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| Preface | |
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| Acknowledgments | |
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| Introduction | |
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| Why Multivariate Analysis? | |
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| Prerequisites | |
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| Objectives | |
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| Basic Types of Data And Analysis | |
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| Matrix Algebra | |
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| Introduction | |
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| Notation and Basic Definitions | |
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| Operations | |
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| Partitioned Matrices | |
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| Rank | |
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| Inverse | |
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| Positive Definite Matrices | |
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| Determinants | |
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| Trace | |
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| Orthogonal Vectors and Matrices | |
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| Eigenvalues and Eigenvectors | |
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| Kronecker and VEC Notation | |
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| Problems | |
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| Characterizing and Displaying Multivariate Data | |
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| Mean and Variance of a Univariate Random Variable | |
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| Covariance and Correlation Of Bivariate Random Variables | |
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| Scatter Plots of Bivariate Samples | |
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| Graphical Displays for Multivariate Samples | |
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| Dynamic Graphics | |
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| Mean Vectors | |
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| Covariance Matrices | |
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| Correlation Matrices | |
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| Mean Vectors and Covariance Matrices for Subsets of Variables | |
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| Two Subsets | |
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| Three or More Subsets | |
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| Linear Combinations of Variables | |
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| Sample Properties | |
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| Population Properties | |
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| Measures of Overall Variability | |
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| Estimation of Missing Values | |
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| Distance Between Vectors | |
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| Problems | |
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| The Multivariate Normal Distribution | |
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| Multivariate Normal Density Function | |
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| Properties of Multivariate Normal Random Variables | |
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| Estimation in the Multivariate Normal | |
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| Assessing Multivariate Normality | |
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| Transformations to Normality | |
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| Outliers | |
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| Problems | |
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| Tests on One or Two Mean Vectors | |
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| Multivariate Versus Univariate Tests | |
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| Tests on � With ??Known | |
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| Tests on � When ??is Unknown | |
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| Comparing two Mean Vectors | |
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| Tests on Individual Variables Conditional on Rejection of H0 by the T2-test | |
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| Computation of T2 | |
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| Paired Observations Test | |
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| Test for Additional Information | |
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| Profile Analysis | |
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| Profile Analysis | |
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| Problems | |
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| Multivariate Analysis of Variance | |
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| One-way Models | |
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| Comparison of the Four Manova Test Statistics | |
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| Contrasts | |
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| Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test | |
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| Two-Way Classification | |
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| Other Models | |
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| Checking on the Assumptions | |
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| Profile Analysis | |
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| Repeated Measures Designs | |
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| Growth Curves | |
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| Tests on a Subvector | |
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| Problems | |
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| Tests on Covariance Matrices | |
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| Introduction | |
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| Testing a Specified Pattern for ∑ | |
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| Tests Comparing Covariance Matrices | |
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| Tests of Independence | |
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| Problems | |
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| Discriminant Analysis: Description of Group Separation | |
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| Introduction | |
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| The Discriminant Function for two Groups | |
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| Relationship Between two-group Discriminant Analysis and Multiple Regression | |
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| Discriminant Analysis for Several Groups | |
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| Standardized Discriminant Functions | |
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| Tests of Significance | |
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| Interpretation of Discriminant Functions | |
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| Scatter Plots | |
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| Stepwise Selection of Variables | |
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| Problems | |
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| Classification Analysis: Allocation of Observations to Groups | |
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| Introduction | |
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| Classification into two Groups | |
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| Classification into Several Groups | |
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| Estimating Misclassification Rates | |
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| Improved Estimates of Error Rates | |
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| Subset Selection | |
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| Nonparametric Procedures | |
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| Problems | |
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| Multivariate Regression | |
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| Introduction | |
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| Multiple Regression: Fixed X’s | |
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| Multiple Regression: Random X’s | |
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| Multivariate Multiple Regression: Estimation | |
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| Multivariate Multiple Regression: Hypothesis Tests | |
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| Multivariate Multiple Regression: Prediction | |
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| Measures of Association Between the Y’s and the X’s | |
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| Subset Selection | |
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| Multivariate Regression: Random X’s | |
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| Problems | |
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| Canonical Correlation | |
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| Introduction | |
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| Canonical Correlations and Canonical Variates | |
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| Properties of Canonical Correlations | |
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| Tests of Significance | |
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| Interpretation | |
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| Relationships of Canonical Correlation Analysis to Other Multivariate Problems | |
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| Principal Component Analysis | |
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| Introduction | |
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| Geometric and Algebraic Bases of Principal Components | |
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| Principal Components and Perpendicular Regression | |
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| Plotting of Principal Components | |
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| Principal Components from the Correlation Matrix | |
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| Deciding How Many Components to Retain | |
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| Information in the Last Few Principal Components | |
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| Interpretation of Principal Components | |
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| Selection of Variables | |
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| Problems | |
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| Exploratory Factor Analysis | |
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| Introduction | |
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| Orthogonal Factor Model | |
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| Estimation of Loadings and Communalities | |
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| Choosing the Number of Factors, m | |
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| Rotation | |
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| Factor Scores | |
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| Validity of the Factor Analysis Model | |
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| Relationship of Factor Analysis to Principal Component Analysis | |
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| Problems | |
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| Confirmatory Factor Analysis | |
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| Introduction | |
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| Model Specification and Identification | |
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| Parameter Estimation and Model Assessment | |
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| Inference for Model Parameters | |
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| Factor Scores | |
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| Problems | |
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| Cluster Analysis | |
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| Introduction | |
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| Measures of Similarity or Dissimilarity | |
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| Hierarchical Clustering | |
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| Nonhierarchical Methods | |
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| Choosing the Number of Clusters | |
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| Cluster Validity | |
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| Clustering Variables | |
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| Problems | |
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| Graphical Procedures | |
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| Multidimensional Scaling | |
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| Correspondence Analysis | |
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| Biplots | |
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| Problems | |
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| Tables | |
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| Answers and Hints to Problems | |
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| Data Sets and SAS Files | |
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| References | |
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| Index | |