Preface | p. xvii |

Acknowledgments | p. xxi |

Introduction | p. 1 |

Why Multivariate Analysis? | p. 1 |

Prerequisites | p. 3 |

Objectives | p. 3 |

Basic Types of Data And Analysis | p. 4 |

Matrix Algebra | p. 7 |

Introduction | p. 7 |

Notation and Basic Definitions | p. 8 |

Operations | p. 11 |

Partitioned Matrices | p. 22 |

Rank | p. 23 |

Inverse | p. 25 |

Positive Definite Matrices | p. 26 |

Determinants | p. 28 |

Trace | p. 31 |

Orthogonal Vectors and Matrices | p. 31 |

Eigenvalues and Eigenvectors | p. 32 |

Kronecker and VEC Notation | p. 37 |

Problems | p. 39 |

Characterizing and Displaying Multivariate Data | p. 47 |

Mean and Variance of a Univariate Random Variable | p. 47 |

Covariance and Correlation Of Bivariate Random Variables | p. 49 |

Scatter Plots of Bivariate Samples | p. 55 |

Graphical Displays for Multivariate Samples | p. 56 |

Dynamic Graphics | p. 58 |

Mean Vectors | p. 63 |

Covariance Matrices | p. 66 |

Correlation Matrices | p. 69 |

Mean Vectors and Covariance Matrices for Subsets of Variables | p. 71 |

Two Subsets | p. 71 |

Three or More Subsets | p. 73 |

Linear Combinations of Variables | p. 75 |

Sample Properties | p. 75 |

Population Properties | p. 81 |

Measures of Overall Variability | p. 81 |

Estimation of Missing Values | p. 82 |

Distance Between Vectors | p. 84 |

Problems | p. 85 |

The Multivariate Normal Distribution | p. 91 |

Multivariate Normal Density Function | p. 91 |

Properties of Multivariate Normal Random Variables | p. 94 |

Estimation in the Multivariate Normal | p. 99 |

Assessing Multivariate Normality | p. 101 |

Transformations to Normality | p. 108 |

Outliers | p. 111 |

Problems | p. 117 |

Tests on One or Two Mean Vectors | p. 125 |

Multivariate Versus Univariate Tests | p. 125 |

Tests on µ With ??Known | p. 126 |

Tests on µ When ??is Unknown | p. 130 |

Comparing two Mean Vectors | p. 134 |

Tests on Individual Variables Conditional on Rejection of H0 by the T2-test | p. 139 |

Computation of T2 | p. 143 |

Paired Observations Test | p. 145 |

Test for Additional Information | p. 149 |

Profile Analysis | p. 152 |

Profile Analysis | p. 154 |

Problems | p. 161 |

Multivariate Analysis of Variance | p. 169 |

One-way Models | p. 169 |

Comparison of the Four Manova Test Statistics | p. 189 |

Contrasts | p. 191 |

Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test | p. 195 |

Two-Way Classification | p. 198 |

Other Models | p. 207 |

Checking on the Assumptions | p. 210 |

Profile Analysis | p. 211 |

Repeated Measures Designs | p. 215 |

Growth Curves | p. 232 |

Tests on a Subvector | p. 241 |

Problems | p. 244 |

Tests on Covariance Matrices | p. 259 |

Introduction | p. 259 |

Testing a Specified Pattern for ∑ | p. 259 |

Tests Comparing Covariance Matrices | p. 265 |

Tests of Independence | p. 269 |

Problems | p. 276 |

Discriminant Analysis: Description of Group Separation | p. 281 |

Introduction | p. 281 |

The Discriminant Function for two Groups | p. 282 |

Relationship Between two-group Discriminant Analysis and Multiple Regression | p. 286 |

Discriminant Analysis for Several Groups | p. 288 |

Standardized Discriminant Functions | p. 292 |

Tests of Significance | p. 294 |

Interpretation of Discriminant Functions | p. 298 |

Scatter Plots | p. 301 |

Stepwise Selection of Variables | p. 303 |

Problems | p. 306 |

Classification Analysis: Allocation of Observations to Groups | p. 309 |

Introduction | p. 309 |

Classification into two Groups | p. 310 |

Classification into Several Groups | p. 314 |

Estimating Misclassification Rates | p. 318 |

Improved Estimates of Error Rates | p. 320 |

Subset Selection | p. 322 |

Nonparametric Procedures | p. 326 |

Problems | p. 336 |

Multivariate Regression | p. 339 |

Introduction | p. 339 |

Multiple Regression: Fixed X’s | p. 340 |

Multiple Regression: Random X’s | p. 354 |

Multivariate Multiple Regression: Estimation | p. 354 |

Multivariate Multiple Regression: Hypothesis Tests | p. 364 |

Multivariate Multiple Regression: Prediction | p. 370 |

Measures of Association Between the Y’s and the X’s | p. 372 |

Subset Selection | p. 374 |

Multivariate Regression: Random X’s | p. 380 |

Problems | p. 381 |

Canonical Correlation | p. 385 |

Introduction | p. 385 |

Canonical Correlations and Canonical Variates | p. 385 |

Properties of Canonical Correlations | p. 390 |

Tests of Significance | p. 391 |

Interpretation | p. 395 |

Relationships of Canonical Correlation Analysis to Other Multivariate Problems | p. 402 |

Principal Component Analysis | p. 405 |

Introduction | p. 405 |

Geometric and Algebraic Bases of Principal Components | p. 406 |

Principal Components and Perpendicular Regression | p. 412 |

Plotting of Principal Components | p. 414 |

Principal Components from the Correlation Matrix | p. 419 |

Deciding How Many Components to Retain | p. 423 |

Information in the Last Few Principal Components | p. 427 |

Interpretation of Principal Components | p. 427 |

Selection of Variables | p. 430 |

Problems | p. 432 |

Exploratory Factor Analysis | p. 435 |

Introduction | p. 435 |

Orthogonal Factor Model | p. 437 |

Estimation of Loadings and Communalities | p. 442 |

Choosing the Number of Factors, m | p. 453 |

Rotation | p. 457 |

Factor Scores | p. 466 |

Validity of the Factor Analysis Model | p. 470 |

Relationship of Factor Analysis to Principal Component Analysis | p. 475 |

Problems | p. 476 |

Confirmatory Factor Analysis | p. 479 |

Introduction | p. 479 |

Model Specification and Identification | p. 480 |

Parameter Estimation and Model Assessment | p. 487 |

Inference for Model Parameters | p. 492 |

Factor Scores | p. 495 |

Problems | p. 496 |

Cluster Analysis | p. 501 |

Introduction | p. 501 |

Measures of Similarity or Dissimilarity | p. 502 |

Hierarchical Clustering | p. 505 |

Nonhierarchical Methods | p. 531 |

Choosing the Number of Clusters | p. 544 |

Cluster Validity | p. 546 |

Clustering Variables | p. 547 |

Problems | p. 548 |

Graphical Procedures | p. 555 |

Multidimensional Scaling | p. 555 |

Correspondence Analysis | p. 565 |

Biplots | p. 580 |

Problems | p. 588 |

Tables | p. 597 |

Answers and Hints to Problems | p. 637 |

Data Sets and SAS Files | p. 727 |

References | p. 729 |

Index | p. 747 |

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