MULTIVARIATE ANALYSIS FOR THE BIOBEHAVIORAL AND SOCIAL SCIENCES: A Graphical Approach -- CONTENTS -- PREFACE -- CHAPTER ONE: OVERVIEW OF MULTIVARIATE AND REGRESSION METHODS -- 1.1 INTRODUCTION -- 1.2 MULTIVARIATE METHODS AS AN EXTENSION OF FAMILIAR UNIVARIATE METHODS -- 1.3 MEASUREMENT SCALES AND DATA TYPES -- 1.4 FOUR BASIC DATA SET STRUCTURES FOR MULTIVARIATE ANALYSIS -- 1.5 PICTORIAL OVERVIEW OF MULTIVARIATE METHODS -- 1.6 CORRELATIONAL VERSUS EXPERIMENTAL METHODS -- 1.7 OLD VERSUS NEW METHODS -- 1.8 SUMMARY -- STUDY QUESTIONS -- A. Essay Questions -- REFERENCES -- CHAPTER TWO: THE SEVEN HABITS OF HIGHLY EFFECTIVE QUANTS: A REVIEW OF ELEMENTARY STATISTICS USING MATRIX ALGEBRA -- 2.1 INTRODUCTION -- 2.2 THE MEANING OF MEASUREMENT SCALES -- 2.3 THE MEANING OF MEASURES OF CENTRAL TENDENCY -- 2.4 VARIANCE AND MATRIX ALGEBRA -- 2.5 COVARIANCE MATRICES AND CORRELATION MATRICES -- 2.6 CLASSICAL PROBABILITY THEORY AND THE BINOMIAL: THE BASIS FOR STATISTICAL INFERENCE -- 2.7 SIGNIFICANCE TESTS: FROM BINOMIAL TO Z-TESTS TO T-TESTS TO ANALYSIS OF VARIANCE -- 2.7.1 The z Test of a Single Mean -- 2.7.2 The z Test of a Single Proportion -- 2.7.3 The z Test of Two Means for Independent Samples -- 2.7.4 The z Test of Two Proportions for Independent Samples -- 2.7.5 The z Test of Two Means for Correlated Samples -- 2.7.6 The z Test of Two Proportions for Correlated Samples -- 2.7.7 The t Test of a Single Mean -- 2.7.8 The t Test of Two Means for Independent Samples -- 2.7.9 The t Test of Two Means for Correlated Samples -- 2.7.10 Assumptions and Sampling Distributions of the Nine Tests -- 2.8 MATRIX APPROACH TO ANALYSIS OF VARIANCE -- 2.9 SUMMARY -- STUDY QUESTIONS -- A. Essay Questions -- B. Calculation Questions -- C. Data Analysis Questions -- REFERENCES -- CHAPTER THREE: FUNDAMENTALS OF MATRIX ALGEBRA -- 3.1 INTRODUCTION -- 3.2 DEFINITIONS AND NOTATION.

3.3 MATRIX OPERATIONS AND STATISTICAL QUANTITIES -- 3.3.1 Addition and Subtraction -- 3.3.2 Scalar Multiplication -- 3.3.3 Transpose of a Matrix -- 3.3.4 Matrix Multiplication -- 3.3.5 Division by a Scalar -- 3.3.6 Symmetric Matrices and Diagonal Matrices -- 3.3.7 The Identity Matrix and the J Matrix -- 3.4 PARTITIONED MATRICES AND ADJOINED MATRICES -- 3.4.1 Adjoined Matrices -- 3.4.2 Partitioned Matrices -- 3.5 TRIANGULAR SQUARE ROOT MATRICES -- 3.5.1 Triangular Matrices -- 3.5.2 The Cholesky Method for Finding a Triangular Square Root Matrix -- 3.6 DETERMINANTS -- 3.6.1 The Bent Diagonals Method -- 3.6.2 The Matrix Extension Method -- 3.6.3 The Method of Cofactors -- 3.6.4 Meaning of the Trace and the Determinant of a Covariance Matrix -- 3.7 MATRIX INVERSION -- 3.7.1 Matrix Inversion by the Method of Cofactors -- 3.7.2 Matrix Inversion by the Cholesky Method -- 3.8 RANK OF A MATRIX -- 3.9 ORTHOGONAL VECTORS AND MATRICES -- 3.10 QUADRATIC FORMS AND BILINEAR FORMS -- 3.10.1 Quadratic Forms -- 3.10.2 Bilinear Forms -- 3.10.3 Covariance Matrix Transformation -- 3.11 EIGENVECTORS AND EIGENVALUES -- 3.12 SPECTRAL DECOMPOSITION, TRIANGULAR DECOMPOSITION, AND SINGULAR VALUE DECOMPOSITION -- 3.12.1 Spectral Decomposition, Square Matrices, and Square Root Matrices -- 3.12.2 Triangular Decomposition Compared to Spectral Decomposition -- 3.12.3 Singular Value Decomposition -- 3.13 NORMALIZATION OF A VECTOR -- 3.14 CONCLUSION -- STUDY QUESTIONS -- A. Essay Questions -- B. Calculation Questions -- C. Data Analysis Questions -- REFERENCES -- CHAPTER FOUR: FACTOR ANALYSIS AND RELATED METHODS: QUINTESSENTIALLY MULTIVARIATE -- 4.1 INTRODUCTION -- 4.2 AN APPLIED EXAMPLE OF FACTORING: THE MENTAL SKILLS OF MICE -- 4.3 CALCULATING FACTOR LOADINGS TO REVEAL THE STRUCTURE OF SKILLS IN MICE -- 4.4 SIMPLEST CASE MATHEMATICAL DEMONSTRATION OF A COMPLETE FACTOR ANALYSIS.

4.5 FACTOR SCORES: THE RELATIONSHIP BETWEEN LATENT VARIABLES AND MANIFEST VARIABLES -- 4.5.1 The Three Types of Eigenvector in Factor Analysis -- 4.5.2 Factor Scores Demonstration Using Simplest Case Data from Section 4.4 -- 4.5.3 Factor Analysis and Factor Scores for Simplest Case Data with a Rank of 2 -- 4.5.4 Factor Analysis as Data Transformation -- 4.6 PRINCIPAL COMPONENT ANALYSIS: SIMPLIFIED FACTORING OF COVARIANCE STRUCTURE -- 4.7 ROTATION OF THE FACTOR PATTERN -- 4.8 THE RICH VARIETY OF FACTOR ANALYSIS MODELS -- 4.9 FACTOR ANALYZING THE MENTAL SKILLS OF MICE: A COMPARISON OF FACTOR ANALYTIC MODELS -- 4.10 DATA RELIABILITY AND FACTOR ANALYSIS -- 4.11 SUMMARY -- STUDY QUESTIONS -- A. Essay Questions -- B. Calculation Questions -- C. Data Analysis Questions -- REFERENCES -- CHAPTER FIVE: MULTIVARIATE GRAPHICS -- 5.1 INTRODUCTION -- 5.2 LATOUR'S GRAPHICITY THESIS -- 5.3 NINETEENTH-CENTURY MALE NAMES: THE CONSTRUCTION OF CONVERGENT MULTIVARIATE GRAPHS -- 5.4 VARIETIES OF MULTIVARIATE GRAPHS -- 5.4.1 Principal-component Plots -- 5.4.2 Ruben Gabriel's Biplot -- 5.4.3 Isoquant Projection Plots -- 5.4.4 Cluster Analysis -- 5.4.5 Cluster Principal-component Plot -- 5.4.6 MANOVA-Based Principal Component Plot -- 5.4.7 PCP Time Series Vector Plots -- 5.4.8 PCP Time-Series Scatter Plots -- 5.4.9 PCP Vector Plots for Linked Multivariate Data Sets -- 5.4.10 PCP Scatter Plots for Linked Multivariate Data Sets -- 5.4.11 Generalized Draftsman's Display -- 5.4.12 Multidimensional Scaling -- 5.5 FLOURISHING FAMILIES: AN ILLUSTRATION OF LINKED GRAPHICS AND STATISTICAL ANALYSES IN DATA EXPLORATION -- 5.6 SUMMARY -- STUDY QUESTIONS -- A. Essay Questions -- B. Computational Questions -- C. Data Analysis Question -- REFERENCES -- CHAPTER SIX: CANONICAL CORRELATION: THE UNDERUSED METHOD -- 6.1 INTRODUCTION.

6.2 APPLIED EXAMPLE OF CANONICAL CORRELATION: PERSONALITY ORIENTATIONS AND PREJUDICE -- 6.3 MATHEMATICAL DEMONSTRATION OF A COMPLETE CANONICAL CORRELATION ANALYSIS -- 6.4 ILLUSTRATIONS OF CANONICAL CORRELATION TABLES AND GRAPHICS WITH FINANCE DATA -- 6.5 SUMMARY AND CONCLUSIONS -- STUDY QUESTIONS -- A. Essay Questions -- B. Computational Questions -- C. Data Analysis -- REFERENCES -- CHAPTER SEVEN: HOTELLING'S T2 AS THE SIMPLEST CASE OF MULTIVARIATE INFERENCE -- 7.1 INTRODUCTION -- 7.2 AN APPLIED EXAMPLE OF HOTELLING'S T2 TEST: FAMILY FINANCES AND RELATIONAL AGGRESSION -- 7.3 MULTIVARIATE VERSUS UNIVARIATE SIGNIFICANCE TESTS -- 7.4 THE TWO SAMPLE INDEPENDENT GROUPS HOTELLING'S T2 TEST -- 7.5 DISCRIMINANT ANALYSIS FROM A HOTELLING'S T2 TEST -- 7.6 SUMMARY AND CONCLUSIONS -- STUDY QUESTIONS -- A. Essay Questions -- B. Computational Questions -- C. Data Analysis Questions -- REFERENCES -- CHAPTER EIGHT: MULTIVARIATE ANALYSIS OF VARIANCE -- 8.1 INTRODUCTION -- 8.2 AN APPLIED EXAMPLE OF MULTIVARIATE ANALYSIS OF VARIANCE (MAV1) -- 8.3 ONE-WAY MULTIVARIATE ANALYSIS OF VARIANCE (MAV1) -- 8.4 THE FOUR MULTIVARIATE SIGNIFICANCE TESTS -- 8.5 SUMMARY AND CONCLUSIONS -- STUDY QUESTIONS -- A. Essay Questions -- B. Computational Questions -- C. Data Analysis Questions -- REFERENCES -- CHAPTER NINE: MULTIPLE REGRESSION AND THE GENERAL LINEAR MODEL -- 9.1 INTRODUCTION -- 9.2 THE FUNDAMENTAL METHOD OF MULTIPLE REGRESSION -- 9.3 TWO-WAY ANALYSIS OF VARIANCE (AV2) USING MULTIPLE REGRESSION -- 9.3.1 AV2 by the Sums of Squares Method -- 9.3.2 AV2 by Multiple Regression: The General Linear Model -- 9.3.3 Nonorthogonal AV2 Design (Unbalanced) and the General Linear Model -- 9.3.4 Other Designs Using Linear Contrasts -- 9.4 ANALYSIS OF COVARIANCE AND THE GENERAL LINEAR MODEL -- 9.5 LINEAR CONTRASTS AND COMPLEX DESIGNS -- 9.6 REGRESSING CATEGORICAL VARIABLES.

9.6.1 Log-Linear Analysis -- 9.6.2 Logistic Regression -- 9.7 SUMMARY AND CONCLUSIONS -- STUDY QUESTIONS -- A. Essay Questions -- B. Computational Questions -- C. Data Analysis Questions -- REFERENCES -- APPENDICES: STATISTICAL TABLES -- NAME INDEX -- SUBJECT INDEX.