Multivariate Statistical Methods: A Primer, Third Edition

Multivariate methods are now widely used in the quantitative sciences as well as in statistics because of the ready availability of computer packages for performing the calculations. While access to suitable computer software is essential to using multivariate methods, using the software still requires a working knowledge of these methods and how they can be used.

Multivariate Statistical Methods: A Primer, Third Edition introduces these methods and provides a general overview of the techniques without overwhelming you with comprehensive details. This thoroughly revised, updated edition of a best-selling introductory text retains the author's trademark clear, concise style but includes a range of new material, new exercises, and supporting materials on the Web.

New in the Third Edition:

Fully updated references

Additional examples and exercises from the social and environmental sciences

A comparison of the various statistical software packages, including Stata, Statistica, SAS Minitab, and Genstat, particularly in terms of their ease of use by beginners

In his efforts to produce a book that is as short as possible and that enables you to begin to use multivariate methods in an intelligent manner, the author has produced a succinct and handy reference. With updated information on multivariate analyses, new examples using the latest software, and updated references, this book provides a timely introduction to useful tools for statistical analysis.

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