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Statistics for Psychology / Edition 4 available in Hardcover

- ISBN-10:
- 0131931679
- ISBN-13:
- 9780131931671
- Pub. Date:
- 09/01/2005
- Publisher:
- Prentice Hall

# Statistics for Psychology / Edition 4

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## Overview

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## Product Details

ISBN-13: | 9780131931671 |
---|---|

Publisher: | Prentice Hall |

Publication date: | 09/01/2005 |

Edition description: | Older Edition |

Pages: | 768 |

Product dimensions: | 8.20(w) x 10.28(h) x 1.29(d) |

## Table of Contents

Preface to the Instructor xiIntroduction to the Student xvi

Displaying the Order in a Group of Numbers Using Tables and Graphs 1

The Two Branches of Statistical Methods 2

Some Basic Concepts 3

Important Trivia for Poetic Statistics Students 6

Frequency Tables 7

Histograms 10

Math Anxiety, Statistics Anxiety, and You: A Message for Those of You Who Are Truly Worried About This Course 12

Shapes of Frequency Distributions 15

Controversy: Misleading Graphs 19

Frequency Tables and Histograms in Research Articles 21

Summary 23

Key Terms 24

Example Worked-Out Problems 24

Practice Problems 25

Using SPSS 29

Chapter Note 32

Central Tendency and Variability 33

Central Tendency 34

Variability 43

The Sheer Joy (Yes, Joy) of Statistical Analysis 51

Controversy: The Tyranny of the Mean 52

Gender, Ethnicity, and Math Performance 53

Central Tendency and Variability in Research Articles 55

Summary 57

Key Terms 57

Example Worked-Out Problems 57

Practice Problems 59

Using SPSS 62

Chapter Notes 65

Some Key Ingredients for Inferential Statistics: Z Scores, the Normal Curve, Sample versus Population, and Probability 67

Z Scores 68

The Normal Curve 73

de Moivre, the Eccentric Stranger Who Invented the Normal Curve 74

Sample and Population 83

Surveys, Polls, and 1948's Costly "Free Sample" 86

Probability 88

Pascal Begins Probability Theory at the Gambling Table, Then Learns to Bet on God 89

Controversies: Is the Normal Curve Really So Normal? and Using Nonrandom Samples 93

Z Scores, Normal Curves, Samples and Populations, and Probabilities in Research Articles 95

Advanced Topics: Probability Rules and Conditional Probabilities 96

Summary 97

Key Terms 98

Example Worked-Out Problems 99

Practice Problems 102

Using SPSS 105

Chapter Notes 106

Introduction to Hypothesis Testing 107

A Hypothesis-Testing Example 108

The Core Logic of Hypothesis Testing 109

The Hypothesis-Testing Process 110

One-Tailed and Two-Tailed Hypothesis Tests 119

Controversy: Should Significance Tests Be Banned? 124

Jacob Cohen, the Ultimate New Yorker: Funny, Pushy, Brilliant, and Kind 126

Hypothesis Tests in Research Articles 127

Summary 128

Key Terms 129

Example Worked-Out Problems 129

Practice Problems 131

Chapter Notes 136

Hypothesis Tests with Means of Samples 137

The Distribution of Means 138

Hypothesis Testing with a Distribution of Means: The Z Test 146

More About Polls: Sampling Errors and Errors in Thinking About Samples 147

Controversy: Marginal Significance 153

Hypothesis Tests About Means of Samples (Z Tests) and Standard Errors in Research Articles 154

Advanced Topic: Estimation, Standard Errors, and Confidence Intervals 156

Advanced Topic Controversy: Confidence Intervals versus Significance Tests 162

Advanced Topic: Confidence Intervals in Research Articles 163

Summary 163

Key Terms 164

Example Worked-Out Problems 164

Practice Problems 167

Chapter Notes 173

Making Sense of Statistical Significance: Decision Errors, Effect Size, and Statistical Power 175

Decision Errors 175

Effect Size 179

Effect Sizes for Relaxation and Meditation: A Restful Meta-Analysis 184

Statistical Power 187

What Determines the Power of a Study? 191

The Power of Typical Psychology Experiments 199

The Role of Power When Planning a Study 203

The Role of Power When Interpreting the Results of a Study 205

Controversy: Statistical Significance versus Effect Size 208

Decision Errors, Effect Size, and Power in Research Articles 210

Advanced Topic: Figuring Statistical Power 212

Summary 214

Key Terms 215

Example Worked-Out Problems 215

Practice Problems 217

Chapter Note 221

Introduction to t Tests: Single Sample and Dependent Means 222

The t Test for a Single Sample 223

William S. Gosset, Alias "Student": Not a Mathematician, But a Practical Man 224

The t Test for Dependent Means 236

Assumptions of the t Test for a Single Sample and the t Test for Dependent Means 247

Effect Size and Power for the t Test for Dependent Means 247

Controversy: Advantages and Disadvantages of Repeated-Measures Designs 250

The Power of Studies Using Difference Scores: How the Lanarkshire Milk Experiment Could Have Been Milked for More 251

Single Sample t Tests and Dependent Means t Tests in Research Articles 252

Summary 253

Key Terms 254

Example Worked-Out Problems 254

Practice Problems 258

Using SPSS 265

Chapter Notes 268

The t Test for Independent Means 270

The Distribution of Differences Between Means 271

Hypothesis Testing with a t Test for Independent Means 278

Assumptions of the t Test for Independent Means 286

Monte Carlo Methods: When Mathematics Becomes Just an Experiment, and Statistics Depend on a Game of Chance 286

Effect Size and Power for the t Test for Independent Means 288

Review and Comparison of the Three Kinds of t Tests 290

Controversy: The Problem of Too Many t Tests 291

The t Test for Independent Means in Research Articles 292

Advanced Topic: Power for the t Test for Independent Means When Sample Sizes Are Not Equal 293

Summary 294

Key Terms 295

Example Worked-Out Problems 295

Practice Problems 298

Using SPSS 305

Chapter Notes 309

Introduction to the Analysis of Variance 310

Basic Logic of the Analysis of Variance 311

Sir Ronald Fisher, Caustic Genius of Statistics 317

Carrying Out an Analysis of Variance 319

Hypothesis Testing with the Analysis of Variance 327

Assumptions in the Analysis of Variance 331

Planned Contrasts 334

Post Hoc Comparisons 337

Effect Size and Power for the Analysis of Variance 339

Controversy: Omnibus Tests versus Planned Contrasts 343

Analyses of Variance in Research Articles 344

Advanced Topic: The Structural Model in the Analysis of Variance 345

Principles of the Structural Model 345

Summary 351

Key Terms 352

Example Worked-Out Problems 353

Practice Problems 357

Using SPSS 364

Chapter Notes 368

Factorial Analysis of Variance 370

Basic Logic of Factorial Designs and Interaction Effects 371

Recognizing and Interpreting Interaction Effects 376

Basic Logic of the Two-Way Analysis of Variance 386

Personality and Situational Influences on Behavior: An Interaction Effect 387

Assumptions in the Factorial Analysis of Variance 389

Extensions and Special Cases of the Analysis of Variance 389

Controversy: Dichotomizing Numeric Variables 391

Factorial Analysis of Variance in Research Articles 393

Advanced Topic: Figuring a Two-Way Analysis of Variance 395

Advanced Topic: Power and Effect Size in the Factorial Analysis of Variance 406

Summary 410

Key Terms 411

Example Worked-Out Problems 412

Practice Problems 415

Using SPSS 426

Chapter Notes 431

Correlation 432

Graphing Correlations: The Scatter Diagram 434

Patterns of Correlation 437

The Correlation Coefficient 443

Galton: Gentleman Genius 446

Significance of a Correlation Coefficient 452

Correlation and Causality 456

Issues in Interpreting the Correlation Coefficient 458

Illusory Correlation: When You Know Perfectly Well That If It's Big, It's Fat-and You Are Perfectly Wrong 460

Effect Size and Power for the Correlation Coefficient 464

Controversy: What Is a Large Correlation? 466

Correlation in Research Articles 467

Summary 469

Key Terms 471

Example Worked-Out Problems 471

Practice Problems 474

Using SPSS 482

Chapter Notes 485

Prediction 487

Predictor (X) and Criterion (Y) Variables 488

The Linear Prediction Rule 488

The Regression Line 492

Finding the Best Linear Prediction Rule 496

The Least Squared Error Principle 498

Issues in Prediction 503

Multiple Regression 506

Limitations of Prediction 508

Controversy: Unstandardized and Standardized Regression Coefficients; Comparing Predictors 509

Clinical versus Statistical Prediction 510

Prediction in Research Articles 511

Advanced Topic: Error and Proportionate Reduction in Error 514

Summary 518

Key Terms 519

Example Worked-Out Problems 519

Practice Problems 524

Using SPSS 532

Chapter Notes 535

Chi-Square Tests 536

Karl Pearson, Inventor of Chi-Square and Center of Controversy 537

The Chi-Square Statistic and the Chi-Square Test for Goodness of Fit 538

The Chi-Square Test for Independence 546

Assumptions for Chi-Square Tests 554

Effect Size and Power for Chi-Square Tests for Independence 554

Controversy: The Minimum Expected Frequency 558

Chi-Square Tests in Research Articles 559

Summary 560

Key Terms 561

Example Worked-Out Problems 561

Practice Problems 565

Using SPSS 572

Chapter Notes 576

Strategies When Population Distributions Are Not Normal: Data Transformations and Rank-Order Tests 577

Assumptions in the Standard Hypothesis-Testing Procedures 578

Data Transformations 580

Rank-Order Tests 585

Comparison of Methods 589

Controversy: Computer-Intensive Methods 591

Where Do Random Numbers Come From? 594

Data Transformations and Rank-Order Tests in Research Articles 595

Summary 596

Key Terms 597

Example Worked-Out Problems 597

Practice Problems 597

Using SPSS 602

Chapter Notes 609

The General Linear Model and Making Sense of Advanced Statistical Procedures in Research Articles 611

The General Linear Model 612

Two Women Make a Point About Gender and Statistics 616

Partial Correlation 617

Reliability 618

Multilevel Modeling 620

Factor Analysis 622

Causal Modeling 625

The Golden Age of Statistics: Four Guys Around London 627

Procedures That Compare Groups 634

Analysis of Covariance (ANCOVA) 634

Multivariate Analysis of Variance (MANOVA) and Multivariate Analysis of Covariance (MANCOVA) 635

Overview of Statistical Techniques 636

Controversy: Should Statistics Be Controversial? 637

The Forced Partnership of Fisher and Pearson 638

How to Read Results Using Unfamiliar Statistical Techniques 639

Summary 641

Key Terms 642

Practice Problems 642

Using SPSS 654

Chapter Notes 662

Tables 664

Answers to Set I Practice Problems 673

Glossary 701

Glossary of Symbols 708

References 710

Index 719

## Preface

Our approach was developed over three decades 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 major, but also in the sense that students come back to us later saying, "I was light-years ahead of my fellow graduate students because of your course," or "Even though I don't do research, your course has really helped me read the journals in my field."

The response to the first and second edition has been overwhelming. We have received hundreds of thank-you e-mails and letters from instructors (and from students themselves!) from all over the English-speaking world. Of course, we were also delighted by the enthusiastic review in *Contemporary Psychology* (Bourgeois, 1997).

In this third edition we have tried to maintain those things that have been especially appreciated, while reworking the book 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 what we said in thefirst edition about how this book from the beginning has been quite different from other statistics texts.

### A BRIEF HISTORY OF THE STATISTICS TEXT GENRE

In the 1950s and 1960s statistics texts were dry, daunting, mathematical tomes that quickly left most students behind. In the 1970s, there was a revolution—in swept the intuitive approach, with much less emphasis on derivations, proofs, and mathematical foundations. The approach worked. Students became less afraid of statistics courses and found the material more accessible, even if not quite clear.

The intuitive trend continued in the 1980s, adding in the 1990s some nicely straightforward writing. A few texts have now also begun to encourage students to use the computer to do statistical analyses. However, discussions of intuitive understandings are becoming briefer and briefer. The standard is a cursory overview of the key idea and sometimes the associated definitional formula for each technique. Then come the procedures and examples for actually doing the computation, using another "computational" formula.

Even with all this streamlining, or perhaps because of it, at the end of the course most students cannot give a clear explanation of the logic behind the techniques they have learned. A few months later they can rarely carry out the procedures either. Most important, the three main purposes of the introductory statistics course ark, not accomplished: Students are not able to make sense of the results of psychology research articles, they are poorly prepared for further courses in statistics (where instructors must inevitably spend half the semester reteaching the introductory course), and the exposure to deep thinking that is supposed to justify the course's meeting general education requirements in the quantitative area has not occurred.

### WHAT WE HAVE DONE DIFFERENTLY

We continue to do what the best of the newer books are already doing well: emphasizing the intuitive, de-emphasizing the mathematical, and explaining everything in direct, simple language. But what we have done differs from these other books in 11 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 practice problems and test bank items are reduced appropriately to keep computations manageable.)

Why this approach? To date, statistics texts have failed to adjust to technological reality. What is important is not that the students learn to calculate a t test 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 directly displayed in the definitional formula (once the student is used to the symbols): Variance = Σ(*I* – *M*)^{2}/*N*. Repeatedly working problems using this formula engrains the meaning in the student's mind. In contrast, the usual computational version of this formula only obscures this meaning: Variance = Σ*X*^{2} – (Σ*X*)^{2}/*N*/*N*. Repeatedly working problems using this formula does nothing but teach the student the difference between Σ*X*^{2} and (Σ*X*)^{2}!

Teaching the old 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 formulas, 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 worked-out formulas, in words (often with a list of steps), and illustrated with an easy-to-grasp figure. Practice problems 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 psychology students 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 lay-language explanation gives them an opportunity to do what they do best.

**3.** A main goal of any introductory statistics course in psychology is to ** prepare students to read research articles.** The way a procedure such as a

*t*test or an analysis of variance 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 the journals (excerpts from current articles). And we don't just leave it there. The practice problems and test bank items also include excerpts from articles for the student to explain.

**4.** The book is ** unusually up to date.** 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 effect size, power, the accumulation of results through meta-analysis, the critical role of models, the underlying unity of difference and association statistics, the growing prominence of regression and associated methods, and a whole host of new orientations arising from the central role of the computer. 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.

**5.** We ** capitalize on the students' motivations.** We do this in two ways. First, our examples 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. Other examples emphasize clinical, organizational, social, and educational psychology while being sure to include sufficient interesting examples from cognitive, developmental, behavioral and cognitive neuroscience, and other areas to inspire students with the value of those specialties. (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 self-confidence 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. Instead, we show students, in the controversy sections in particular, how much there is for them to consider deeply, even in an introductory course.

**6.** ** We emphasize statistical methods as a living, growing field of research.** We take the time to describe the issues, such as the recent upheaval about the value of significance testing. In addition, each chapter includes one or more "boxes" about famous statisticians or interesting side-lights. 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.** ** Chapter 16 integrates the major techniques that have been taught,** explaining that the t test is a special case of the analysis of variance and that both the t test and the analysis of variance are special cases of correlation and regression. (In short, we introduce the general linear model.) In the past, when this point has been made at all, it has usually been only in advanced texts. But many students find it valuable for digesting and retaining what they have learned, as well as for sensing that they have penetrated deeply into the foundations of statistical methods.

**8.** ** 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 psychology 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 ill-equipped 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.

**9.** The accompanying ** Student's Study Guide and Computer Workbook** focuses on mastering concepts and also includes instructions and examples for working problems on the computer. Most study guides concentrate 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 self tests, including multiplechoice, fill-in, 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 carry out 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 step-by-step 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.

**10.** We have written an ** Instructor's Resource 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

*worked-out examples not found in the text*(in a form suitable for copying onto transparencies or for student handouts). These worked-out 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.

**11.** Our ** Test Bank makes preparing exams easy.** We supply approximately 40 multiple-choice, 25 fill-in, and 10 to 12 problem/essay questions for each chapter. Considering that the emphasis of the course is so conceptual, the multiple-choice questions will be particularly useful for those of you who do not have the resources to grade essays.

### INFLUENCES ON THE THIRD EDITION

We did the revision for the third edition over a summer in Tiburon, a small town overlooking the San Francisco Bay. We hope that this has not resulted in a loss of whatever romance the first edition gained from being written in Paris. On the other hand, this edition has been leavened by some beautiful Bay views.

More important, this revision is enriched by what we learned teaching with the first and second editions and by what we learned from the many instructors and students 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 the two of us in our own research programs in personality and social psychology. (For overviews of our main research programs, see A. Aron et al., 2001; E. Aron, 2000.) Our most recent adventure has been in social neuroscience, learning brain-imaging techniques, which it turns out are almost as fascinating for the statistical analysis challenges they pose as for the opportunities they provide for deepening knowledge of the issues we were previously studying with more conventional methods. Perhaps particularly useful has been that one of us (A. A.) has been serving 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 assess 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

**New pedagogic features.**The most obvious changes to those familiar with the book will be the following additions we made to ease the learning process:**"How Are You Doing?" sections.**These are brief self-tests focusing on concepts, inserted at three or four appropriate points in each chapter. These give students a chance to check that they have learned what they have just read, help them identify the central material in what they have just read, reinforce this material before going on to the next section, an4 divide the chapter into more accessible "chunks."**Doubling the number of practice problems.**Each chapter now bas at least 20. This provides the instructor with greater flexibility in the kinds and numbers of problems to assign.**Examples of Worked-Out Computational Problems.**These are included just before the practice problems at the end of each chapter. These give the student the chance to check their knowledge before starting their assigned problems and provide a model to follow when working them out, thus easing anxiety and helping the student do the problems correctly.**With each new formula there is a boxed concise statement of the formula in words.**This is important for helping students who fear symbols and math to see the underlying principle embedded in the formula, and keeps this verbal understanding directly available to them as they become accustomed to working with the symbols.

We have once again in this revision 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.*Writing.*We have replaced over 60 examples from the second edition with new ones published in the last year or two. This is particularly important for the sections on how to understand and evaluate statistics in research articles.*Updating examples.*Most obvious to those familiar with earlier editions will be the discussion of the APA Task Force report and the new*Updating content and controversies.**APA Publication Manual*'s statements on data analysis. But the updates are everywhere in subtle ways—even with newly identified anecdotes about historical figures in the boxes!We have substantially reworked our treatment of a few topics that some students were struggling with, including grouped frequency tables, raw-score regression, confidence intervals, and effect size in analysis of variance. We have also made some changes in emphasis and coverage in response to instructors' suggestions, including more on the issue of causality and correlation and a fuller treatment of multiple comparisons in analysis of variance.*Reworking of some specific topics students had found difficult.*available to instructors who adopt the book and to their students. We are particularly excited about the potential of the Web for aiding learning of statistics. Elliot Coups, has created an outstanding, dramatically innovative site. Some unique features (in addition to the usual chapter outline and objectives) include*There is now a unique Web page*- For instructors: Powerpoint presentation materials for teaching the course, including examples from the text and examples from the
*Instructor's Resource Manual*that are not in the text. - Downloadable mini-chapter for students on applying statistics in their own research projects.
- Downloadable mini-chapter for students on repeated measures analysis of variance.
- Chapter objectives
- Downloadable mini-chapter on the logic and language of research (this was Appendix A in the earlier editions)
- Tips for Success: What to practice, and what to study.
- Learn More! sections: Practice problems that include tables from the text on the Web, giving the students the opportunity to use the tables to work through problems.
- On-line student study guide, including practice problems, true/false questions, and fill in the blanks.
- Flash card exercises for each chapter's key terms.
- All formulas
- Links to statistic sites

**Some changes we have not made.** The 11 points listed earlier in this Preface remain as the central, unique features of this book. Also, except in a few cases where we felt we could make a significant improvement in pedagogy, 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.

### KEEP IN TOUCH

Our goal is to do whatever we can to help you make your course a success. If you have any questions or suggestions, please write or e-mail. Also, if you should find an error somewhere, for everyone's benefit, please let us know right away. When errors have come up in the past, we have usually been able to fix them in the very next printing.