A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate distributions from first principles. After a chapter on the multivariate normal distribution reviewing the classical parametric theory, methods of estimation are explored using the plug-in principles as well as maximum likelihood. Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests. Finally, the powerful self-consistency principle is used to introduce principal components as a method of approximation, rounded off by a chapter on finite mixture analysis.

Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.

Get up-to-speed on the latest methods of multivariate statistics Multivariate statistical methods provide a powerful tool for analyzing data when observations are taken over a period of time on the same subject. With the advent of fast and efficient computers and the availability of computer packages such as S-plus and SAS, multivariate methods once too complex to tackle are now within reach of most researchers and data analysts. With an emphasis on computing techniques in combination with a full understanding of the mathematics behind the methods, Methods of Multivariate Statistics offers an up-to-date account of multivariate methods. Focusing on the maximum likelihood method for estimation, testing of hypotheses, and "profile analysis," this book offers comprehensive discussions of commonly encountered multivariate data and also covers some practical and important problems lacking in other texts. These include: * Missing at-random observations * "Growth Curve Models" and multivariate one-sided tests applicable in pharmaceutical and medical trials * Bootstrap methods * Principal component method for predicting a multivariate response vector * Outlier detection and handling inference when covariance is singular With clear chapter introductions and numerous problem sets, Methods of Multivariate Statistics meets every statistician's need for a comprehensive investigation of the latest methods in multivariate statistics.

Select the Optimal Model for Interpreting Multivariate DataIntroduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedu

AN UPDATED GUIDE TO STATISTICAL MODELING TECHNIQUES USED IN THE SOCIAL AND NATURAL SCIENCES This revised and updated second edition of Applied Univariate, Bivariate, and Multivariate Statistics: Understanding Statistics for Social and Natural Scientists, with Applications in SPSS and R contains an accessible introduction to statistical modeling techniques commonly used in the social and natural sciences. The text offers a blend of statistical theory and methodology and reviews both the technical and theoretical aspects of good data analysis. Featuring applied resources at various levels, the book includes statistical techniques using software packages such as R and SPSS®. To promote a more in-depth interpretation of statistical techniques across the sciences, the book surveys some of the technical arguments underlying formulas and equations. The second edition has been designed to be more approachable by minimizing theoretical or technical jargon and maximizing conceptual understanding with easy-to-apply software examples. This important text: Offers demonstrations of statistical techniques using software packages such as R and SPSS® Contains examples of hypothetical and real data with statistical analyses Provides historical and philosophical insights into many of the techniques used in modern science Includes a companion website that features further instructional details, additional data sets, and solutions to selected exercises Written for students of social and applied sciences, Applied Univariate, Bivariate, and Multivariate Statistics, Second Edition offers a thorough introduction to the world of statistical modeling techniques in the sciences.

Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.

This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear multivariate models and exploratory data analysis techniques. Each chapter contains the development of basic theoretical results with numerous applications illustrated using examples from the social and behavioral sciences, and other disciplines. All examples are analyzed using SAS for Windows Version 8.0.

A practical source for performing essential statistical analyses and data management tasks in R Univariate, Bivariate, and Multivariate Statistics Using R offers a practical and very user-friendly introduction to the use of R software that covers a range of statistical methods featured in data analysis and data science. The author— a noted expert in quantitative teaching —has written a quick go-to reference for performing essential statistical analyses and data management tasks in R. Requiring only minimal prior knowledge, the book introduces concepts needed for an immediate yet clear understanding of statistical concepts essential to interpreting software output. The author explores univariate, bivariate, and multivariate statistical methods, as well as select nonparametric tests. Altogether a hands-on manual on the applied statistics and essential R computing capabilities needed to write theses, dissertations, as well as research publications. The book is comprehensive in its coverage of univariate through to multivariate procedures, while serving as a friendly and gentle introduction to R software for the newcomer. This important resource: Offers an introductory, concise guide to the computational tools that are useful for making sense out of data using R statistical software Provides a resource for students and professionals in the social, behavioral, and natural sciences Puts the emphasis on the computational tools used in the discovery of empirical patterns Features a variety of popular statistical analyses and data management tasks that can be immediately and quickly applied as needed to research projects Shows how to apply statistical analysis using R to data sets in order to get started quickly performing essential tasks in data analysis and data science Written for students, professionals, and researchers primarily in the social, behavioral, and natural sciences, Univariate, Bivariate, and Multivariate Statistics Using R offers an easy-to-use guide for performing data analysis fast, with an emphasis on drawing conclusions from empirical observations. The book can also serve as a primary or secondary textbook for courses in data analysis or data science, or others in which quantitative methods are featured.

Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.