Samples from the Multivariate Normal Population | p. 1 |
Introduction | p. 1 |
Why Do We Need Multivariate Methods? | p. 1 |
Multidimensional Random Variables | p. 3 |
The Multivariate Normal Distribution | p. 8 |
Conditional and Marginal Distributions of Multinormal Variates | p. 14 |
Samples from the Multinormal Population | p. 20 |
Correlation and Regression | p. 25 |
Simultaneous Inferences about Regression Coefficients | p. 34 |
Inferences about the Correlation Matrix | p. 38 |
Samples with Incomplete Observations | p. 43 |
Exercises | p. 46 |
Tests of Hypotheses on Means | p. 55 |
Introduction | p. 55 |
Tests on Means and the T[superscript 2] Statistic | p. 55 |
Simultaneous Inferences for Means | p. 62 |
The Case of Two Samples | p. 64 |
The Analysis of Repeated-Measurements | p. 68 |
Groups of Repeated Measurements: The Paired T[superscript 2] Test | p. 84 |
Profile Analysis for Two Independent Groups | p. 87 |
The Power of Tests on Mean Vectors | p. 93 |
Some Tests with Known Covariance Matrices | p. 97 |
Tests for Outlying Observations | p. 99 |
Testing the Normality Assumption | p. 103 |
Exercises | p. 108 |
The Multivariate Analysis of Variance | p. 131 |
Introduction | p. 131 |
The Multivariate General Linear Model | p. 131 |
The Multivariate Analysis of Variance | p. 140 |
The Multivariate Analysis of Covariance | p. 156 |
Multiple Comparisons in the Multivariate Analysis of Variance | p. 164 |
Profile Analysis | p. 172 |
Curve Fitting for Repeated Measurements | p. 183 |
Other Test Criteria | p. 190 |
Exercises | p. 192 |
Classification by Discriminant Functions | p. 209 |
Introduction | p. 209 |
The Linear Discriminant Function for Two Groups | p. 210 |
Classification with Known Parameters | p. 213 |
The Case of Unequal Covariance Matrices | p. 215 |
Estimation of the Misclassification Probabilities | p. 218 |
Classification for Several Groups | p. 221 |
Linear Discrimination with a Singular Covariance Matrix | p. 226 |
Classification by Logistic Regression | p. 230 |
Some Further Aspects of Classification | p. 232 |
Exercises | p. 234 |
Inferences from Covariance Matrices | p. 242 |
Introduction | p. 242 |
Hypothesis Tests for a Single Covariance Matrix | p. 242 |
Tests for Two Special Patterns | p. 245 |
Testing the Equality of Several Covariance Matrices | p. 247 |
Testing the Independence of Sets of Variates | p. 249 |
Canonical Correlation | p. 255 |
Exercises | p. 260 |
The Structure of Multivariate Observations: I. Principal Components | p. 264 |
Introduction | p. 264 |
The Principal Components of Multivariate Observations | p. 265 |
The Geometrical Meaning of Principal Components | p. 274 |
The Interpretation of Principal Components | p. 278 |
Some Patterned Matrices and Their Principal Components | p. 282 |
The Sampling Properties of Principal Components | p. 285 |
Some Further Topics | p. 293 |
Exercises | p. 298 |
The Structure of Multivariate Observations: II. Factor Analysis | p. 317 |
Introduction | p. 317 |
The Mathematical Model for Factor Analysis | p. 318 |
Estimation of the Factor Loadings | p. 322 |
Testing the Goodness of Fit of the Factor Model | p. 327 |
Examples of Factor Analyses | p. 329 |
Factor Rotation | p. 334 |
An Alternative Model for Factor Analysis | p. 340 |
The Evaluation of Factors | p. 342 |
Models for the Dependence Structure of Ordered Responses | p. 345 |
Clustering Sampling Units | p. 351 |
Multidimensional Scaling | p. 357 |
Exercises | p. 364 |
References | p. 371 |
Tables and Charts | p. 400 |
Upper Critical Values of the Standard Normal Distribution | p. 400 |
Upper Critical Values of the Chi-squared Distribution | p. 401 |
Upper Percentage Points of the t Distribution | p. 402 |
Upper Percentage Points of the F Distribution | p. 403 |
The Fisher z Transformation | p. 405 |
Minimum Sample Sizes for a Single-Sample Repeated Measures Design | p. 406 |
Charts 1-8: Power Functions of the F Test | p. 410 |
Charts 9-16 and Table 7-15: Upper percentage points of the largest characteristic root | p. 418 |
Data Sets | p. 443 |
Wechsler Adult Intelligence Scale subtest scores | p. 443 |
Iris Species Petal and Sepal Measurements | p. 445 |
Obesity Study Biochemical Levels | p. 447 |
Financial Ratios of Solvent and Financially Distressed Property Liability Insurers | p. 449 |
Financial Ratios of Bankrupt and Solvent Companies | p. 452 |
Dimensions and Characteristics of Winged Aphids (Alate adelges) | p. 454 |
Exchangeable Cations in Forest Soil | p. 455 |
Average Instructor and Course Evaluations for Business School Faculty Members | p. 457 |
Name Index | p. 461 |
Subject Index | p. 465 |
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