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Multivariate Analysis for the Biobehavioral and Social Sciences A Graphical Approach

by: Brown, Bruce L.; Hendrix, Suzanne B.; Hedges, Dawson W.; Smith, Timothy B.

Multivariate Analysis for the Biobehavioral and Social Sciences A Graphical Approach

by: Brown, Bruce L.; Hendrix, Suzanne B.; Hedges, Dawson W.; Smith, Timothy B.

ISBN 13:
9780470537565
ISBN 10:
0470537566
Edition: 1st
Format: Hardcover
Copyright: 12/27/2011
Publisher: 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.

Preface	p. xiii
Overview of Multivariate and Regression Methods	p. 1
Introduction	p. 1
Multivariate Methods as an Extension of Familiar Univariate Methods	p. 2
Measurement Scales and Data Types	p. 4
Four Basic Data Set Structures for Multivariate Analysis	p. 5
Pictorial Overview of Multivariate Methods	p. 7
Correlational versus Experimental Methods	p. 15
Old versus New Methods	p. 16
Summary	p. 17
Study Questions	p. 18
Essay Questions	p. 18
References	p. 19
The Seven Habits of Highly Effective Quants: A Review of Elementary Statistics Using Matrix Algebra	p. 20
Introduction	p. 20
The Meaning of Measurement Scales	p. 22
The Meaning of Measures of Central Tendency	p. 23
Variance and Matrix Algebra	p. 26
Covariance Matrices and Correlation Matrices	p. 34
Classical Probability Theory and the Binomial: The Basis for Statistical Inference	p. 43
Significance Tests: From Binomial to z-Tests to f-Tests to Analysis of Variance	p. 58
The z Test of a Single Mean	p. 67
The z Test of a Single Proportion	p. 68
The z Test of Two Means for Independent Samples	p. 69
The z Test of Two Proportions for Independent Samples	p. 70
The z Test of Two Means for Correlated Samples	p. 72
The z Test of Two Proportions for Correlated Samples	p. 72
The t Test of a Single Mean	p. 72
The t Test of Two Means for Independent Samples	p. 73
The t Test of Two Means for Correlated Samples	p. 75
Assumptions and Sampling Distributions of the Nine Tests	p. 77
Matrix Approach to Analysis of Variance	p. 79
Summary	p. 83
Study Questions	p. 84
Essay Questions	p. 84
Calculation Questions	p. 85
Data Analysis Questions	p. 86
References	p. 87
Fundamentals of Matrix Algebra	p. 88
Introduction	p. 88
Definitions and Notation	p. 89
Matrix Operations and Statistical Quantities	p. 89
Addition and Subtraction	p. 89
Scalar Multiplication	p. 90
Transpose of a Matrix	p. 91
Matrix Multiplication	p. 91
Division by a Scalar	p. 95
Symmetric Matrices and Diagonal Matrices	p. 97
The Identity Matrix and the J Matrix	p. 100
Partitioned Matrices and Adjoined Matrices	p. 108
Adjoined Matrices	p. 108
Partitioned Matrices	p. 109
Triangular Square Root Matrices	p. 110
Triangular Matrices	p. 110
The Cholesky Method for Finding a Triangular Square Root Matrix	p. 110
Determinants	p. 112
The Bent Diagonals Method	p. 113
The Matrix Extension Method	p. 114
The Method of Cofactors	p. 115
Meaning of the Trace and the Determinant of a Covariance Matrix	p. 117
Matrix Inversion	p. 118
Matrix Inversion by the Method of Cofactors	p. 119
Matrix Inversion by the Cholesky Method	p. 120
Rank of a Matrix	p. 123
Orthogonal Vectors and Matrices	p. 124
Quadratic Forms and Bilinear Forms	p. 125
Quadratic Forms	p. 126
Bilinear Forms	p. 126
Covariance Matrix Transformation	p. 127
Eigenvectors and Eigenvalues	p. 128
Spectral Decomposition, Triangular Decomposition, and Singular Value Decomposition	p. 129
Spectral Decomposition, Square Matrices, and Square Root Matrices	p. 130
Triangular Decomposition Compared to Spectral Decomposition	p. 133
Singular Value Decomposition	p. 134
Normalization of a Vector	p. 134
Conclusion	p. 136
Study Questions	p. 136
Essay Questions	p. 136
Calculation Questions	p. 136
Data Analysis Questions	p. 137
References	p. 138
Factor Analysis and Related Methods: Quintessentially Multivariate	p. 139
Introduction	p. 139
An Applied Example of Factoring: The Mental Skills of Mice	p. 142
Calculating Factor Loadings to Reveal the Structure of Skills in Mice	p. 149
Simplest Case Mathematical Demonstration of a Complete Factor Analysis	p. 153
Factor Scores: The Relationship between Latent Variables and Manifest Variables	p. 169
The Three Types of Eigenvector in Factor Analysis	p. 169
Factor Scores Demonstration Using Simplest Case Data from Section 4.4	p. 171
Factor Analysis and Factor Scores for Simplest Case Data with a Rank of 2	p. 172
Factor Analysis as Data Transformation	p. 174
Principal Component Analysis: Simplified Factoring of Covariance Structure	p. 176
Rotation of the Factor Pattern	p. 188
The Rich Variety of Factor Analysis Models	p. 194
Factor Analyzing the Mental Skills of Mice: A Comparison of Factor Analytic Models	p. 200
Data Reliability and Factor Analysis	p. 210
Summary	p. 221
Study Questions	p. 222
Essay Questions	p. 222
Calculation Questions	p. 223
Data Analysis Questions	p. 224
References	p. 224
Multivariate Graphics	p. 227
Introduction	p. 227
Latour's Graphicity Thesis	p. 231
Nineteenth-Century Male Names: The Construction of Convergent Multivariate Graphs	p. 233
Varieties of Multivariate Graphs	p. 240
Principal-component Plots	p. 241
Ruben Gabriel's Biplot	p. 241
Isoquant Projection Plots	p. 248
Cluster Analysis	p. 252
Cluster Principal-component Plot	p. 253
MANOVA-Based Principal Component Plot	p. 254
PCP Time Series Vector Plots	p. 258
PCP Time-Series Scatter Plots	p. 263
PCP Vector Plots for Linked Multivariate Data Sets	p. 264
PCP Scatter Plots for Linked Multivariate Data Sets	p. 264
Generalized Draftsman's Display	p. 264
Multidimensional Scaling	p. 266
Flourishing Families: An Illustration of Linked Graphics and Statistical Analyses in Data Exploration	p. 268
Summary	p. 278
Study Questions	p. 278
Essay Questions	p. 278
Computational Questions	p. 279
Data Analysis Questions	p. 279
References	p. 279
Canonical Correlation: The Underused Method	p. 283
Introduction	p. 283
Applied Example of Canonical Correlation: Personality Orientations and Prejudice	p. 286
Mathematical Demonstration of a Complete Canonical Correlation Analysis	p. 297
Illustrations of Canonical Correlation Tables and Graphics with Finance Data	p. 320
Summary and Conclusions	p. 328
Study Questions	p. 329
Essay Questions	p. 329
Computational Questions	p. 330
Data Analysis	p. 330
References	p. 331
Hotelling's T² as the Simplest Case of Multivariate Inference	p. 333
Introduction	p. 333
An Applied Example of Hotelling's T² Test: Family Finances and Relational Aggression	p. 335
Multivariate versus Univariate Significance Tests	p. 337
The Two Sample Independent Groups Hotelling's T² Test	p. 339
Discriminant Analysis from a Hotelling's T² Test	p. 344
Summary and Conclusions	p. 347
Study Questions	p. 348
Essay Questions	p. 348
Computational Questions	p. 348
Data Analysis Questions	p. 349
References	p. 349
Multivariate Analysis of Variance	p. 351
Introduction	p. 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 Tests	p. 365
Summary and Conclusions	p. 368
Study Questions	p. 369
Essay Questions	p. 369
Computational Questions	p. 370
Data Analysis Questions	p. 370
References	p. 371
Multiple Regression and the General Linear Model	p. 373
Introduction	p. 373
The Fundamental Method of Multiple Regression	p. 374
Two-Way Analysis of Variance (AV2) Using Multiple Regression	p. 385
AV2 by the Sums of Squares Method	p. 386
AV2 by Multiple Regression: The General Linear Model	p. 390
Nonorthogonal AV2 Design (Unbalanced) and the General Linear Model	p. 397
Other Designs Using Linear Contrasts	p. 404
Analysis of Covariance and the General Linear Model	p. 408
Linear Contrasts and Complex Designs	p. 413
Regressing Categorical Variables	p. 428
Log-Linear Analysis	p. 429
Logistic Regression	p. 435
Summary and Conclusions	p. 437
Study Questions	p. 438
Essay Questions	p. 438
Computational Questions	p. 438
Data Analysis Questions	p. 439
References	p. 440
Appendices: Statistical Tables	p. 443
Name Index	p. 456
Subject Index	p. 460
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Multivariate Analysis for the Biobehavioral and Social Sciences A Graphical Approach

Multivariate Analysis for the Biobehavioral and Social Sciences A Graphical Approach

9780470537565

0470537566

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Table of Contents

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