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More About This Textbook
Overview
This unique book capitalizes on a successful approach of using definitional formulas to emphasize concepts of statistics, rather than rote memorization. This conceptual approach constantly reminds readers of the logic behind what they are learning. Procedures are taught verbally, numerically, and visually, which appeals to a variety of users with different learning styles. Focusing on understanding, the book emphasizes the intuitive, deemphasizes the mathematical, and explains everything in clear, simple language—with a large number of practice problems. For those trying to master statistics, as well as reading and understanding research articles.
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Table of Contents
1. Displaying the Order in a Group of Numbers.
2. The Mean, Variance, Standard Deviation, and Z Scores.
3. Correlation and Prediction.
4. Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample.
5. Introduction to Hypothesis Testing.
6. Hypothesis Testing and the Means of Samples.
7. Making Sense of Statistical Significance: Decision Errors, Effect Size, and Statistical Power.
8. Introduction to the t Test.
9. The t Test for Independent means.
10. Introduction to the Analysis of Variance.
11. ChiSquare Tests and Strategies When Population Distributions Are Not Normal.
12. Making Sense of Advanced Statistical Procedures and Research Articles.
Preface
TO THE INSTRUCTOR
The heart of this book was written over a summer in a small apartment near the Place Saint Ferdinand, having been outlined in nearby cafes and on walks in the Bois de Boulogne. It is based on our 40 years of experience teaching, researching, and writing. We believe that this book is as different from the conventional lot of statistics books as Paris is from Calcutta, yet still comfortable and stimulating to the longsuffering community of statistics instructors.
The approach embodied in this text has been developed during our combined 40 years of successful teaching—successful not only in the sense that students have consistently rated the course (a statistics course, remember) as a highlight of their undergraduate years, but also in the sense that students come back to us later saying, "I was lightyears ahead of my fellow graduate students because of your course," or "Even though I don't do research, your course has really helped me understand statistics that I read about in my field."
In this third edition of this Brief Course we have tried to maintain those things about the book that have been especially appreciated, while reworking the text to take into account the feedback we have received, our own experiences, and advances and changes in the field. We have also added new pedagogical features to make the book even more accessible for students. However, before turning to the third edition, we want to reiterate some comments. we made in the first edition about how this book from the beginning has been quite different from other statistics texts.
WHAT WE HAVE DONE DIFFERENTLY
We continue to do whatthe best of the newer books are already doing well: emphasizing the intuitive, deemphasizing the mathematical, and explaining everything in direct, simple language. But what we have done differs from these other books in 10 key respects.
1. The definitional formulas are brought to center stage because they provide a concise symbolic summary of the logic of each particular procedure. All our explanations, examples, practice problems, and test bank items are based on these definitional formulas. (The amount of data to be processed in our practice problems and test items are reduced appropriately to keep computations manageable.)
Why this approach? To date, statistics texts have failed to adjust to technologic reality. What is important is not that the students learn to calculate a correlation coefficient with a large data set—computers can do that for them. What is important is that students work problems in a way that they remain constantly aware of the underlying logic of what they are doing. Consider the population variance—the average of the squared deviations from the mean. This concept is immediately clear from the definitional formula (once the student is used to the symbols)
Teaching computational formulas today is an anachronism. Researchers do their statistics on computers now. At the same time, the use of statistical software makes the understanding of the basic principles, as they are symbolically expressed in the definitional formula, more important than ever. Students still need to work lots of problems by hand to learn the material. But they need to work them using the definitional formulas that reinforce the concepts, not using the computational formulas that obscure them. Those formulas once made some sense as timesavers for researchers who had to work with large data sets by hand, but they were always poor teaching tools. (Because some instructors may feel naked without them, we still provide the computational formulas, usually in a brief footnote, at the point in the chapter where they would traditionally have been introduced.)
2. Each procedure is taught both verbally and numerically—and usually visually as well.
In fact, when we introduce every formula, it has attached to it a concise statement of the formula in words. Typically, each example lays out the procedures in workedout formulas, in words (often with a list of steps), and illustrated with an easytograsp figure. Practice exercises and test bank items, in turn, require the student to calculate results, write a short explanation in layperson's language of what they have done, and make a sketch (for example, of the distributions involved in a t test). The chapter material completely prepares the student for these kinds of practice problems and test questions.
It is our repeated experience that these different ways of expressing an idea are crucial for permanently establishing a concept in a student's mind. Many students in the social and behavioral sciences are more at ease with words than with numbers. In fact, some have a positive fear of all mathematics. Writing the formula in words and providing the laylanguage explanation gives them an opportunity to do what they do best.
3. A main goal of any introductory statistics course in the social and behavioral sciences is to prepare students to read research articles. The way a procedure such as a t test or chisquare is described in a research article is often quite different from what the student expects from the standard textbook discussions. Therefore, as this book teaches a statistical method, it also gives examples of how that method is reported in journal articles. And we don't just leave it there. The practice problems and test bank items also include excerpts from journal articles for the student to explain.
4. The book is unusually uptodate. For some reason, most introductory statistics textbooks read as if they were written in the 1950s. The basics are still the basics, but statisticians and researchers think far more subtly about those basics now. Today, the basics are undergirded by a new appreciation of issues like effect size, power, the accumulation of results through metaanalysis, the critical role of models, and a whole host of new orientations arising from the central role of the computer in statistical analyses. We are much engaged in the latest developments in statistical theory and application, and this book reflects that engagement. For example, we devote an entire early chapter to effect size and power and then return to these topics as we teach each technique. Furthermore, we discuss how to handle situations in which assumptions are violated, and we cover data transformations (this widely used approach is easily accessible to introductory students but is rarely mentioned in current introductory texts).
5. We capitalize on the students' motivations. We do this in two ways. First, our examples, while attempting to represent the diversity of social and behavioral science research, emphasize topics or populations that students seem to find most interesting. The very first example is from a real study in which 151 students in their first week of an introductory statistics class rate how much stress they feel they are under. Also, our examples continually emphasize the usefulness of statistical methods and ideas as tools in the research process, never allowing students to feel that what they are learning is theory for the sake of theory.
Second, we have worked to make the book extremely straightforward and systematic in its explanation of basic concepts so that students can have frequent "aha!" experiences. Such experiences bolster selfconfidence and motivate further learning. It is quite inspiring to us to see even fairly modest students glow from having mastered some concept like negative correlation or the distinction between failing to reject the null hypothesis and supporting the null hypothesis. At the same time, we do not constantly remind them how greatly oversimplified we have made things, as some books do.
6. We emphasize statistical methods as a living, growing field of research. Each chapter includes one or more "boxes" about famous statisticians or interesting sidelights. The goal is for students to see statistical methods as human efforts to make sense out of the jumble of numbers generated by a research study; to see that statistics are not "given" by nature, not infallible, not perfect descriptions of the events they try to describe but rather constitute a language that is constantly improving through the careful thought of those who use it. We hope that this orientation will help them maintain a questioning, alert attitude as students and later as professionals.
7. The final chapter looks at advanced procedures without actually teaching them in detail. It explains in simple terms how to make sense out of these statistics when they are encountered in research articles. Most research articles today use methods such as analysis of covariance, multivariate analysis of variance, hierarchical multiple regression, factor analysis, or structural equation modeling. Students completing the ordinary introductory statistics course are illequipped to comprehend most of the articles they must read to prepare a paper or study a course topic in further depth. This chapter makes use of the basics that students have just learned (along with extensive excerpts from current research articles) to give a rudimentary understanding of these advanced procedures. This chapter also serves as a reference guide that students can keep and use in the future when reading such articles.
8. The accompanying Student's Study Guide and Computer Workbook focuses on mastering concepts and also includes instructions and examples for working problems using a computer. Most study guides focus on plugging numbers into formulas and memorizing rules (which is consistent with the emphasis of the textbooks they accompany). For each chapter, our Student's Study Guide and Computer Workbook provides learning objectives, a detailed chapter outline, the chapter's formulas (with all symbols defined), and summaries of steps of conducting each procedure covered in the chapter, plus a set of selftests, including multiplechoice, fillin, and problem/essay questions. In addition, for each procedure covered in the chapter, the study guide furnishes a thorough outline for writing an essay explaining the procedure to a person who has never had a course in statistics (a task they are frequently given in the practice problems and test bank items).
Also, our Student's Study Guide and Computer Workbook provides the needed support for teaching students to conduct statistical analyses on the computer. First, there is a special appendix on getting started with SPSS. Then, in each chapter corresponding to the text chapters, there is a section showing in detail how to carry out the chapter's procedures with SPSS. (These sections include stepbystep instructions, examples, and illustrations of how each menu and each output appears on the screen.) There are also special activities for using the computer to strengthen understanding. As far as we know, no other statistics textbook package provides this much depth of explanation.
9. We have written an Instructor's Manual that really helps teach the course. The manual begins with a chapter summarizing what we have gleaned from our own teaching experience and the research literature on effectiveness in college teaching. The next chapter discusses alternative organizations of the course, including tables of possible schedules and a sample syllabus. Then each chapter, corresponding to the text chapters, provides full lecture outlines and additional workedout examples not found in the text (in a form suitable for copying onto transparencies or for student handouts). These workedout examples are especially useful to new instructors or those using our book for the first time, since creating good examples is one of the most difficult parts of preparing statistics lectures.
10. Our Test Bank section of the Instructor's Manual makes preparing good exams easy. We supply approximately 40 multiplechoice, 25 fillin, and 10 to 12 problem/essay questions for each chapter. Considering that the emphasis of the course is so conceptual, the multiplechoice questions will be particularly useful for those of you who do not have the resources to grade essays. This supplement also includes computational answers to each textbook chapter's practice problems that are not given in the text. (The textbook provides answers to selected practice problems, including at least one example answer to an essaytype question for each chapter.)
ABOUT THIS BRIEF COURSE
We were thrilled by the enthusiastic response of instructors and students to the first, second, and third editions of our Statistics for Psychology (Aron & Aron, 1994, 1999, 2003), as well as the positive comments of reviewers, including the most encouraging evaluation in Contemporary Psychology (Bourgeois, 1997).
This Brief Course was our answer to the many requests we received from instructors and students for a textbook usipg our approach that is (a) more general in its focus than psychology alone and (b) shorter, to accommodate less comprehensive courses. Of course, we tried to retain all the qualities that endeared the original to our readers. At the same time, the Brief Course was not a cosmetic revision. The broadening of focus meant using examples from the entire range of the social and behavioral sciences, from anthropology to political science. Most important, the broadening informed the relative emphasis (and inclusion) of different topics and the tenor of the discussion of these topics. The shortening was also dramatic: This Brief Course is substantially shorter than the original, making it quite feasible to do the whole book, even in a quarterlength course.
INFLUENCES ON THE THIRD EDITION
We did the revision for the third edition in New York. We hope that this has not resulted in a loss of whatever romance the first edition gained from being written in Paris. We have also added an author to the book: Drawing on his experience using earlier editions of the book, Elliot Coups has joined us in developing this new edition of the text. As you will see, we have made many exciting enhancements in this third edition.
This revision is enriched by what we learned teaching with the first and second editions and by what we learned from the many instructors who have written to us about their experiences using the book. This revision is also informed by our own use of statistical methods. The last several years have been quite productive for all of us in our own research programs. Our recent research endeavors have focused on diverse topics in personality, social, and health psychology, including the social neuroscience of romantic attraction, childhood roots of adult experience, and health behaviors among cancer survivors. Perhaps particularly useful has been that during much of the last few years, one of us (A. A.) served as an associate editor for the Journal of Personality and Social Psychology. This has kept us in touch with how the best researchers are using statistics (as well as how reviewers rate their colleagues' use of statistics). In addition to reworking the book to keep it up to date in obvious and subtle ways, we have made a special effort in this edition to bring in to the text significant new pedagogical features.
SPECIFIC CHANGES IN THE THIRD EDITION
1. New pedagogical features. The most obvious changes to those familiar with the book will be the following additions we have made to ease the learning process.
2. Writing. In this revision, we have once again thoroughly reviewed every sentence, simplifying constructions and terminology wherever possible and sometimes rewriting from scratch entire paragraphs or sections. It is hard enough to learn statistics without having to read complicated sentences.
3. Updating examples. In the sections on how to understand and evaluate statistics in research articles we have replaced dozens of examples with new ones published in the last year or two.
4. There is now a unique Website for the text available to instructors and students. We are particularly excited about the potential of the Web for aiding learning of statistics. Features of the website include: Powerpoint presentation materials, online student study guide, flash card exercises, all formulas in symbols and in words, a downloadable minichapter for students on the logic and language of research, and a downloadable minichapter for students on applying statistics in their own research projects.
5. Some changes we have not made. The 10 points noted earlier in this Preface remain as the central, unique features of this book. Also, we have not changed each chapter's major teaching examples. Instructors using the second edition told us they have built their lectures around these examples and don't want to have to start from scratch with new ones.
TO THE STUDENT
The goal of this book is to help you understand statistics. We emphasize meaning and concepts, not just symbols and numbers.
This emphasis plays to your strength. Most social and behavioral science students are not lovers of mathematics but are keenly attuned to ideas. And we want to underscore the following, based on our 40 years' experience in teaching: We have never had a student who could do well in other college courses who could not also do well in this course. (However, we will admit that doing well in this course may require more work than doing well in others.)
In this introduction, we discuss why you are taking this course and how you can gain the most from it.
WHY LEARN STATISTICS? (BESIDES FULFILLING A REQUIREMENT)
1. Understanding statistics is crucial to being able to read research results. In most of the social and behavioral sciences, nearly every course you take will emphasize the results of research studies, and these usually include statistics. If you do not understand the basic logic of statistics—if you cannot make sense of the jargon, the tables, and the graphs that are at the heart of any research report—your reading of research will be very superficial. (We also recommend that you take a course on how to design good research. In this book, we focus on the statistical methods for making sense of the data collected through research. However, we have included a downloadable minichapter on the website for the book that provides an overview of the logic and language of behavioral and social sciences research.)
2. Understanding statistics is crucial to doing research yourself. Many students eventually go on to graduate school. Graduate study in the social and behavioral sciences almost always involves doing research. In fact, learning to do research on your own is often the entire focus of graduate school, and doing research almost always involves statistics. This course gives you a solid foundation in the statistics you need for doing research. Further, by mastering the basic logic and ways of thinking about statistics, you will be unusually well prepared for the advanced courses, which focus on the nittygritty of analyzing research results.
Many universities also offer opportunities for undergraduates to do research. The main focus of this book is understanding statistics, not using statistics. Still, you will learn the basics you need to analyze the results of the kinds of research you are likely to do. (Also, the website that accompanies this book has a special minichapter to help you with practical issues in using what you learn in this book for analyzing results of your own research.)
3. Understanding statistics develops your analytic and critical thinking. Social and behavioral science students are often most interested in people and in improving things in the practical world. This does not mean that you avoid abstractions. In fact, the students we know are exhilarated most by the almost philosophical levels of abstraction where the secrets of human experience so often seem to hide. Yet even this kind of abstraction often is grasped only superficially at first, as slogans instead of useful knowledge. Of all the courses you are likely to take in the social and behavioral sciences, this course will probably do the most to help you learn to think precisely, to evaluate information, and to apply logical analysis at a very high level.
HOW TO GAIN THE MOST FROM THIS COURSE
There are five things we can advise:
1. Keep your attention on the concepts. Treat this course less like a math course and more like a course in logic. When you read a section of a chapter, your attention should be on grasping the principles. When working the exercises, think about why you are doing each step. If you simply try to memorize how to come up with the right numbers, you will have learned very little of use in your future studiesnor will you do very well on the tests in this course.
2. Be sure you know each concept before you go on to the next. Statistics is cumulative. Each new concept is built on the last one. There are short "How Are You Doing?" selftests at the end of each main chapter section. Be sure you do them. And if you are having trouble answering a question—or even if you can answer it but aren't sure you really understand it—stop. Reread the section, rethink it, ask for help. Do whatever you need to do to grasp it. Don't go on to the next section until you are completely confident you have gotten this one. (If you are not sure, and you've already done the "How Are You Doing?" questions, take a look at the "Example WorkedOut Problems" towards the end of the chapter, or try working a practice problem on this material from the end of the chapter.)
Having to read the material in this book over and over does not mean that you are stupid. Most students have to read each chapter several times. And each reading in statistics is usually much slower than that in other textbooks. Statistics reading has to be pored over with clear, calm attention for it to sink in. Allow plenty of time for this kind of reading and rereading.
3. Keep up. Again, statistics is cumulative. If you fall behind in your reading or miss lectures, the lectures you then attend will be almost meaningless. It will get harder and harder to catch up.
4. Study especially intensely in the first half of the course. It is especially important to master the material thoroughly at the start of the course. Everything else you learn in statistics is built on what you learn at the start. Yet the beginning of the semester is often when students study least.
If you have mastered the first half of the course—not just learned the general idea, but really know it—the second half will be easier. If you have not mastered the first half, the second half will be close to impossible.
5. Help each other. There is no better way to solidify and deepen your understanding of statistics than to try to explain it to someone having a harder time. (Of course, this explaining has to be done with patience and respect.) For those of you who are having a harder time, there is no better way to work through the difficult parts than by learning from another student who has just mastered the material.
Thus, we strongly urge you to form study groups with one to three other students. It is best if your group includes some who expect this material to come easily and some who don't. Those who learn statistics easily will get the very most from helping others who have to struggle with it—the latter will tax the former's supposed understanding enormously. Those who fear trouble ahead, you need to work with those who do not—the blind leading the blind is no way to learn. Pick group members who live near you so that it is easy for you to get together. Also, meet often—between each class, if possible.