10.1 Introduction 10.2 Descriptive Discriminant Analysis 10.3 Dimension Reduction Analysis 10.4 Interpreting the Discriminant Functions 10.5 Minimum Sample Size 10.6 Graphing the Groups in the Discriminant Plane 10.7 Example With SeniorWISE Data 10.8 National Merit Scholar Example 10.9 Rotation of the Discriminant Functions 10.10 Stepwise Discriminant Analysis 10.11 The Classification Problem 10.12 Linear Versus Quadratic Classification Rule 10.13 Characteristics of a Good Classification Procedure 10.14 Analysis Summary of Descriptive Discriminant Analysis 10.15 Example Results Section for Discriminant Analysis of theNational Merit Scholar Example 10.16 Summary 10.17 Exercises y Logistic Regression 11.1 Introduction 11.2 The Research Example 11.3 Problems With Linear Regression Analysis 11.4 Transformations and the Odds Ratio With aDichotomous Explanatory Variable 11.5 The Logistic Regression Equation With a SingleDichotomous Explanatory Variable 11.6 The Logistic Regression Equation With a SingleContinuous Explanatory Variable 11.7 Logistic Regression as a Generalized Linear Model 11.8 Parameter Estimation 11.9 Significance Test for the Entire Model and Sets of Variables 11.10 McFadden’s Pseudo R-Square for Strength of Association 11.11 Significance Tests and Confidence Intervals forSingle Variables 11.12 Preliminary Analysis 11.13 Residuals and Influence 8450451451xi

xii↜æ å ↜æ å er Data Issues 457Classification 458Using SAS and SPSS for Multiple Logistic Regression 461Using SAS and SPSS to Implement the Box–TidwellProcedure 46311.19 Example Results Section for Logistic RegressionWith Diabetes Prevention Study 46511.20 Analysis Summary 46611.21 Exercises 46812.13.Repeated-Measures Analysis 12.1 Introduction 12.2 Single-Group Repeated Measures 12.3 The Multivariate Test Statistic for Repeated Measures 12.4 Assumptions in Repeated-Measures Analysis 12.5 Computer Analysis of the Drug Data 12.6 Post Hoc Procedures in Repeated-Measures Analysis 12.7 Should We Use the Univariate or Multivariate Approach? 12.8 One-Way Repeated Measures—A Trend Analysis 12.9 Sample Size for Power  .80 in Single-Sample Case 12.10 Multivariate Matched-Pairs Analysis 12.11 One-Between and One-Within Design 12.12 Post Hoc Procedures for the One-Between andOne-Within Design 12.13 One-Between and Two-Within Factors 12.14 Two-Between and One-Within Factors 12.15 Two-Between and Two-Within Factors 12.16 Totally Within Designs 12.17 Planned Comparisons in Repeated-Measures Designs 12.18 Profile Analysis 12.19 Doubly Multivariate Repeated-Measures Designs 12.20 Summary 12.21 Exercises 471471475477480482487488

Now in its 6th edition, the authoritative textbook Applied Multivariate Statistics for . 1.12 Some Issues Unique to Multivariate Analysis 36 1.13 Data Collection and Integrity 37 1.14 Internal and External Validity 39 1.15 Conflict of Interest 40 1.16 Summary 40 1.17 Exercises 41 2. Matrix Algebra 44 2.1 Introduction 44 2.2 Addition, Subtraction, and Multiplication of a Matrix by a Scalar 47 .