Multivariate Statistical Methods (McGraw-Hill Series in Probability and Statistics)

A revison of a text designed to make multivariate techniques available to the behavioural, social, biological and medical student. It includes expansion of exercises and examples, updating of references and the addition of several data sets in a new appendix.

1. SOME ELEMENTARY STATISTICAL CONCEPTS. Introduction. Random Variables. Normal Random Variables. Random Samples and Estimation. Tests of Hypothesis for the Parameters of Normal Populations. Testing the Equality of Several Means: The Analysis of Variance. 2. MATRIX ALGEBRA. Introduction. Some Definitions. Elementary Operations with Matrices and Vectors. The Determinant of a Square Matrix. The Inverse Matrix. The Rank of a Matrix. Simultaneous Linear Equations. Orthogonal Vectors and Matrices. Quadratic Forms. The Characteristics Roots and Vectors of a Matrix. Partitioned Matrices. Differentiation with Vectors and Matrices. Further Reading. 3. SAMPLES FROM THE MULTIVARIATE NORMAL POPULATION. Introduction. Multidimensional Random Variables. The Multivariate Normal Distribution. Conditional and Marginal Distributions of Multinormal Random Variables. Samples from the Multinormal Population. Correlation and Regression. Simultaneous Inference about Regression Coefficients. Inferences about the Correlation Matrix. Samples with Incomplete Observations. Exercises. 4. TESTS OF HYPOTHESES ON MEANS. Introduction. Tests on Means and the T2 ?Statistic. Simultaneous Inferences for Means. The Case of Two Samples. The Analysis of Repeated Measurements. Groups of Repeated Measurements: The Paired T2 Test. Profile Analysis for Two Independent Groups. The Power of Tests on Mean Vectors. Some Tests with Known Covariance Matrices. Tests for Outlying Observations. Testing the Normality Assumption. Exercises. 5. MULTIVARIATE ANALYSIS OF VARIANCE. Introduction. The Multivariate General Linear Model. The Multivariate Analysis of Variance. MANOVA for Unbalanced Two-Way Layouts. The Multivariate Analysis of Covariance. Multiple Comparisons in the Multivariate Analysis of Variance. Profile Analysis. Power and Sample Size Determination. Curve Fitting for Repeated Measurements. MANOVA Robustness. Exercises. 6. CLASSIFICATION BY DISCRIMINANT FUNCTIONS. Introduction. The Linear Discriminant Function for Two Groups. Classification with Known Parameters. The Case of Unequal Covariance Matrices. Estimation of the Misclassification Probabilities. Classification for Several Groups. Exercises. 7. INFERENCES FROM COVARIANCE MATRICES. Introduction. Hypothesis Tests for a Single Covariance Matrix. Tests for Two Special Patterns. Testing the Equality of Several Covariance Matrices. Testing the Independence of Sets of Variates. Canonical Correlation. Exercises. 8. THE PRINCIPLE COMPONENTS OF MULTIVARIATE DATA. Introduction. The Principal Components of Multivariate Observations. The Geometrical Meaning of Principal Components. The Interpretation of Principal Components. Biplots. Some Patterned Matrices and Their Principal Components. The Sampling Properties of Principal Components. Further Extensions. Exercises. 9. THE FACTOR STRUCTURE OF MULTIVARIATE DATA. Introduction. The Mathematical Model for Factor Structure. Estimation of the Factor Loadings. Testing the Goodness of Fit of the Factor Model. Examples of Factor Analysis. Factor Rotation. An Alternative Model for Factor Analysis. The Evaluation of Factors. Sampling Properties of Factor Model Estimates. Models for the Dependence Structure of Ordered Responses. Clustering Sample Units. Multidimensional Scaling. Exercises. REFERENCES. TABLES AND CHARTS. DATA SETS. NAME INDEX. SUBJECT INDEX.