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: 9780470537565 | 0470537566
- Cover: Hardcover
- Copyright: 12/27/2011
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 |
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