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Unformatted text preview: P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 W. H. Freeman and Company New York The Basic Practice of Statistics Fourth Edition David S. Moore Purdue University P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU July 7, 2006 20:49 Publisher: Craig Bleyer Executive Editor: Ruth Baruth Associate Acquisitions Editor: Laura Hanrahan Marketing Manager: Victoria Anderson Editorial Assistant: Laura Capuano Photo Editor: Bianca Moscatelli Photo Researcher: Brian Donnelly Cover and Text Designer: Vicki Tomaselli Cover and Interior Illustrations: Mark Chickinelli Senior Project Editor: Mary Louise Byrd Illustration Coordinator: Bill Page Illustrations: Techbooks Production Manager: Julia DeRosa Composition: Techbooks Printing and Binding: Quebecor World TI-83TM screen shots are used with permission of the publisher: C 1996, Texas Instruments Incorporated. TI-83TM Graphic Calculator is a registered trademark of Texas Instruments Incorporated. Minitab is a registered trademark of Minitab, Inc. Microsoft C and Windows C are registered trademarks of the Microsoft Corporation in the United States and other countries. Excel screen shots are reprinted with permission from the Microsoft Corporation. S-PLUS is a registered trademark of the Insightful Corporation. Library of Congress Control Number: 2006926755 ISBN: 0-7167-7478-X (Hardcover) EAN: 9780716774785 (Hardcover) ISBN: 0-7167-7463-1 (Softcover) EAN: 978-0-7167-7463-1 (Softcover) C 2007 All rights reserved. Printed in the United States of America First printing W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 Brief Contents PART I Exploring Data 1 CHAPTER 17 Exploring Data: Variables and Distributions CHAPTER 1 CHAPTER 2 CHAPTER 3 Picturing Distributions with Graphs Describing Distributions with Numbers The Normal Distributions 3 37 64 Exploring Data: Relationships CHAPTER 4 CHAPTER 5 CHAPTER 6 CHAPTER 7 Scatterplots and Correlation Regression Two-Way Tables∗ Exploring Data: Part I Review 90 115 149 167 PART III Inference about Variables CHAPTER 18 CHAPTER 19 Producing Data: Sampling Producing Data: Experiments COMMENTARY: Data Ethics∗ CHAPTER 20 CHAPTER 11 CHAPTER 12 CHAPTER 13 Introducing Probability Sampling Distributions General Rules of Probability∗ Binomial Distributions∗ 189 213 235 246 271 302 326 Introducing Inference CHAPTER 14 CHAPTER 15 CHAPTER 16 ∗ Confidence Intervals: The Basics Tests of Significance: The Basics Inference in Practice Inference about a Population Proportion Comparing Two Proportions Inference about Variables: Part III Review PART IV Inference about Probability and Sampling Distributions CHAPTER 10 Inference about a Population Mean Two-Sample Problems 433 460 491 512 530 186 Producing Data CHAPTER 8 CHAPTER 9 430 Categorical Response Variable CHAPTER 22 to Inference 412 Quantitative Response Variable CHAPTER 21 PART II From Exploration From Exploration to Inference: Part II Review Relationships Two Categorical Variables: The Chi-Square Test CHAPTER 24 Inference for Regression CHAPTER 25 One-Way Analysis of Variance: Comparing Several Means 544 CHAPTER 23 547 581 620 PART V Optional Companion Chapters (available on the BPS CD and online) CHAPTER 26 362 387 26-1 CHAPTER 27 Statistical Process Control 27-1 CHAPTER 28 343 Nonparametric Tests Multiple Regression 28-1 CHAPTER 29 Two-Way Analysis of Variance (available online only) 29-1 Starred material is optional. iii P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 Contents To the Instructor: About This Book To the Student: Statistical Thinking xi xxvii PART I Exploring Data 1 with Graphs CHAPTER 2 Describing Distributions with Numbers 3 6 37 Regression lines 115 The least-squares regression line 118 Using technology 120 Facts about least-squares regression 123 Residuals 126 Influential observations 129 Cautions about correlation and regression 132 Association does not imply causation 134 CHAPTER 6 Two-Way Tables∗ 149 CHAPTER 7 Exploring Data: Part I Review 167 Part I summary 169 Review exercises 172 Supplementary exercises 180 EESEE case studies 184 64 186 CHAPTER 8 Producing Data: Sampling 189 78 81 ∗ PART II From Exploration to Inference 74 Density curves 64 Describing density curves 67 Normal distributions 70 The 68−95−99.7 rule 71 The standard Normal distribution Finding Normal proportions 76 Using the standard Normal table∗ Finding a value given a proportion iv 115 Marginal distributions 150 Conditional distributions 153 Simpson’s paradox 158 Measuring center: the mean 38 Measuring center: the median 39 Comparing the mean and the median 40 Measuring spread: the quartiles 41 The five-number summary and boxplots 43 Spotting suspected outliers∗ 45 Measuring spread: the standard deviation 47 Choosing measures of center and spread 50 Using technology 51 Organizing a statistical problem 53 CHAPTER 3 The Normal Distributions 90 Explanatory and response variables 90 Displaying relationships: scatterplots 92 Interpreting scatterplots 94 Adding categorical variables to scatterplots 97 Measuring linear association: correlation 99 Facts about correlation 101 CHAPTER 5 Regression CHAPTER 1 Picturing Distributions Individuals and variables 3 Categorical variables: pie charts and bar graphs Quantitative variables: histograms 10 Interpreting histograms 14 Quantitative variables: stemplots 19 Time plots 22 CHAPTER 4 Scatterplots and Correlation Observation versus experiment Sampling 192 How to sample badly 194 Starred material is optional. 189 P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 Contents Simple random samples 196 Other sampling designs 200 Cautions about sample surveys Inference about the population CHAPTER 13 Binomial Distributions∗ 201 204 CHAPTER 9 Producing Data: Experiments Experiments 213 How to experiment badly 215 Randomized comparative experiments 217 The logic of randomized comparative experiments Cautions about experimentation 222 Matched pairs and other block designs 224 Commentary: Data Ethics∗ Institutional review boards 236 Informed consent 237 Confidentiality 237 Clinical trials 238 Behavioral and social science experiments 213 220 The binomial setting and binomial distributions 326 Binomial distributions in statistical sampling 327 Binomial probabilities 328 Using technology 331 Binomial mean and standard deviation The Normal approximation to binomial distributions 334 The Basics 343 Estimating with confidence 344 Confidence intervals for the mean μ 349 How confidence intervals behave 353 Choosing the sample size 355 240 CHAPTER 15 Tests of Significance: CHAPTER 10 Introducing Probability 246 The Basics 362 The reasoning of tests of significance 363 Stating hypotheses 365 Test statistics 367 P-values 368 Statistical significance 371 Tests for a population mean 372 Using tables of critical values∗ 376 Tests from confidence intervals 379 The idea of probability 247 Probability models 250 Probability rules 252 Discrete probability models 255 Continuous probability models 257 Random variables 260 Personal probability∗ 261 CHAPTER 11 Sampling Distributions 271 Parameters and statistics 271 Statistical estimation and the law of large numbers Sampling distributions 275 The sampling distribution of x 278 The central limit theorem 280 Statistical process control∗ 286 x charts∗ 287 Thinking about process control∗ 292 CHAPTER 12 General Rules of Probability∗ Independence and the multiplication rule The general addition rule 307 Conditional probability 309 The general multiplication rule 311 Independence 312 Tree diagrams 314 326 332 CHAPTER 14 Confidence Intervals: 235 v 303 CHAPTER 16 Inference in Practice 273 302 387 Where did the data come from? 388 Cautions about the z procedures 389 Cautions about confidence intervals 391 Cautions about significance tests 392 The power of a test∗ 396 Type I and Type II errors∗ 399 CHAPTER 17 From Exploration to Inference: Part II Review Part II summary 414 Review exercises 417 Supplementary exercises 424 Optional exercises 426 EESEE case studies 429 412 P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls vi QC: PBU/OVY T1: PBU June 29, 2006 23:11 Contents PART III Inference about Variables 430 CHAPTER 18 Inference about a Population Mean Conditions for inference 433 The t distributions 435 The one-sample t confidence interval The one-sample t test 439 Using technology 441 Matched pairs t procedures 444 Robustness of t procedures 447 433 CHAPTER 19 Two-Sample Problems 460 CHAPTER 22 Inference about Variables: Part III Review PART IV Inference about Relationships CHAPTER 23 Two Categorical Variables: The Chi-Square Test 466 530 Population Proportion 547 491 CHAPTER 24 Inference for Regression ˆ The sample proportion p 492 ˆ The sampling distribution of p 492 Large-sample confidence intervals for a proportion 496 Accurate confidence intervals for a proportion 499 Choosing the sample size 502 Significance tests for a proportion 504 CHAPTER 21 Comparing Two Proportions 544 Two-way tables 547 The problem of multiple comparisons 550 Expected counts in two-way tables 552 The chi-square test 554 Using technology 555 Cell counts required for the chi-square test 559 Uses of the chi-square test 560 The chi-square distributions 563 The chi-square test and the z test∗ 565 The chi-square test for goodness of fit∗ 566 476 476 CHAPTER 20 Inference about a Two-sample problems: proportions 512 The sampling distribution of a difference between proportions 513 Large-sample confidence intervals for comparing proportions 514 Using technology 516 520 Part III summary 532 Review exercises 533 Supplementary exercises 539 EESEE case studies 543 437 Two-sample problems 460 Comparing two population means 462 Two-sample t procedures 464 Examples of the two-sample t procedures Using technology 470 Robustness again 473 Details of the t approximation∗ 473 Avoid the pooled two-sample t procedures∗ Avoid inference about standard deviations∗ The F test for comparing two standard deviations∗ 477 Accurate confidence intervals for comparing proportions 517 Significance tests for comparing proportions 512 Conditions for regression inference 583 Estimating the parameters 584 Using technology 587 Testing the hypothesis of no linear relationship Testing lack of correlation 592 Confidence intervals for the regression slope 594 Inference about prediction 596 Checking the conditions for inference 600 CHAPTER 25 One-Way Analysis of Variance: Comparing Several Means Comparing several means 622 The analysis of variance F test 623 Using technology 625 581 591 620 P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 Contents The idea of analysis of variance 630 Conditions for ANOVA 632 F distributions and degrees of freedom 637 Some details of ANOVA: the two-sample case∗ 639 Some details of ANOVA∗ 641 Hypotheses and conditions for the Kruskal-Wallis test 26-26 The Kruskal-Wallis test statistic 657 660 Tables 683 Table A Standard Normal probabilities 684 Table B Random digits 686 Table C t distribution critical values 687 Table D F distribution critical values 688 Table E Chi-square distribution critical values 692 Table F Critical values of the correlation r 693 Answers to Selected Exercises Index 694 721 PART V Optional Companion Chapters (on the BPS CD and online) CHAPTER 26 Nonparametric Tests Comparing two samples: the Wilcoxon rank sum test 26-3 The Normal approximation for W 26-7 Using technology 26-9 What hypotheses does Wilcoxon test? 26-11 Dealing with ties in rank tests 26-12 Matched pairs: the Wilcoxon signed rank test 26-17 The Normal approximation for W + 26-20 Dealing with ties in the signed rank test 26-22 Comparing several samples: the Kruskal-Wallis test 26-25 26-27 CHAPTER 27 Statistical Process Control Statistical Thinking Revisited Notes and Data Sources 26-1 vii 27-1 Processes 27-2 Describing processes 27-2 The idea of statistical process control 27-6 x charts for process monitoring 27-8 s charts for process monitoring 27-14 Using control charts 27-21 Setting up control charts 27-24 Comments on statistical control 27-30 Don’t confuse control with capability! 27-33 Control charts for sample proportions 27-35 Control limits for p charts 27-36 CHAPTER 28 Multiple Regression Parallel regression lines 28-2 Estimating parameters 28-6 Using technology 28-11 Inference for multiple regression 28-15 Interaction 28-26 The multiple linear regression model 28-32 The woes of regression coefficients 28-38 A case study for multiple regression 28-42 Inference for regression parameters 28-54 Checking the conditions for inference 28-59 CHAPTER 29 Two-Way Analysis of Variance (available online only) Extending the one-way ANOVA model Two-way ANOVA models Using technology Inference for two-way ANOVA Inference for a randomized block design Multiple comparisons Contrasts Conditions for two-way ANOVA 28-1 P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To The Instructor: About This Book The Basic Practice of Statistics (BPS) is an introduction to statistics for college and university students that emphasizes balanced content, working with real data, and statistical ideas. It is designed to be accessible to students with limited quantitative background—just “algebra” in the sense of being able to read and use simple equations. The book is usable with almost any level of technology for calculating and graphing—from a $15 “two-variable statistics” calculator through a graphing calculator or spreadsheet program through full statistical software. BPS was the pioneer in presenting a modern approach to statistics in a genuinely elementary text. In the following I describe for instructors the nature and features of the book and the changes in this fourth edition. Guiding principles BPS is based on three principles: balanced content, experience with data, and the importance of ideas. Balanced content. Once upon a time, basic statistics courses taught probability and inference almost exclusively, often preceded by just a week of histograms, means, and medians. Such unbalanced content does not match the actual practice of statistics, where data analysis and design of data production join with probability-based inference to form a coherent science of data. There are also good pedagogical reasons for beginning with data analysis (Chapters 1 to 7), then moving to data production (Chapters 8 and 9), and then to probability (Chapters 10 to 13) and inference (Chapters 14 to 29). In studying data analysis, students learn useful skills immediately and get over some of their fear of statistics. Data analysis is a necessary preliminary to inference in practice, because inference requires clean data. Designed data production is the surest foundation for inference, and the deliberate use of chance in random sampling and randomized comparative experiments motivates the study of probability in a course that emphasizes data-oriented statistics. BPS gives a full presentation of basic probability and inference (20 of the 29 chapters) but places it in the context of statistics as a whole. viii Experience with data. The study of statistics is supposed to help students work with data in their varied academic disciplines and in their unpredictable later employment. Students learn to work with data by working with data. BPS is full of data from many fields of study and from everyday life. Data are more than mere numbers—they are numbers with a context that should play a role in making sense of the numbers and in stating conclusions. Examples and exercises in BPS, though intended for beginners, use real data and give enough background to allow students to consider the meaning of their calculations. Even the first examples carry a message: a look at Arbitron data on radio station formats (page 7) and on P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To The Instructor: About This Book use of portable music players in several age groups (page 8) shows that the Arbitron data don’t help plan advertising for a music-downloading Web site. Exercises often ask for conclusions that are more than a number (or “reject H 0 ”). Some exercises require judgment in addition to right-or-wrong calculations and conclusions. Statistics, more than mathematics, depends on judgment for effective use. BPS begins to develop students’ judgment about statistical studies. The importance of ideas. A first course in statistics introduces many skills, from making a stemplot and calculating a correlation to choosing and carrying out a significance test. In practice (even if not always in the course), calculations and graphs are automated. Moreover, anyone who makes serious use of statistics will need some specific procedures not taught in her college stat course. BPS therefore tries to make clear the larger patterns and big ideas of statistics, not in the abstract, but in the context of learning specific skills and working with specific data. Many of the big ideas are summarized in graphical outlines. Three of the most useful appear inside the front cover. Formulas without guiding principles do students little good once the final exam is past, so it is worth the time to slow down a bit and explain the ideas. These three principles are widely accepted by statisticians concerned about teaching. In fact, statisticians have reached a broad consensus that first courses should reflect how statistics is actually used. As Richard Scheaffer says in discussing a survey paper of mine, “With regard to the content of an introductory statistics course, statisticians are in closer agreement today than at any previous time in my career.”1 ∗ Figure 1 is an outline of the consensus as summarized by the Joint Curriculum Committee of the American Statistical Association and the Mathematical Association of America.2 I was a member of the ASA/MAA committee, and I agree with their conclusions. More recently, the College Report of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Project has emphasized exactly the same themes.3 Fostering active learning is the business of the teacher, though an emphasis on working with data helps. BPS is guided by the content emphases of the modern consensus. In the language of the GAISE recommendations, these are: develop statistical thinking, use real data, stress conceptual understanding. Accessibility The intent of BPS is to be modern and accessible. The exposition is straightforward and concentrates on major ideas and skills. One principle of writing for beginners is not to try to tell them everything. Another principle is to offer frequent stopping points. BPS presents its content in relatively short chapters, each ending with a summary and two levels of exercises. Within chapters, a few “Apply Your Knowledge” exercises follow each new idea or skill for a quick check of basic ∗ All notes are collected in the Notes and Data Sources section at the end of the book. APPLY YOUR KNOWLEDGE ix P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls x QC: PBU/OVY T1: PBU June 29, 2006 23:11 To The Instructor: About This Book 1. Emphasize the elements of statistical thinking: (a) (b) (c) (d) 2. the need for data; the importance of data production; the omnipresence of variability; the measuring and modeling of variability. Incorporate more data and concepts, fewer recipes and derivations. Wherever possible, automate computations and graphics. An introductory course should: (a) rely heavily on real (not merely realistic) data; (b) emphasize statistical concepts, e.g., causation vs. association, experimental vs. observational, and longitudinal vs. cross-sectional studies; (c) rely on computers rather than computational recipes; (d) treat formal derivations as secondary in importance. 3. Foster active learning, through the following alternatives to lecturing: (a) (b) (c) (d) (e) group problem solving and discussion; laboratory exercises; demonstrations based on class-generated data; written and oral presentations; projects, either group or individual. F I G U R E 1 Recommendations of the ASA/MAA Joint Curriculum Committee. mastery—and also to mark off digestible bites of material. Each of the first three parts of the book ends with a review chapter that includes a point-by-point outline of skills learned and many review exercises. (Instructors can choose to cover any or none of the chapters in Parts IV and V, so each of these chapters includes a skills outline.) The review chapters present many additional exercises without the “I just studied that” context, thus asking for another level of learning. I think it is helpful to assign some review exercises. Look at the first five exercises of Chapter 22 (the Part III review) to see the advantage of the part reviews. Many instructors will find that the review chapters appear at the right points for pre-examination review. Technology Automating calculations increases students’ ability to complete problems, reduces their frustration, and helps them concentrate on ideas and problem recognition rather than mechanics. All students should have at least a “two-variable statistics”calculator with functions for correlation and the least-squares regression line as well as for the mean and standard deviation. Because students have calculators, the text doesn’t discuss out-of-date “computing formulas”for the sample standard deviation or the least-squares regression line. Many instructors will take advantage of more elaborate technology, as ASA/MAA and GAISE recommend. And many students who don’t use technology in their college statistics course will find themselves using (for example) P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU July 10, 2006 21:58 To The Instructor: About This Book Excel on the job. BPS does not assume or require use of software except in Chapters 24 and 25, where the work is otherwise too tedious. It does accommodate software use and tries to convince students that they are gaining knowledge that will enable them to read and use output from almost any source. There are regular “Using Technology” sections throughout the text. Each of these displays and comments on output from the same four technologies, representing graphing calculators (the Texas Instruments TI-83 or TI-84), spreadsheets (Microsoft Excel), and statistical software (CrunchIt! and Minitab). The output always concerns one of the main teaching examples, so that students can compare text and output. A quite different use of technology appears in the interactive applets created to my specifications and available online and on the text CD. These are designed primarily to help in learning statistics rather than in doing statistics. An icon calls attention to comments and exercises based on the applets. I suggest using selected applets for classroom demonstrations even if you do not ask students to work with them. The Correlation and Regression, Confidence Interval, and new P-value applets, for example, convey core ideas more clearly than any amount of chalk and talk. Using technology A P P LE T APPLET What’s new? BPS has been very successful. There are no major changes in the statistical content of this new edition, but longtime users will notice the following: • • • Many new examples and exercises. Careful rewriting with an eye to yet greater clarity. Some sections, for example, Normal calculations in Chapter 3 and power in Chapter 16, have been completely rewritten. A new commentary on Data Ethics following Chapter 9. Students are increasingly aware that science often poses ethical issues. Instruction in science should therefore not ignore ethics. Statistical studies raise questions about privacy and protection of human subjects, for example. The commentary describes such issues, outlines accepted ethical standards, and presents striking examples for discussion. In preparing this edition, I have concentrated on pedagogical enhancements designed to make it easier for students to learn. • • A handy ‘‘Caution’’ icon in the margin calls attention to common confusions or pitfalls in basic statistics. Many small marginal photos are chosen to enhance examples and exercises. Students see, for example, a water-monitoring station in the Everglades (page 22) or a Heliconia flower (page 54) when they work with data from these settings. CAUTION UTION xi P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xii QC: PBU/OVY T1: PBU June 29, 2006 23:11 To The Instructor: About This Book Check Your Skills 4 • • STE P STEP • A set of ‘‘Check Your Skills’’ multiple-choice items opens each set of chapter exercises. These are deliberately straightforward, and answers to all appear in the back of the book. Have your students use them to assess their grasp of basic ideas and skills, or employ them in a “clicker” classroom response system for class review. A new four-step process (State, Formulate, Solve, Conclude) guides student work on realistic statistical problems. See the inside front cover for an overview. I outline and illustrate the process early in the text (see page 53), but its full usefulness becomes clear only as we accumulate the tools needed for realistic problems. In later chapters this process organizes most examples and many exercises. The process emphasizes a major theme in BPS: statistical problems originate in a real-world setting (“State”) and require conclusions in the language of that setting (“Conclude”). Translating the problem into the formal language of statistics (“Formulate”) is a key to success. The graphs and computations needed (“Solve”) are essential but not the whole story. A marginal icon helps students see the four-step process as a thread through the text. I have been careful not to let this outline stand in the way of clear exposition. Most examples and exercises, especially in earlier chapters, intend to teach specific ideas and skills for which the full process is not appropriate. It is absent from some entire chapters (for example, those on probability) where it is not relevant. Nonetheless, the cumulative effect of this overall strategy for problem solving should be substantial. CrunchIt! statistical software is available online with new copies of BPS. Developed by Webster West of Texas A&M University, CrunchIt! offers capabilities well beyond those needed for a first course. It implements modern procedures presented in BPS, including the “plus four” confidence intervals for proportions. More important, I find it the easiest true statistical software for student use. Check out, for example, CrunchIt!’s flexible and straightforward process for entering data, often a real barrier to software use. I encourage teachers who have avoided software in the past for reasons of availability, cost, or complexity to consider CrunchIt!. Why did you do that? There is no single best way to organize our presentation of statistics to beginners. That said, my choices reflect thinking about both content and pedagogy. Here are comments on several “frequently asked questions”about the order and selection of material in BPS. Why does the distinction between population and sample not appear in Part I? This is a sign that there is more to statistics than inference. In fact, statistical inference is appropriate only in rather special circumstances. The chapters in Part I present tools and tactics for describing data—any data. These tools and tactics do not depend on the idea of inference from sample to population. Many P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To The Instructor: About This Book data sets in these chapters (for example, the several sets of data about the 50 states) do not lend themselves to inference because they represent an entire population. John Tukey of Bell Labs and Princeton, the philosopher of modern data analysis, insisted that the population-sample distinction be avoided when it is not relevant. He used the word “batch” for data sets in general. I see no need for a special word, but I think Tukey is right. Why not begin with data production? It is certainly reasonable to do so—the natural flow of a planned study is from design to data analysis to inference. But in their future employment most students will use statistics mainly in settings other than planned research studies. I place the design of data production (Chapters 8 and 9) after data analysis to emphasize that data-analytic techniques apply to any data. One of the primary purposes of statistical designs for producing data is to make inference possible, so the discussion in Chapters 8 and 9 opens Part II and motivates the study of probability. Why do Normal distributions appear in Part I? Density curves such as the Normal curves are just another tool to describe the distribution of a quantitative variable, along with stemplots, histograms, and boxplots. Professional statistical software offers to make density curves from data just as it offers histograms. I prefer not to suggest that this material is essentially tied to probability, as the traditional order does. And I find it very helpful to break up the indigestible lump of probability that troubles students so much. Meeting Normal distributions early does this and strengthens the “probability distributions are like data distributions” way of approaching probability. Why not delay correlation and regression until late in the course, as is traditional? BPS begins by offering experience working with data and gives a conceptual structure for this nonmathematical but essential part of statistics. Students profit from more experience with data and from seeing the conceptual structure worked out in relations among variables as well as in describing single-variable data. Correlation and least-squares regression are very important descriptive tools and are often used in settings where there is no population-sample distinction, such as studies of all a firm’s employees. Perhaps most important, the BPS approach asks students to think about what kind of relationship lies behind the data (confounding, lurking variables, association doesn’t imply causation, and so on), without overwhelming them with the demands of formal inference methods. Inference in the correlation and regression setting is a bit complex, demands software, and often comes right at the end of the course. I find that delaying all mention of correlation and regression to that point means that students often don’t master the basic uses and properties of these methods. I consider Chapters 4 and 5 (correlation and regression) essential and Chapter 24 (regression inference) optional. What about probability? Much of the usual formal probability appears in the optional Chapters 12 and 13. Chapters 10 and 11 present in a less formal way the ideas of probability and sampling distributions that are needed to understand xiii P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xiv QC: PBU/OVY T1: PBU June 29, 2006 23:11 To The Instructor: About This Book inference. These two chapters follow a straight line from the idea of probability as long-term regularity, through concrete ways of assigning probabilities, to the central idea of the sampling distribution of a statistic. The law of large numbers and the central limit theorem appear in the context of discussing the sampling distribution of a sample mean. What is left to Chapters 12 and 13 is mostly “general probability rules” (including conditional probability) and the binomial distributions. I suggest that you omit Chapters 12 and 13 unless you are constrained by external forces. Experienced teachers recognize that students find probability difficult. Research on learning confirms our experience. Even students who can do formally posed probability problems often have a very fragile conceptual grasp of probability ideas. Attempting to present a substantial introduction to probability in a data-oriented statistics course for students who are not mathematically trained is in my opinion unwise. Formal probability does not help these students master the ideas of inference (at least not as much as we teachers often imagine), and it depletes reserves of mental energy that might better be applied to essentially statistical ideas. Why use the z procedures for a population mean to introduce the reasoning of inference? This is a pedagogical issue, not a question of statistics in practice. Sometime in the golden future we will start with resampling methods. I think that permutation tests make the reasoning of tests clearer than any traditional approach. For now the main choices are z for a mean and z for a proportion. I find z for means quite a bit more accessible to students. Positively, we can say up front that we are going to explore the reasoning of inference in an overly simple setting. Remember, exactly Normal population and true simple random sample are as unrealistic as known σ . All the issues of practice—robustness against lack of Normality and application when the data aren’t an SRS as well as the need to estimate σ —are put off until, with the reasoning in hand, we discuss the practically useful t procedures. This separation of initial reasoning from messier practice works well. Negatively, starting with inference for p introduces many side issues: no exactly Normal sampling distribution, but a Normal approximation to a discrete disˆ tribution; use of p in both the numerator and the denominator of the test statistic ˆ to estimate both the parameter p and p ’s own standard deviation; loss of the direct link between test and confidence interval. Once upon a time we had at least the compensation of developing practically useful procedures. Now the often gross inaccuracy of the traditional z confidence interval for p is better understood. See the following explanation. Why does the presentation of inference for proportions go beyond the traditional methods? Recent computational and theoretical work has demonstrated convincingly that the standard confidence intervals for proportions can be trusted only for very large sample sizes. It is hard to abandon old friends, but I think that a look at the graphs in Section 2 of the paper by Brown, Cai, and DasGupta in the May 2001 issue of Statistical Science is both distressing and persuasive.4 The standard intervals often have a true confidence level much less than P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To The Instructor: About This Book what was requested, and requiring larger samples encounters a maze of “lucky” and “unlucky” sample sizes until very large samples are reached. Fortunately, there is a simple cure: just add two successes and two failures to your data. I present these “plus four intervals” in Chapters 20 and 21, along with guidelines for use. Why didn’t you cover Topic X? Introductory texts ought not to be encyclopedic. Including each reader’s favorite special topic results in a text that is formidable in size and intimidating to students. I chose topics on two grounds: they are the most commonly used in practice, and they are suitable vehicles for learning broader statistical ideas. Students who have completed the core of BPS, Chapters 1 to 11 and 14 to 22, will have little difficulty moving on to more elaborate methods. There are of course seven additional chapters in BPS, three in this volume and four available on CD and/or online, to guide the next stages of learning. I am grateful to the many colleagues from two-year and four-year colleges and universities who commented on successive drafts of the manuscript. Special thanks are due to Patti Collings (Brigham Young University), Brad Hartlaub (Kenyon College), and Dr. Jackie Miller (The Ohio State University), who read the manuscript line by line and offered detailed advice. Others who offered comments are: Holly Ashton, Pikes Peak Community College Sanjib Basu, Northern Illinois University Diane L. Benner, Harrisburg Area Community College Jennifer Bergamo, Cicero-North Syracuse High School David Bernklau, Long Island University, Brooklyn Campus Grace C. Cascio-Houston, Ph.D., Louisiana State University at Eunice Dr. Smiley Cheng, University of Manitoba James C. Curl, Modesto Junior College Nasser Dastrange, Buena Vista University Mary Ellen Davis, Georgia Perimeter College Dipak Dey, University of Connecticut Jim Dobbin, Purdue University Mark D. Ecker, University of Northern Iowa Chris Edwards, University of Wisconsin, Oshkosh Teklay Fessahaye, University of Florida Amy Fisher, Miami University, Middletown Michael R. Frey, Bucknell University Mark A. Gebert, Ph.D., Eastern Kentucky University Jonathan M. Graham, University of Montana Betsy S. Greenberg, University of Texas, Austin Ryan Hafen, University of Utah Donnie Hallstone, Green River Community College James Higgins, Kansas State University Lajos Horvath, University of Utah xv P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xvi QC: PBU/OVY T1: PBU July 7, 2006 20:49 To The Instructor: About This Book Patricia B. Humphrey, University of Alaska Lloyd Jaisingh, Morehead State University A. Bathi Kasturiarachi, Kent State University, Stark Campus Mohammed Kazemi, University of North Carolina, Charlotte Justin Kubatko, The Ohio State University Linda Kurz, State University of New York, Delhi Michael Lichter, University of Buffalo Robin H. Lock, St. Lawrence University Scott MacDonald, Tacoma Community College Brian D. Macpherson, University of Manitoba Steve Marsden, Glendale Community College Kim McHale, Heartland Community College Kate McLaughlin, University of Connecticut Nancy Role Mendell, State University of New York, Stonybrook Henry Mesa, Portland Community College Dr. Panagis Moschopoulos, The University of Texas, El Paso Kathy Mowers, Owensboro Community and Technical College Perpetua Lynne Nielsen, Brigham Young University Helen Noble, San Diego State University Erik Packard, Mesa State College Christopher Parrett, Winona State University Eric Rayburn, Danville Area Community College Dr. Therese Shelton, Southwestern University Thomas H. Short, Indiana University of Pennsylvania Dr. Eugenia A. Skirta, East Stroudsburg University Jeffrey Stuart, Pacific Lutheran University Chris Swanson, Ashland University Mike Turegun, Oklahoma City Community College Ramin Vakilian, California State University, Northridge Kate Vance, Hope College Dr. Rocky Von Eye, Dakota Wesleyan University Joseph J. Walker, Georgia State University I am particularly grateful to Craig Bleyer, Laura Hanrahan, Ruth Baruth, Mary Louise Byrd, Vicki Tomaselli, Pam Bruton, and the other editorial and design professionals who have contributed greatly to the attractiveness of this book. Finally, I am indebted to the many statistics teachers with whom I have discussed the teaching of our subject over many years; to people from diverse fields with whom I have worked to understand data; and especially to students whose compliments and complaints have changed and improved my teaching. Working with teachers, colleagues in other disciplines, and students constantly reminds me of the importance of hands-on experience with data and of statistical thinking in an era when computer routines quickly handle statistical details. David S. Moore P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 Media and Supplements For students A full range of media and supplements is available to help students get the most out of BPS. Please contact your W. H. Freeman representative for ISBNs and value packages. NEW! One click. One place. For all the statistical tools you need. www.whfreeman.com/statsportal (Access code required. Available packaged with The Basic Practice of Statistics 4th Edition or for purchase online.) StatsPortal is the digital gateway to BPS 4e, designed to enrich your course and enhance your students’ study skills through a collection of Web-based tools. StatsPortal integrates a rich suite of diagnostic, assessment, tutorial, and enrichment features, enabling students to master statistics at their own pace. Organized around three main teaching and learning components: • Interactive eBook offers a complete online version of the text, fully integrated with all of the media resources available with BPS 4e. xvii P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xviii QC: PBU/OVY T1: PBU July 7, 2006 20:49 Media and Supplements • StatsResource Center organizes all of the resources for BPS 4e into one location for the student’s ease of use. Includes: • [email protected] Simulations put the student in the role of the statistical consultant, helping them better understand statistics interactively within the context of real-life scenarios. Students will be asked to interpret and analyze data presented to them in report form, as well as to interpret current event news stories. All tutorials are graded and offer helpful hints and feedback. • StatTutor Tutorials offer 84 audio-embedded tutorials tied directly to the textbook, containing videos, applets, and animations. • Statistical Applets these sixteen interactive applets help students master statistics interactively. • EESEE Case Studies developed by The Ohio State University Statistics Department provide students with a wide variety of timely, real examples with real data. Each case study is built around several thought-provoking questions that make students think carefully about the statistical issues raised by the stories. • Podcast Chapter Summary provides students with an audio version of chapter summaries so they can download and review on their mp3 player! • CrunchIt! Statistical Software allows users to analyze data from any Internet location. Designed with the novice user in mind, the software is not only easily accessible but also easy to use. Offers all the basic statistical routines covered in the introductory statistics courses and more! • Datasets are offered in ASCII, Excel, JMP, Minitab, TI, SPSS, S-Plus, Minitab, ASCII, and Excel format. • Online Tutoring with SmarThinking is available for homework help from specially trained, professional educators. • Student Study Guide with Selected Solutions includes explanations of crucial concepts and detailed solutions to key text problems with step-through models of important statistical techniques. • Statistical Software Manuals for TI-83, Minitab, Excel, and SPSS provide chapter-to-chapter applications and exercises using specific statistical software packages with BPS 4e. • Interactive Table Reader allows students to use statistical tables interactively to seek the information they need. • Tables and Formulas provide each table and formulas from the chapter. • Excel Macros. StatsResources (instructor-only) • Instructor’s Manual with Full Solutions includes worked-out solutions to all exercises, teaching suggestions, and chapter comments. P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU July 10, 2006 21:34 Media and Supplements • • Test Bank contains complete solutions for textbook exercises. • Lecture PowerPoint Slides gives instructors detailed slides to use in lectures. • Activities and Projects offers ideas for projects for Web-based exploration asking students to write critically about statistics. • i>clicker Questions these conceptually-based questions help instructors to query students using i>clicker’s personal response units in class lectures. • Instructor-to-Instructor Videos provide instructors with guidance on how to use these interactive examples in the classroom. • Biology Examples identify areas of BPS 4e that relate to the field of biology. Assignment Center organizes assignments and guides instructors through an easy-to-create assignment process providing access to questions from the Test Bank, Check Your Skills, Apply Your Knowledge, Web Quizzes, and Exercises from BPS 4e. Enables instructors to create their own assignments from a variety of question-types for self-graded assignments. This powerful assignment manager allows instructors to select their preferred policies in regard to scheduling, maximum attempts, time limitations, feedback, and more! New! Online Study Center: www.whfreeman.com/bps4e/osc (Access code required. Available for purchase online.) In addition to all the offerings available on the Companion Web site, the OSC offers: • • • • • StatTutor Tutorials CrunchIt! Statistical Software [email protected] Simulations Study Guide Statistical Software Manuals The Companion Web Site: www.whfreeman.com/bps. Seamlessly integrates topics from the text. On this open-access Web site, students can find: • • • • • Interactive statistical applets that allow students to manipulate data and see the corresponding results graphically. Datasets in ASCII, Excel, JMP, Minitab, TI, SPSS, and S-Plus formats. Interactive exercises and self-quizzes to help students prepare for tests. Key tables and formulas summary sheet. All tables from the text in .pdf format for quick, easy reference. xix P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xx QC: PBU/OVY T1: PBU July 11, 2006 16:31 Media and Supplements • • • • Additional exercises for every chapter written by David Moore, giving students more opportunities to make sure they understand key concepts. Solutions to odd-numbered additional exercises are also included. Optional Companion Chapters 26, 27, 28, and 29, covering nonparametric tests, statistical process control, multiple regression, and two-way analysis of variance, respectively. CrunchIt! statistical software is available via an access-code-protected Web site. Access codes are available in every new text or can be purchased online for $5. EESEE case studies are available via an access-code-protected Web site. Access codes are available in every new text or can be purchased online. Interactive Student CD-ROM: Included with every new copy of BPS, the CD contains access to most of the content available on the Web site. CrunchIt! statistical software and EESEE case studies are available via an access-code-protected Web site. (Access code is included with every new text.) Special Software Packages: Student versions of JMP, Minitab, S-PLUS, and SPSS are available on a CD-ROM packaged with the textbook. This software is not sold separately and must be packaged with a text or a manual. Contact your W. H. Freeman representative for information or visit www.whfreeman.com . NEW! SMARTHINKING Online Tutoring: (Access code required) W. H. Freeman and Company is partnering with SMARTHINKING to provide students with free online tutoring and homework help from specially trained, professional educators. Twelve-month subscriptions are available to be packaged with BPS. The following supplements are available in print: • • Student Study Guide with Selected Solutions. Activities and Projects Book. For instructors The Instructor’s Web site requires user registration as an instructor and features all of the student Web material plus: • • • Instructor version of EESEE (Electronic Encyclopedia of Statistical Examples and Exercises), with solutions to the exercises in the student version. The Instructor’s Guide, including full solutions to all exercises in .pdf format. Text art images in jpg format. P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU July 7, 2006 20:49 Media and Supplements • • • • PowerPoint slides containing textbook art embedded into each slide. Lecture PowerPoint slides offering a detailed lecture presentation of statistical concepts covered in each chapter of BPS. Class Teaching Examples, one or more new examples for each chapter of BPS with suggestions for classroom use by David Moore. Tables and graphs are in a form suitable for making transparencies. Full solutions to the more than 400 extra exercises in the Additional Exercises supplement on the student Web site. Enhanced Instructor’s Resource CD-ROM: Designed to help instructors create lecture presentations, Web sites, and other resources, this CD allows instructors to search and export all the resources contained below by key term or chapter: • • • • • All text images Statistical applets, datasets, and more Instructor’s Manual with full solutions PowerPoint files and lecture slides Test bank files Annotated Instructor’s Edition Printed Instructor’s Guide with Full Solutions Test Bank: Printed or computerized (Windows and Mac on one CD-ROM). Course Management Systems: W. H. Freeman and Company provides courses for Blackboard, WebCT (Campus Edition and Vista), and Angel course management systems. These are completely integrated solutions that you can easily customize and adapt to meet your teaching goals and course objectives. Upon request, we also provide courses for users of Desire2Learn and Moodle. Visit www.bfwpub.com/lms for more information. NEW! i-clicker Radio Frequency Classroom Response System: Offered by W. H. Freeman and Company, in partnership with i-clicker, and created by educators for educators, i-clicker’s system is the hassle-free way to make class time more interactive. Visit www.iclicker.com for more information. xxi P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xxii QC: PBU/OVY T1: PBU July 7, 2006 20:49 Media and Supplements Applications The Basic Practice of Statistics presents a wide variety of applications from diverse disciplines. The list below indicates the number of examples and exercises which relate to different fields: Examples Agriculture: 8 Biological and environmental sciences: 25 Business and economics: 10 Education: 29 Entertainment: 5 People and places: 20 Physical sciences: 5 Political Science and public policy: 3 Psychology and behavioral sciences: 6 Public health and medicine: 33 Sports: 7 Technology: 16 Transportation and automobiles: 14 Exercises Agriculture: 56 Biological and environmental sciences: 128 Business and economics: 145 Education: 162 Entertainment: 33 People and places: 168 Physical sciences: 23 Political Science and public policy: 37 Psychology and behavioral sciences: 22 Public health and medicine: 189 Sports: 36 Technology: 37 Transportation and automobiles: 65 For a complete index of applications of examples and exercises, please see the Annotated Instructor’s Edition or the Web site: www.whfreeman.com/bps . P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To the Student: Statistical Thinking Statistics is about data. Data are numbers, but they are not “just numbers.” Data are numbers with a context. The number 10.5, for example, carries no information by itself. But if we hear that a friend’s new baby weighed 10.5 pounds at birth, we congratulate her on the healthy size of the child. The context engages our background knowledge and allows us to make judgments. We know that a baby weighing 10.5 pounds is quite large, and that a human baby is unlikely to weigh 10.5 ounces or 10.5 kilograms. The context makes the number informative. Statistics is the science of data. To gain insight from data, we make graphs and do calculations. But graphs and calculations are guided by ways of thinking that amount to educated common sense. Let’s begin our study of statistics with an informal look at some principles of statistical thinking. DATA BEAT ANECDOTES Stockbyte/PictureQuest An anecdote is a striking story that sticks in our minds exactly because it is striking. Anecdotes humanize an issue, but they can be misleading. Does living near power lines cause leukemia in children? The National Cancer Institute spent 5 years and $5 million gathering data on this question. The researchers compared 638 children who had leukemia with 620 who did not. They went into the homes and measured the magnetic fields in the children’s bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother’s residence when she was pregnant. Result: no connection between leukemia and exposure to magnetic fields of the kind produced by power lines. The editorial that accompanied the study report in the New England Journal of Medicine thundered, “It is time to stop wasting our research resources” on the question.1 Now compare the effectiveness of a television news report of a 5-year, $5 million investigation against a televised interview with an articulate mother whose child has leukemia and who happens to live near a power line. In the public mind, the anecdote wins every time. A statistically literate person knows better. Data are more reliable than anecdotes because they systematically describe an overall picture rather than focus on a few incidents. ALWAYS LOOK AT THE DATA Yogi Berra said it: “You can observe a lot by just watching.” That’s a motto for learning from data. A few carefully chosen graphs are often more instructive than great piles of numbers. Consider the outcome of the 2000 presidential election in Florida. xxiii P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 3500 To the Student: Statistical Thinking 3000 • Palm Beach County What happened in Palm Beach County? Votes for Buchanan 1000 1500 2000 2500 500 0 xxiv QC: PBU/OVY •• •• •• • •• • • • • • •• •• •• • •••••• • • ••• • 0 • • • • • 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 Votes for Gore F I G U R E 1 Votes in the 2000 presidential election for Al Gore and Patrick Buchanan in Florida’s 67 counties. What happened in Palm Beach County? Elections don’t come much closer: after much recounting, state officials declared that George Bush had carried Florida by 537 votes out of almost 6 million votes cast. Florida’s vote decided the election and made George Bush, rather than Al Gore, president. Let’s look at some data. Figure 1 displays a graph that plots votes for the third-party candidate Pat Buchanan against votes for the Democratic candidate Al Gore in Florida’s 67 counties. What happened in Palm Beach County? The question leaps out from the graph. In this large and heavily Democratic county, a conservative third-party candidate did far better relative to the Democratic candidate than in any other county. The points for the other 66 counties show votes for both candidates increasing together in a roughly straight-line pattern. Both counts go up as county population goes up. Based on this pattern, we would expect Buchanan to receive around 800 votes in Palm Beach County. He actually received more than 3400 votes. That difference determined the election result in Florida and in the nation. The graph demands an explanation. It turns out that Palm Beach County used a confusing “butterfly” ballot, in which candidate names on both left and right pages led to a voting column in the center. It would be easy for a voter who intended to vote for Gore to in fact cast a vote for Buchanan. The graph is P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To the Student: Statistical Thinking convincing evidence that this in fact happened, more convincing than the complaints of voters who (later) were unsure where their votes ended up. BEWARE THE LURKING VARIABLE The Kalamazoo (Michigan) Symphony once advertised a “Mozart for Minors” program with this statement: “Question: Which students scored 51 points higher in verbal skills and 39 points higher in math? Answer: Students who had experience in music.” 2 Who would dispute that early experience with music builds brainpower? The skeptical statistician, that’s who. Children who take music lessons and attend concerts tend to have prosperous and well-educated parents. These same children are also likely to attend good schools, get good health care, and be encouraged to study hard. No wonder they score well on tests. We call family background a lurking variable when we talk about the relationship between music and test scores. It is lurking behind the scenes, unmentioned in the symphony’s publicity. Yet family background, more than anything else we can measure, influences children’s academic performance. Perhaps the Kalamazoo Youth Soccer League should advertise that students who play soccer score higher on tests. After all, children who play soccer, like those who have experience in music, tend to have educated and prosperous parents. Almost all relationships between two variables are influenced by other variables lurking in the background. WHERE THE DATA COME FROM IS IMPORTANT The advice columnist Ann Landers once asked her readers, “If you had it to do over again, would you have children?”A few weeks later, her column was headlined “70% OF PARENTS SAY KIDS NOT WORTH IT.” Indeed, 70% of the nearly 10,000 parents who wrote in said they would not have children if they could make the choice again. Do you believe that 70% of all parents regret having children? You shouldn’t. The people who took the trouble to write Ann Landers are not representative of all parents. Their letters showed that many of them were angry at their children. All we know from these data is that there are some unhappy parents out there. A statistically designed poll, unlike Ann Landers’s appeal, targets specific people chosen in a way that gives all parents the same chance to be asked. Such a poll showed that 91% of parents would have children again. Where data come from matters a lot. If you are careless about how you get your data, you may announce 70% “No” when the truth is close to 90% “Yes.” Here’s another question: should women take hormones such as estrogen after menopause, when natural production of these hormones ends? In 1992, several major medical organizations said “Yes.”In particular, women who took hormones seemed to reduce their risk of a heart attack by 35% to 50%. The risks of taking hormones appeared small compared with the benefits. Brendan Byrne/Agefotostock xxv P1: PBU/OVY P2: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls xxvi QC: PBU/OVY T1: PBU June 29, 2006 23:11 To the Student: Statistical Thinking The evidence in favor of hormone replacement came from a number of studies that compared women who were taking hormones with others who were not. Beware the lurking variable: women who choose to take hormones are richer and better educated and see doctors more often than women who do not. These women do many things to maintain their health. It isn’t surprising that they have fewer heart attacks. To get convincing data on the link between hormone replacement and heart attacks, do an experiment. Experiments don’t let women decide what to do. They assign women to either hormone replacement or to dummy pills that look and taste the same as the hormone pills. The assignment is done by a coin toss, so that all kinds of women are equally likely to get either treatment. By 2002, several experiments with women of different ages agreed that hormone replacement does not reduce the risk of heart attacks. The National Institutes of Health, after reviewing the evidence, concluded that the first studies were wrong. Taking hormones after menopause quickly fell out of favor.3 The most important information about any statistical study is how the data were produced. Only statistically designed opinion polls can be trusted. Only experiments can completely defeat the lurking variable and give convincing evidence that an alleged cause really does account for an observed effect. VARIATION IS EVERYWHERE The company’s sales reps file into their monthly meeting. The sales manager rises. “Congratulations! Our sales were up 2% last month, so we’re all drinking champagne this morning. You remember that when sales were down 1% last month I fired half of our reps.” This picture is only slightly exaggerated. Many managers overreact to small short-term variations in key figures. Here is Arthur Nielsen, head of the country’s largest market research firm, describing his experience: Too many business people assign equal validity to all numbers printed on paper. They accept numbers as representing Truth and find it difficult to work with the concept of probability. They do not see a number as a kind of shorthand for a range that describes our actual knowledge of the underlying condition.4 Business data such as sales and prices vary from month to month for reasons ranging from the weather to a customer’s financial difficulties to the inevitable errors in gathering the data. The manager’s challenge is to say when there is a real pattern behind the variation. Start by looking at the data. Figure 2 plots the average price of a gallon of regular unleaded gasoline each month from January 1990 to February 2006.5 There certainly is variation! But a close look shows a pattern: gas prices normally go up during the summer driving season each year, then down as demand drops in the fall. Against this regular pattern we see the effects of international events: prices rose because of the 1990 Gulf War and dropped because of the 1998 financial crisis in Asia and the September 11, 2001, terrorist attacks in the United States. The year 2005 brought the P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 High demand from U.S., China, Gulf Coast hurricanes, Middle East violence Gulf War Asian financial crisis, demand drops September 11 attacks, world economy slumps 100 Gasoline price (cents per gallon) 150 200 250 300 To the Student: Statistical Thinking 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 20042005 2006 Year F I G U R E 2 Variation is everywhere: the average retail price of regular unleaded gasoline, 1990 to early 2006. perfect storm: the ability to produce oil and refine gasoline was overwhelmed by high demand from China and the United States, continued violence in Iraq, and hurricanes on the U.S. Gulf Coast. The data carry an important message: because the United States imports much of its oil, we can’t control the price we pay for gasoline. Variation is everywhere. Individuals vary; repeated measurements on the same individual vary; almost everything varies over time. One reason we need to know some statistics is that statistics helps us deal with variation. CONCLUSIONS ARE NOT CERTAIN Most women who reach middle age have regular mammograms to detect breast cancer. Do mammograms reduce the risk of dying of breast cancer? To defeat the lurking variable, doctors rely on experiments (called “clinical trials” in medicine) that compare different ways of screening for breast cancer. The conclusion from 13 such trials is that mammograms reduce the risk of death in women aged 50 to 64 years by 26%.6 AP/Wide World Photos xxvii P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 xxviii To the Student: Statistical Thinking On the average, then, women who have regular mammograms are less likely to die of breast cancer. But because variation is everywhere, the results are different for different women. Some women who have yearly mammograms die of breast cancer, and some who never have mammograms live to 100 and die when they crash their motorcycles. Statistical conclusions are “on-the-average” statements only. Well then, can we be certain that mammograms reduce risk on the average? No. We can be very confident, but we can’t be certain. Because variation is everywhere, conclusions are uncertain. Statistics gives us a language for talking about uncertainty that is used and understood by statistically literate people everywhere. In the case of mammograms, the doctors use that language to tell us that “mammography reduces the risk of dying of breast cancer by 26 percent (95 percent confidence interval, 17 to 34 percent).” That 26% is, in Arthur Nielsen’s words, a “shorthand for a range that describes our actual knowledge of the underlying condition.” The range is 17% to 34%, and we are 95 percent confident that the truth lies in that range. We will soon learn to understand this language. We can’t escape variation and uncertainty. Learning statistics enables us to live more comfortably with these realities. Statistical Thinking and You What Lies Ahead in This Book The purpose of The Basic Practice of Statistics (BPS) is to give you a working knowledge of the ideas and tools of practical statistics. We will divide practical statistics into three main areas: 1. Data analysis concerns methods and strategies for exploring, organizing, and describing data using graphs and numerical summaries. Only organized data can illuminate reality. Only thoughtful exploration of data can defeat the lurking variable. Part I of BPS (Chapters 1 to 7) discusses data analysis. 2. Data production provides methods for producing data that can give clear answers to specific questions. Where the data come from really is important. Basic concepts about how to select samples and design experiments are the most influential ideas in statistics. These concepts are the subject of Chapters 8 and 9. 3. Statistical inference moves beyond the data in hand to draw conclusions about some wider universe, taking into account that variation is everywhere and that conclusions are uncertain. To describe variation and uncertainty, inference uses the language of probability, introduced in Chapters 10 and 11. Because we are concerned with practice rather than theory, we need only a limited knowledge of probability. Chapters 12 and 13 offer more probability for those who want it. Chapters 14 to 16 discuss the reasoning of statistical inference. These chapters are the key to the rest of the book. Chapters 18 to 22 present inference as used in practice in the most common settings. Chapters 23 to 25, and the Optional Companion Chapters 26 to 29 on the text CD or online, concern more advanced or specialized kinds of inference. P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY GTBL011-FM GTBL011-Moore-v20.cls T1: PBU June 29, 2006 23:11 To the Student: Statistical Thinking Because data are numbers with a context, doing statistics means more than manipulating numbers. You must state a problem in its real-world context, formulate the problem by recognizing what specific statistical work is needed, solve the problem by making the necessary graphs and calculations, and conclude by explaining what your findings say about the real-world setting. We’ll make regular use of this four-step process to encourage good habits that go beyond graphs and calculations to ask, “What do the data tell me?” Statistics does involve lots of calculating and graphing. The text presents the techniques you need, but you should use a calculator or software to automate calculations and graphs as much as possible. Because the big ideas of statistics don’t depend on any particular level of access to computing, BPS does not require software. Even if you make little use of technology, you should look at the “Using Technology” sections throughout the book. You will see at once that you can read and use the output from almost any technology used for statistical calculations. The ideas really are more important than the details of how to do the calculations. You will need a calculator with some built-in statistical functions. Specifically, your calculator should find means and standard deviations and calculate correlations and regression lines. Look for a calculator that claims to do “two-variable statistics” or mentions “regression.” Because graphing and calculating are automated in statistical practice, the most important assets you can gain from the study of statistics are an understanding of the big ideas and the beginnings of good judgment in working with data. BPS tries to explain the most important ideas of statistics, not just teach methods. Some examples of big ideas that you will meet (one from each of the three areas of statistics) are “always plot your data,” “randomized comparative experiments,” and “statistical significance.” You learn statistics by doing statistical problems. As you read, you will see several levels of exercises, arranged to help you learn. Short “Apply Your Knowledge”problem sets appear after each major idea. These are straightforward exercises that help you solidify the main points as you read. Be sure you can do these exercises before going on. The end-of-chapter exercises begin with multiple-choice “Check Your Skills”exercises (with all answers in the back of the book). Use them to check your grasp of the basics. The regular “Chapter Exercises” help you combine all the ideas of a chapter. Finally, the three part review chapters look back over major blocks of learning, with many review exercises. At each step you are given less advance knowledge of exactly what statistical ideas and skills the problems will require, so each type of exercise requires more understanding. The part review chapters (and the individual chapters in Part IV) include point-by-point lists of specific things you should be able to do. Go through that list, and be sure you can say “I can do that” to each item. Then try some of the review exercises. The book ends with a review titled “Statistical Thinking Revisited,” which you should read and think about no matter where in the book your course ends. The key to learning is persistence. The main ideas of statistics, like the main ideas of any important subject, took a long time to discover and take some time to master. The gain will be worth the pain. 4 STE P STEP xxix ...
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This note was uploaded on 10/15/2011 for the course SPAN 101-103 taught by Professor All during the Spring '11 term at Tacoma Community College.

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