Multivariate Statistical Methods

A First Course

George A. Marcoulides, Scott L. Hershberger

• Publisher: Psychology Press
• Year: 2014
• eBook ISBN: 9781317778547
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

Multivariate statistics refer to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two variables or measures can loosely be considered a multivariate statistical analysis.

An introductory text for students learning multivariate statistical methods for the first time, this book keeps mathematical details to a minimum while conveying the basic principles. One of the principal strategies used throughout the book--in addition to the presentation of actual data analyses--is pointing out the analogy between a common univariate statistical technique and the corresponding multivariate method. Many computer examples--drawing on SAS software --are used as demonstrations.

Throughout the book, the computer is used as an adjunct to the presentation of a multivariate statistical method in an empirically oriented approach. Basically, the model adopted in this book is to first present the theory of a multivariate statistical method along with the basic mathematical computations necessary for the analysis of data. Subsequently, a real world problem is discussed and an example data set is provided for analysis. Throughout the presentation and discussion of a method, many references are made to the computer, output are explained, and exercises and examples with real data are included.

CHAPTER ONE

Introduction

Multivariate statistics refers to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two variables or measures can loosely be considered a multivariate statistical analysis. For example, researchers (e.g., Marcoulides & Heck, 1993) are interested in learning how organizational culture can play a key role in determining levels of organizational performance. A common hypothesis about this role suggests that if an organization possesses “strong culture” by exhibiting a well-integrated and effective set of specific values, beliefs, and behavior patterns, then it will perform at a higher level of productivity. Multivariate statistics are required to study the multiple relationships among these variables adequately and obtain a more complete understanding for decision making.

This admittedly rather loose introduction to the subject matter of this book is intentionally a very broad one. It would include, for example, multiple regression analysis, which involves the study of the relationship between one dependent variable and several independent variables. But these topics are almost always covered in an upper division first-semester introductory statistics course. And yet, multiple regression analysis will serve as an excellent introduction to the “true” multivariate technique of canonical correlation commonly used to examine relationships between several dependent and independent variables.

Pointing out the analogy between a common univariate statistical technique and the corresponding multivariate method is one of the principal didactic strategies used throughout this book. Besides the drawing of analogies, actual data analyses are presented using the computer. The book is not intended to be particularly comprehensive; rather, the intention is to keep mathematical details to a minimum while conveying the basic principles of multivariate statistical methods.

One way to articulate the rationale for the mode of presentation is to draw a distinction between mathematical statisticians, like Hotelling or Wilks, who gave birth to the field of multivariate statistics, and those who focus on methods for data analysis and the interpretation of results. Possibly the distinction between Pythagoreans (mathematicians) and Archimedeans (scientists) is useful, as long as one does not assume that Pythagoreans are not interested in data analysis and Archimedeans are not interested in contributing to the mathematical foundations of their discipline. Therefore, this book is primarily written for individuals concerned with data analysis, although true expertise requires familiarity with both approaches. But rigorous mathematical proofs and derivatives are eliminated. Only chapter 2 is devoted to providing the necessary background in matrix algebra for understanding the multivariate techniques. The reader who is interested in pursuing a more mathematical approach to multivariate statistics should consult such books as Morrison (1991) and Johnson and Wichern (1988).

THE IMPACT OF COMPUTERS

One of the main reasons that multivariate statistical methods have gained popularity is due to the availability of statistical packages to perform the laborious calculations. The most popular statistical packages on the market are the Statistical Analysis System (SAS Institute, Inc., 1979, 1989a, 1989b), Statistical Packages for the Social Sciences (SPSS, Inc., 1990), and Biomedical Computer Programs: P Series¹ (Dixon, 1990a, 1990b). These three packages are available for mainframe computers and microcomputers (basically IBM-compatible and Macintosh computers). The microcomputer versions tend to have a more “user-friendly” environment feel in terms of setup, but the outputs match those of the mainframe versions of the programs.

Originally the three packages had very distinctive users. SAS was perceived as most closely tied to statistics, and was heavily used for agricultural and economic data analysis. SPSS was for social scientists, while BMDP was for biomedical applications. Nowadays, these three packages do not have distinct users, in part because of their similar capabilities and flavor. In fact, at times output from these packages is so similar that only seasoned users are able to distinguish between them. For these reasons the three different statistical packages are not stressed in ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1 Introduction
• 2 Basic Matrix Algebra
• 3 The Multivariate Normal Distribution and Tests of Significance
• 4 Factorial Multivariate Analysis of Variance
• 5 Discriminant Analysis
• 6 Canonical Correlation
• 7 Principal Components and Factor Analysis
• 8 Confirmatory Factor Analysis and Structural Equation Modeling
• Appendix A
• Appendix B
• References
• Author Index
• Subject Index