Chapter 0

Preface

When my students began requesting that I make my online text available on their tablets, I thought I could make a few tweaks to the existing pages and they would load just fine. I soon found out differently. As I began reading and understanding about HTML 5, it quickly became apparent that a few tweaks simply wouldn't do. When I created the 2nd edition of the text in 2001, I used what I thought was state of the art HTML coding. When I began researching HTML 5, such coding (frames) was referred to as *grandpa's HTML*
. Ouch.

In late 2015 I was asked by Sage Publishers to write an entry for a forthcoming statistical encyclopedia on discriminant function analysis. When I looked at the work I had done earlier for the multivariate text, I was disappointed, both in the old format and the content. In writing the entry, I was very limited in the content that I could include, so I decided that I could update my text and include much more detailed information on the topic.

I will give myself credit for semantic coding the second edition of the text using XML. The semantic codes in HTML 5 are different, of course, but transformations are fairly straightforward using XSL. I didn't foresee tablets and the changes they would bring to the table, however. My mind boggles at their potential. The opportunity exists to make a book that is truly interactive, where exercises, audio, and video are available in a single package. My online course programs and existing text can be joined into a MOOC.

While technology can enhance the learning experience of the student, it cannot totally replace the human interaction necessary for student learning. When I attempted to make my online statistics course more *learning focused*
, I found that I had to spend more of my time sharing my expertise with students. I wish I had the time to work with many more students, but this edition of the text is my attempt to share what I can with the widest possible audience.

Please consider the third web edition of this text as a work in progress. I have a vision for what I would like it to become, but it will be a long road to get there. I welcome comments.

The book, *Multivariate Statistics: Concepts, Models, and Applications*, is an extension of my web text, *Introductory Statistics: Concepts, Models, and Applications*. An understanding of the concepts presented in the introductory text is necessary to grasp the concepts presented in this text. In my one-semester graduate course, I spend the first third of the course reviewing the material in the introductory text. The book is designed for the last two-thirds of a one-semester course in multivariate statistics for first year graduate or advanced undergraduates.

It has been said that some texts are written to impress one's colleagues and others are written for students. This one is written for students. It is neither a mathematical treatise nor a cookbook. Instead of complicated mathematical proofs I have attempted to write a book about mathematical ideas. I have substituted examples for proofs and require that the reader "believe!" on more than one occasion. The result is a text that can be understood by students. A grasp of the fundamental ideas presented in this text will prepare the student for a much more thorough treatment of multivariate statistics in a later course.

In some ways I hesitate to call this a "multivariate" text. Univariate statistical methods are expanded gradually, first thoroughly exploring bivariate statistical methods (linear transformations with two variables, multiple regression with two independent variables) and culminating with multiple regression models. Analysis of Variance is approached as a special case of multiple regression. The goal is to provide a path from the simple case leading to the complex. The complex case is rarely presented in this text. The issues surrounding the complex case, however, will be familiar to any reader who masters this material.

In the summer of 1996 I attended a four-week multivariate statistics course in Ann Arbor, Michigan. The textbook used for the course was Johnson and Wickren's (1992) Multivariate Statistics. I watched as my fellow graduate students (some of the best from around the world) struggled with matrix theory and operations. I knew that as much as I would like to teach my graduate statistics course in a similar manner, most of my students simply did not have the mathematical background to deal with a course of this level of difficulty. This text is an attempt to explain multivariate statistical concepts in a way that is accessible to graduate students with a background of a single undergraduate statistics course.

This is not an argument against a matrix approach to multivariate statistics. In many ways, I believe that only through matrix operations can the interrelationships between the various multivariate methods be truly appreciated. My goal is to present the material in a manner such that the student can develop a feeling about what and how the various multivariate statistical methods achieve their goal. My hope is that I can treat the material in such a way that the student who wants to go on is better prepared for the experience.

My guess is that students will use this text in an unofficial capacity more often than an official one. If so, I have partially succeeded in my goal.

- An emphasis on mathematical concepts.
- Use of interactive graphics to illustrate multivariate concepts. For example, by rotating a two-dimensional scatter plot and examining the effect on the variances of the resulting variables, the idea of what eigenvectors and eigenvalues mean becomes clear. The ability to view a three-dimensional scatter plot with a plane drawn through the points illustrates conceptually how multiple regression models work.
- Copious examples of the use of SPSS v10.0 to do statistical procedures. It is my intention to eventually make this a dynamic text, allowing the user to specify what statistical package is available and generating a text designed for that specific statistical package.
- There are numerous small assignments associated with each chapter. Each assignment is designed to illustrate a single concept. The assignments are individualized for each student and presented as web pages. Active server programs grade the assignments and return an answer key.

Throughout the text it is often necessary to document the procedure to compute a statistic using the SPSS statistical package. For example, in the following screen, the user has clicked on

"Analyze", followed by "Regression", and then "Linear". This sequence of clicks will be denoted as Analyze/Regression/ in this text.

To understand the relationship between statistics and the scientific method and how it applies to psychology and the behavioral sciences.

To be able to read and understand the statistics presented in the professional literature.

To be able to calculate and communicate statistical information to others.

Throughout the book various icons or pictures will be placed in the left margin. They should be loosely interpreted as follows:

A Thought Question

An SPSS Data File

A Note to the Teacher

A Note to the Student

David Stockburger has been teaching undergraduate and graduate statistics for twenty-six years as a professor of Psychology at Southwest Missouri State University. He earned his Ph.D. degree at the Ohio State University in 1975 with a major area of Mathematical Psychology and a minor area of Statistics. He has been involved during that time in the application of technology to education, specifically statistics education, and has presented papers and written numerous articles on the topic. One of his proudest accomplishments is the faculty sponsorship of a student-run Bulletin Board System for six years before the web became a common appliance. When off-campus, he resides with his wife in Springfield, Missouri and enjoys golf, tennis, camping, traveling, and developing computer software in his leisure time.

I wrote this book for a number of reasons, the most important one being my students. As I taught over a period of years, my approach to teaching introductory statistics began to deviate more and more from traditional textbooks. All too often students would come up to me and say that they seemed to understand the material in class, thought they took good notes, but when they got home the notes didn't seem to make much sense. Because the textbook I was using didn't seem to help much, I wrote this book. I took my lectures, added some documentation, and stirred everything with a word processor with this book as the result.

This book is dedicated to all the students I have had over the years. Some made me think about the material in ways that I had not previously done, questioning the very basis of what this course was all about. Others were a different challenge in terms of how I could explain what I knew and understood in a manner in which they could comprehend. All have had an impact in one way or another.

Three students had a more direct input into the book and deserve special mention. Eve Shellenberger, an ex-English teacher, earned many quarters discovering various errors in earlier editions of the text. Craig Shealy took his editorial pencil to a very early draft and improved the quality greatly. Wendy Hoyt has corrected many errors in the Web Edition. To all I am especially grateful.

I wish to thank my former dean, Dr. Jim Layton, and my department head, Dr. Fred Maxwell, both of whom found the necessary funds for hardware and software acquisition to enable this project. Recently I have received funds from the Southwest Missouri State University academic vice president, Dr. Bruno Schmidt, to assist me in the transfer of this text from paper to Web format.

The following books are placed in the public domain and may be copied with the following restrictions:

The restrictions must be posted with the work. No profit may be made from the works. If any portion of the materials is used I must appear as an author. If over fifty percent of the completed work is from the following sources I must appear as first author.