Student Friendly Statistics
PREFACE TO THE INSTRUCTORThe purpose of this text is to make the major statistics accessible to all students while revealing the depth of the statistics and their meaning within research design. The statistics are explained completely, with simple terms and an interactive style. The main statistics concepts treated are the logic of statistical inference, the t-test, single-factor and multifactor analysis of variance (including interaction), linear regression and correlation, and chi-square. Because the tools of ANOVA, interaction, and correlation/regression are extremely important; I provide a foundation for them in the first parts of the book that is solid yet brief enough to allow major coverage of these advanced statistics in a semester course. Relations to experimental design are covered in order to increase the meaningfulness of statistics.Any instructor knows that consistent effort is needed to learn statistics and to individuate them from each other. To get this idea across, I have developed the mountain-climbing journey metaphor illustrated. Each statistic is pictured as a mountain that can be unpacked into more basic concepts. The hikers represent student progress along the journey. A pair of hikers indicates the student's position as each chapter begins, and the spacing between hikers corresponds to chapter length. Initial chapters are short and easy for a gradual warm-up, followed by longer chapters as the material becomes more advanced. The journey metaphor also helps students learn to individuate statistics, an issue that is emphasized in the last chapter, as students look back at their path and the differences between statistics.The exposition of the statistics is motivated by the psychologies of perception, cognition, and learning. The goal is to help students establish a core understanding that will be maintained in memory. All statistics are taught in the context of tables that break the computations into meaningful pieces. Page layouts are designed to group related ideas and figures, and to facilitate student interaction. Definitional formulas are used because they are meaningful; opaque computational formulas are eschewed because they are unnecessary in this age of computers. Major ideas common to most statistics are reinforced throughout the book.Because context aids learning, the statistics are presented within meaningful research contexts. To simplify exposition, the most prototypical forms of statistics are emphasized. Other important distinctions are covered, but after the main exposition.Active learning is encouraged throughout. You are invited to have students copy activity pages and hand them in for checking. Encourage students to copy formulas and tables on their own paper (the tight spacing of this text was dictated by economics). Overheads can be found at the Internet address that follows.This book is designed to be covered sequentially. However, it is possible to omit any of the more advanced chapters without loss of continuity. (These are Chapters 9 and 10 on multilevel and multifactor ANOVA, respectively, Chapter 11 on regression and correlation, and Chapter 12 on chi-square).I thank the many students who have found statistics rewarding to learn. And I am happy to acknowledge the helpful comments and advice on this text from Madeline Altabe, Judy Bourgeois-Smith, Jacquelyn Fresenius, Jennifer Kisamore, Evelyn Mott, and Doug Rohrer. I am deeply indebted to Tracy Krueger and Jennifer Perone for writing the Exercises. And I thank Allison Westlake for finding a great cover, and Anne Mattson and the PRD Group for being so helpful in the production of this book. I am sure students will find that I've made some small errors, but (hopefully!) no large ones.Thomas SanockiEmail: Sanocki@chuma.cas.usf   PREFACE TO THE STUDENTLearning statistics is a journey that will require steady effort, but that will reward you and sometimes even surprise you pleasantly. This prefactory chapter provides a brief introduction to your journey, including tips for making the journey more pleasant. Statistics does not have to be a scary 'subject, as you will learn.To help you maintain perspective along your journey, a "trail map" will be provided at the start of each chapter. It provides important landmarks. For example, the first large goal—the t-test—is represented by "Mount t." It is built on smaller concepts that we will take one step at a time. The placement of the hikers at the far left indicates that you are just beginning your journey.   WHY DO STATISTICS SEEM DIFFICULT?It helps to know what you are up against. Contrary to popular belief, behavioral statistics are not difficult because of the mathematics. Good teachers reduce mathematics for students of behavioral science. In this text, the math has been minimized. All concepts are taught in terms of their meaning first, and only simple arithmetic will be required. The real problem with statistics, in my view, is that statistics are very abstract and unlike anything you have met or even thought about previously. They are strange for your brain! This means that they are difficult to learn and very easy to forget.How do you get to know a strange, different thing? The best way to get to know anything is to spend time with it, interact with it, and even play with it. Gradually, it can become familiar, even friendly. In the case of statistics, doing the statistics-doing the step-by-step calculation procedures—is an excellent way to get to know them. At the same time, remember that statistics are also meaningful, even deeply meaningful. While doing calculations, think about their meaning and act on their meaning. Write their meanings in your own words in spaces in the book or on your own paper. All of the procedures you will do in this book are designed to make their meaning apparent.   THINGS TO LOOK FORYour trail is well marked with signs. Look for them:Important Definitions: These will be highlighted in boxes. Especially important idea units are set off by CONCEPTUALIZATION AHEAD and CONCEPT DONE markings.Other concepts will be designated by a simple boldface title or italics. These often are important linking concepts. You will also see white spaces; these are great places to summarize your thinking in your own words.Important terms are listed at the end of each chapter. Learn by actively summarizing their meaning. Exercises are also provided. No better way to learn!   THE MOST IMPORTANT FEATURE OF THIS BOOKAll of the features of this book pale in comparison to the most important feature—you! You will produce learning by interacting with this book. A substantial body of research on learning and memory indicates that self-relatedness adds greatly to memory. This is vitally important when you are learning something strange like statistics. The more you make the concepts meaningful to yourself, the better you will remember statistics. That means writing in this book, and on your own paper, using your own words to rephrase definitions, and doing calculations while thinking about what they mean.The content of this book has been formatted to make it easier for you to integrate concepts. As much as possible, related text, figures, and tables have been grouped together on the same pages. This allows you to focus on meaning rather than looking for figures. What is critical is that you are creating a memory image, or an episodic trace (a record of your experience), that will become part of your memory. If the memory is meaningful and well integrated, it will last longer and be easier to recall later. Careful, active study of the concepts will be rewarded with better recall at testing time and in the future when you need to refer back to this book. Note that even advanced statisticians often return to their old textbooks. Their memory needs refreshing too. What a good course and text on statistics should do is make it easy for you to return to your text years later and, after some review, to remember what you had learned.   A PREVIEW OF WHAT IS AHEADYour journey will begin with a steady "climb" involving smaller concepts that build on each other. They climax at your first major statistic, the t-test (Mount t). The t-test was quite an intellectual feat when it was created, and your comprehension of it will also be worthy of praise. Once you understand the t-test, you will gain a new perspective on statistics. On the next part of your journey, you will cross a convenient bridge to an important series of statistics called analysis of variance (ANOVA). The most outstanding of these allows you to examine the multidimensional (multicausal) nature of behavior—multifactor ANOVA.Next will be statistics that allow you to examine relations between variables, including complex relations involving multiple variables (correlation, regression, and multiple regression). The last statistic, chi-square, allows you to examine categories of behavior. Your introduction to statistics will be complete in the last chapter, when you will look back and gain perspective: This chapter compares statistics and begins to handle the question "How do I choose a statistic?"   THE STEP-BY-STEP PROCEDURESEach statistic taught can be calculated with a step-by-step procedure. You can find these procedures on the following pages:Standard Deviation p. 28t-test p.72Analysis of Variance (one factor) p. 108Analysis of Variance (multi-factor) p. 138Correlation/Regression p.170Chi-Square p. 178   GET PROVISIONS FIRSTMy last advice is to prepare yourself each time you travel on this journey. Your brain will learn much more efficiently if it is relaxed and well nourished. If statistics or test taking makes you anxious, the Appendix provides helpful tips. If this book's type seems small, try an inexpensive pair of reading lenses from a local drugstore-they can make interactions with this book more pleasant. Successful interactions will also generate good feelings, and there are plenty of those ahead.You will need two provisions: a simple calculator and a pencil. Happy trails!