Multivariate Statistical Methods: A Primer.

Abstract

THE MATERIAL OF MULTIVARIATE ANALYSIS Examples of Multivariate Data Preview of Multivariate Methods The Multivariate Normal Distribution Computer Programs Graphical Methods Chapter Summary References MATRIX ALGEBRA The Need for Matrix Algebra Matrices and Vectors Operations on Matrices Matrix Inversion Quadratic Forms Eigenvalues and Eigenvectors Vectors of Means and Covariance Matrices Further Reading Chapter Summary References DISPLAYING MULTIVARIATE DATA The Problem of Displaying Many Variables in Two Dimensions Plotting index Variables The Draftsman's Plot The Representation of Individual Data P:oints Profiles of Variables Discussion and Further Reading Chapter Summary References TESTS OF SIGNIFICANCE WITH MULTIVARIATE DATA Simultaneous Tests on Several Varables Comparison of Mean Values for Two Samples: The Single Variable Case Comparison of Mean Values for Two Samples: The Multivariate Case Multivariate Versus Univariate Tests Comparison of Variation for Two Samples: The Single Variable Case Comparison of Variation for Two Samples: The Multivariate Case Comparison of Means for Several Samples Comparison of Variation for Several Samples Discussion Chapter Summary Exercises References MEASURING AND TESTING MULTIVARIATE DISTANCES Multivariate Distances Distances Between Individual Observations Distances Between Populations and Samples Distances Based on Proportions Presence-Absence data The Mantel Randomization Test Computer Programs Discussion and Further Reading Chapter Summary Exercise References PRINCIPAL COMPONENTS ANALYSIS Definition of Principal Components Procedure for a Principal Components Analysis Computer Programs Further Reading Chapter Summary Exercises References FACTOR ANALYSIS The Factor Analysis Model Procedure for a Factor Analysis Principal Components Factor Analysis Using a Factor Analysis Program to do Principal Components Analysis Options in Analyses The Value of Factor Analysis Computer Programs Discussion and Further Reading Chapter Summary Exercise References DISCRIMINANT FUNCTION ANALYSIS The Problem of Separating Groups Discrimination Using Mahalanobis Distances Canonical Discriminant Functions Tests of Significance Assumptions Allowing for Prior Probabilities of Group Membership Stepwise Discriminant Function Analysis Jackknife Classification of Individuals Assigning of Ungrouped Individuals to Groups Logistic Regression Computer Programs Discussion and Further Reading Chapter Summary Exercises References CLUSTER ANALYSIS Uses of Cluster analysis Types of Cluster Analysis Hierarchic Methods Problems of Cluster Analysis Measures of Distance Principal Components Analysis with Cluster Analysis Computer Programs Discussion and Further Reading Chapter Summary Exercises References CANONICAL CORRELATION ANALYSIS Generalizing a Multiple Regression Analysis Procedure for a Canonical Correlation Analysis Tests of Significance Interpreting Canonical Variates Computer Programs Further Reading Chapter Summary Exercise References MULTIDIMENSIONAL SCALING Constructing a Map from a Distance Matrix Procedure for Multidimensional Scaling Computer Programs Further Reading Chapter Summary Exercise References ORDINATION The Ordination Problem Principal Components Analysis Principal Coordinates Analysis Multidimensional Scaling Correspondence Analysis Comparison of Ordination Methods Computer Programs Further Reading Chapter Summary Exercise References EPILOGUE The Next Step Some General Reminders Missing Values References APPENDIX Computer Packages for Multivariate Analyses References