Multivariate Analysis for the Biobehavioral and Social Sciences A Graphical Approach

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Edition: 1st
Format: Hardcover
Pub. Date: 2011-12-27
Publisher(s): Wiley
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Summary

Multivariate Analysis for the Social Sciences provides clear guidelines combined with the insight needed to understand the methods and applications of multivariate statistics. This easy-to-follow book provides students in social, behavioral, and health science-whose focus is not primarily in mathematics-with an abundance of chapter-ending questions and answers, including: conceptual questions about the meaning of each method; questions that test the reader's ability to carry out the computational procedures on simple datasets; and data analysis questions for using analytical packages to analyze both simplest case data and also to practice with more realistic datasets.

Author Biography

Bruce L. Brown, PhD, is Professor of Psychology at Brigham Young University. He has over thirty years of academic experience working with large scale data analysis methods, and he currently focuses his research on applying these methods to cognitive neuroscience and vocal emotion. Suzanne B. Hendrix, PhD, is President of Pentara Corporation and an independent consultant to the pharmaceutical industry, with extensive experience in clinical biostatistics. Dr. Hendrix's current areas of research interest include clinical trial design and reporting in neurodegenerative diseases such as Alzheimer's and Parkinson's. Dawson W. Hedges, MD, is Professor of Psychology at Brigham Young University. He has published extensively in his areas of research interest, which include neuroimaging, posttraumatic stress disorder, psychopharmacology, and psychopathology. Timothy B. Smith, PhD, is Chair of the Department of Counseling Psychology and Special Education at Brigham Young University. He currently focuses his research on multiculturalism and diversity as well as spirituality and religion in education or counseling.

Table of Contents

Prefacep. xiii
Overview of Multivariate and Regression Methodsp. 1
Introductionp. 1
Multivariate Methods as an Extension of Familiar Univariate Methodsp. 2
Measurement Scales and Data Typesp. 4
Four Basic Data Set Structures for Multivariate Analysisp. 5
Pictorial Overview of Multivariate Methodsp. 7
Correlational versus Experimental Methodsp. 15
Old versus New Methodsp. 16
Summaryp. 17
Study Questionsp. 18
Essay Questionsp. 18
Referencesp. 19
The Seven Habits of Highly Effective Quants: A Review of Elementary Statistics Using Matrix Algebrap. 20
Introductionp. 20
The Meaning of Measurement Scalesp. 22
The Meaning of Measures of Central Tendencyp. 23
Variance and Matrix Algebrap. 26
Covariance Matrices and Correlation Matricesp. 34
Classical Probability Theory and the Binomial: The Basis for Statistical Inferencep. 43
Significance Tests: From Binomial to z-Tests to f-Tests to Analysis of Variancep. 58
The z Test of a Single Meanp. 67
The z Test of a Single Proportionp. 68
The z Test of Two Means for Independent Samplesp. 69
The z Test of Two Proportions for Independent Samplesp. 70
The z Test of Two Means for Correlated Samplesp. 72
The z Test of Two Proportions for Correlated Samplesp. 72
The t Test of a Single Meanp. 72
The t Test of Two Means for Independent Samplesp. 73
The t Test of Two Means for Correlated Samplesp. 75
Assumptions and Sampling Distributions of the Nine Testsp. 77
Matrix Approach to Analysis of Variancep. 79
Summaryp. 83
Study Questionsp. 84
Essay Questionsp. 84
Calculation Questionsp. 85
Data Analysis Questionsp. 86
Referencesp. 87
Fundamentals of Matrix Algebrap. 88
Introductionp. 88
Definitions and Notationp. 89
Matrix Operations and Statistical Quantitiesp. 89
Addition and Subtractionp. 89
Scalar Multiplicationp. 90
Transpose of a Matrixp. 91
Matrix Multiplicationp. 91
Division by a Scalarp. 95
Symmetric Matrices and Diagonal Matricesp. 97
The Identity Matrix and the J Matrixp. 100
Partitioned Matrices and Adjoined Matricesp. 108
Adjoined Matricesp. 108
Partitioned Matricesp. 109
Triangular Square Root Matricesp. 110
Triangular Matricesp. 110
The Cholesky Method for Finding a Triangular Square Root Matrixp. 110
Determinantsp. 112
The Bent Diagonals Methodp. 113
The Matrix Extension Methodp. 114
The Method of Cofactorsp. 115
Meaning of the Trace and the Determinant of a Covariance Matrixp. 117
Matrix Inversionp. 118
Matrix Inversion by the Method of Cofactorsp. 119
Matrix Inversion by the Cholesky Methodp. 120
Rank of a Matrixp. 123
Orthogonal Vectors and Matricesp. 124
Quadratic Forms and Bilinear Formsp. 125
Quadratic Formsp. 126
Bilinear Formsp. 126
Covariance Matrix Transformationp. 127
Eigenvectors and Eigenvaluesp. 128
Spectral Decomposition, Triangular Decomposition, and Singular Value Decompositionp. 129
Spectral Decomposition, Square Matrices, and Square Root Matricesp. 130
Triangular Decomposition Compared to Spectral Decompositionp. 133
Singular Value Decompositionp. 134
Normalization of a Vectorp. 134
Conclusionp. 136
Study Questionsp. 136
Essay Questionsp. 136
Calculation Questionsp. 136
Data Analysis Questionsp. 137
Referencesp. 138
Factor Analysis and Related Methods: Quintessentially Multivariatep. 139
Introductionp. 139
An Applied Example of Factoring: The Mental Skills of Micep. 142
Calculating Factor Loadings to Reveal the Structure of Skills in Micep. 149
Simplest Case Mathematical Demonstration of a Complete Factor Analysisp. 153
Factor Scores: The Relationship between Latent Variables and Manifest Variablesp. 169
The Three Types of Eigenvector in Factor Analysisp. 169
Factor Scores Demonstration Using Simplest Case Data from Section 4.4p. 171
Factor Analysis and Factor Scores for Simplest Case Data with a Rank of 2p. 172
Factor Analysis as Data Transformationp. 174
Principal Component Analysis: Simplified Factoring of Covariance Structurep. 176
Rotation of the Factor Patternp. 188
The Rich Variety of Factor Analysis Modelsp. 194
Factor Analyzing the Mental Skills of Mice: A Comparison of Factor Analytic Modelsp. 200
Data Reliability and Factor Analysisp. 210
Summaryp. 221
Study Questionsp. 222
Essay Questionsp. 222
Calculation Questionsp. 223
Data Analysis Questionsp. 224
Referencesp. 224
Multivariate Graphicsp. 227
Introductionp. 227
Latour's Graphicity Thesisp. 231
Nineteenth-Century Male Names: The Construction of Convergent Multivariate Graphsp. 233
Varieties of Multivariate Graphsp. 240
Principal-component Plotsp. 241
Ruben Gabriel's Biplotp. 241
Isoquant Projection Plotsp. 248
Cluster Analysisp. 252
Cluster Principal-component Plotp. 253
MANOVA-Based Principal Component Plotp. 254
PCP Time Series Vector Plotsp. 258
PCP Time-Series Scatter Plotsp. 263
PCP Vector Plots for Linked Multivariate Data Setsp. 264
PCP Scatter Plots for Linked Multivariate Data Setsp. 264
Generalized Draftsman's Displayp. 264
Multidimensional Scalingp. 266
Flourishing Families: An Illustration of Linked Graphics and Statistical Analyses in Data Explorationp. 268
Summaryp. 278
Study Questionsp. 278
Essay Questionsp. 278
Computational Questionsp. 279
Data Analysis Questionsp. 279
Referencesp. 279
Canonical Correlation: The Underused Methodp. 283
Introductionp. 283
Applied Example of Canonical Correlation: Personality Orientations and Prejudicep. 286
Mathematical Demonstration of a Complete Canonical Correlation Analysisp. 297
Illustrations of Canonical Correlation Tables and Graphics with Finance Datap. 320
Summary and Conclusionsp. 328
Study Questionsp. 329
Essay Questionsp. 329
Computational Questionsp. 330
Data Analysisp. 330
Referencesp. 331
Hotelling's T2 as the Simplest Case of Multivariate Inferencep. 333
Introductionp. 333
An Applied Example of Hotelling's T2 Test: Family Finances and Relational Aggressionp. 335
Multivariate versus Univariate Significance Testsp. 337
The Two Sample Independent Groups Hotelling's T2 Testp. 339
Discriminant Analysis from a Hotelling's T2 Testp. 344
Summary and Conclusionsp. 347
Study Questionsp. 348
Essay Questionsp. 348
Computational Questionsp. 348
Data Analysis Questionsp. 349
Referencesp. 349
Multivariate Analysis of Variancep. 351
Introductionp. 351
An Applied Example of Multivariate Analysis of Variance (MAV1)p. 353
One-Way Multivariate Analysis of Variance (MAVI)p. 357
The Four Multivariate Significance Testsp. 365
Summary and Conclusionsp. 368
Study Questionsp. 369
Essay Questionsp. 369
Computational Questionsp. 370
Data Analysis Questionsp. 370
Referencesp. 371
Multiple Regression and the General Linear Modelp. 373
Introductionp. 373
The Fundamental Method of Multiple Regressionp. 374
Two-Way Analysis of Variance (AV2) Using Multiple Regressionp. 385
AV2 by the Sums of Squares Methodp. 386
AV2 by Multiple Regression: The General Linear Modelp. 390
Nonorthogonal AV2 Design (Unbalanced) and the General Linear Modelp. 397
Other Designs Using Linear Contrastsp. 404
Analysis of Covariance and the General Linear Modelp. 408
Linear Contrasts and Complex Designsp. 413
Regressing Categorical Variablesp. 428
Log-Linear Analysisp. 429
Logistic Regressionp. 435
Summary and Conclusionsp. 437
Study Questionsp. 438
Essay Questionsp. 438
Computational Questionsp. 438
Data Analysis Questionsp. 439
Referencesp. 440
Appendices: Statistical Tablesp. 443
Name Indexp. 456
Subject Indexp. 460
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