1.1 Getting the Most from the Book
The most important advice I can give to a student at the start of a course on any topic is the same:
Aim for understanding!
If you understand the material, you will remember it, and you will find connections to other things you know about it. If you understand the material, you will earn a good grade in the course (the reverse is not always true!). In the case of statistics, you will find that a basic understanding of statistical concepts and procedures is useful. If you never take another course in statistics, you will forget the procedures and all the details. However, if you achieve an understanding of the aims of descriptive statistics and the logic of the core inferential procedures covered in this book, you will be able to recognize and make sense of the many encounters with statistics you will have in your lifetime. Statistics will make sense to you.
Let me be specific about what my goals are for students in the introductory course that I teach. Students will learn many procedures during the course, but unless they have future occasions to continue to use those procedures, they will forget the procedures quickly. I know that, and it doesn’t really bother me. I want my students to understand three things at the end of the course: First, I want them to know the basics of descriptive statistics. I want them to know how to construct and read a table and graph of the distribution of a variable. And I want them to know the basic statistics of mean, median, mode, range, variance, and standard deviation. I suspect you already are well on the way to having this first objective under your belt!
Second, I want my students to understand that the process of drawing general conclusions from a single set of observations is a risky business because no sample is a perfect reflection of the population from which it was drawn. Therefore, the process of drawing general conclusions requires the ability to compute probabilities, and the fundamental goal of “inferential statistics” is all about how we determine and use probabilities in our inference-making.
Third, I want my students to develop a good understanding of the logic of the four major inferential procedures in conventional statistical applications: namely, hypothesis testing, confidence intervals, effect size estimation, and power.
Goal number 1 is relatively easy. Goals 2 and 3 require the hard work. But if you have achieved these goals by the conclusion of your course, you will retain your understanding for your lifetime. Okay, so how do you go about understanding statistics?
Treat all material as comprehensible (because it is).
Every formula you will encounter is meaningful. Every calculation captures information, and you should expect me to explain what information each calculation gathers, how it gathers it, and therefore what the outcome of any calculation means. In my teaching, I never require students to memorize formulas but I always require them to verbalize—and understand—what the result of a calculation means.
Every procedure you will learn has an underlying logic, and your goal should be to understand the logic. Now, some procedures have what may first appear to be a weird logic! But there is always a logic.
This second bit of advice is, of course, an implication of the first piece of advice. But it seems worth making the point because many of us carry bad habits from previous experiences in math courses. Don’t let your eyes glaze over when you encounter a formula!
Be patient.
Be patient with the material and be patient with yourself. This book has a lot of new stuff for you to learn! Some of it will come easily for you, but not all of it. When you hit something frustrating, step away, take a breath, and get some help. You may need to think differently about concepts in this book than you think in other domains. Isn’t that what it means to learn?
Don’t read the book; study it.
You have already figured out this book is not a summer romance novel. You cannot expect to read this material at 300 words per minute and come away with an understanding of what you have read. You will encounter many concepts and procedures that you have never encountered before. Take it slowly. Don’t simply read, think! Verbalize the symbols. Reason through the procedures. Unpack the formulas. Do the examples and answer the self-study questions. Take whatever time you need to make sense of what you are reading . . . and ask for help if you are not able to make sense of the material.
Learn the language.
Oh, boy, there is Greek in this book! No kidding—there really is Greek in this book. Expect to see symbols like µ, 𝜎, 𝜎2, 𝛴, η2, and a couple of others. There will also be non-Greek symbols like Mx, sx, sx2, Mdn, and others. You will need to learn some new notations, and you should take the time to do so; otherwise, you will fail to make important distinctions and that will interfere with your learning. Pay close attention to the similarities and the distinctions in the symbols. For example, sx, sd, sM and sMx-My share a term, s, but differ in their subscripts. The shared term indicates some shared meaning, but the different subscripts indicate that the symbols refer to different variables. The point is that seemingly minor differences indicate important distinctions. The best way to learn the distinctions is (1) to pay close attention to the meaning of a symbol when it is introduced, and then (2) verbalize the symbol and remind yourself of its meaning each time you see the symbol again. Eventually, the connection between the symbol and its meaning will become automatic; however, until it does, take the time to verbalize and remind yourself.
Do the problems!
Ultimately, statistical procedures are applied to data. You may think you fully understand the meaning of the concepts and the logic of the procedures and how to execute the procedures, but then you are presented a description of a problem, and you discover that you have some confusion. Much of your understanding of statistics will come from doing problems because that is where you will discover and resolve any glitches in your understanding.
You will find that the problems in the book are rarely “plug and chug” where you just enter numbers into a formula and an answer happens. That’s the easy part. The tough part is setting up the problem: What, exactly, is the question to be answered? What information do I have that is relevant to helping me answer the question? What procedure is most appropriate to apply? How do I make sense of the numbers I have computed and apply the outcome back to the question I started with?
Use your resources.
You have many resources in your course. You have a knowledgeable instructor who will present the material clearly in class and answer your questions. You will have homework problems. You have this book. The book is your most complete source of information, is always available to you, and is infinitely patient with you. Use it. You have classmates who are working to learn the same material and solve the same problems, so form a group. Study groups are potentially your most valuable and enjoyable resource when learning statistics. Finally, you can also search for presentations online if you want an alternative approach to some topic you are struggling to understand. But a warning: There is a lot of misinformation out there. Not all the “experts” who produce videos know their stuff! Also, even accurate presentations can differ from this book in symbols, language, and approach to solving a particular type of problem. That can, of course, increase your confusion. One resource that is generally reliable are videos produced by the Khan Academy.
Use the learning aids available in the book.
Most chapters of the book include five instructional devices that are intended to be used in a coordinated fashion. First, most major sections of each chapter begin with one or more “Learning Question.” Pause to read the questions and get them in your head because they orient you to the key issues in the section. Second, most major sections of each chapter conclude with a box labeled “Key Takeaways.” Each Key Takeaway contains the summarized answers to the Learning Questions that began the section. If you do not understand the Key Takeaways, you need to reread the section or seek help. Third, most major sections include a “Self-Study” component consisting of several multiple-choice questions testing your understanding of the material in the section. Together, the Learning Questions, Key Takeaways, and Self-Study items for a section will keep you focused on the important points and give you feedback on your understanding.
Fourth, at the end of each chapter is a set of open-ended questions titled “Test Your Understanding.” These questions simply list the Learning Questions you encountered while studying the chapter. I strongly encourage you to try to verbalize your answers to these questions as an exercise in testing and consolidating your understanding of the chapter. Yes, this takes more time and effort than doing the multiple-choice questions of the Self-Study components, but the effort will pay off in deeper understanding of the material. Note that if you find yourself struggling with a question, simply return to the corresponding section of the chapter and re-read the Key Takeaways—better yet, reread the section and think some more about the question!
Finally, you will see that each chapter ends with a set of Exercises. These problems are an excellent device to push your understanding of the material in the chapter and clear up any confusion you may still have. Your instructor has a full set of elaborated answers to the exercises.