F I F T H E D I T I O N The Basic Practice of Statistics DAVID S MOORE Purdue University W H Freeman and Company New York Senior Publisher: Craig Bleyer Publisher: Ruth Baruth Senior Media Editor: Roland Cheyney Developmental Editors: Bruce Kaplan, Shona Burke Executive Marketing Manager: Jennifer Somerville Media Editor: Brian Tedesco Associate Editor: Laura Capuano Editorial Assistant: Katrina Wilhelm Photo Editor: Cecilia Varas Photo Researcher: Elyse Rieder Cover and Text Designer: Vicki Tomaselli Cover and Interior Illustrations: Mark Chickinelli Senior Project Editor: Mary Louise Byrd Illustrations: Aptara Production and Illustration Coordinator: Paul W Rohloff Composition: Aptara Printing and Binding: Quebecor 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 About the Cover: Completing a jigsaw puzzle makes a meaningful whole out of what seemed like unconnected pieces Statistics does something similar with data, combining information about the source of the data with graphical displays, numerical summaries, and probability reasoning until meaning emerges from seemed like a jumble The cover represents how statistics puts everything together Library of Congress Control Number: 2008932350 ISBN-13: 978-1-4292-0121-6 ISBN-10: 1-4292-0121-5 C 2010 All right 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 B R I E F C O N T E N T S To the Instructor: About This Book I NTRODUCING I NFERENCE To the Student: Statistical Thinking CHAPTER 14 Introduction to Inference 359 CHAPTER 15 Thinking about Inference 393 CHAPTER 16 From Exploration to Inference: Part II Review 421 P A R T I: Exploring Data | E XPLORING D ATA : V ARIABLES CHAPTER CHAPTER CHAPTER AND D ISTRIBUTIONS Picturing Distributions with Graphs PART III: Inference about Variables | 440 Q UANTITATIVE R ESPONSE V ARIABLE Describing Distributions with Numbers 39 CHAPTER 17 Inference about a Population Mean 443 The Normal Distributions 67 CHAPTER 18 Two-Sample Problems 471 C ATEGORICAL R ESPONSE V ARIABLE E XPLORING D ATA : R ELATIONSHIPS CHAPTER Scatterplots and Correlation 95 CHAPTER Regression 125 CHAPTER Two-Way Tables∗ 161 CHAPTER Exploring Data: Part I Review 177 CHAPTER 19 Inference about a Population Proportion CHAPTER 20 Comparing CHAPTER 21 Two Proportions Inference about Variables: Part III Review 501 523 541 PART IV: P A R T I I: Inference about Relationships | 558 From Exploration to Inference | 198 CHAPTER 22 Two Categorical Variables: The Chi-Square Test P RODUCING D ATA CHAPTER 23 Inference CHAPTER Producing Data: Sampling 201 CHAPTER Producing Data: Experiments 223 COMMENTARY: DATA ETHICS* 249 for Regression Analysis of Variance: Comparing Several Means 561 595 CHAPTER 24 One-Way 633 PART V: Optional Companion Chapters P ROBABILITY AND S AMPLING D ISTRIBUTIONS (AVAILABLE ON THE BPS CD AND ONLINE) CHAPTER 10 Introducing Probability 261 CHAPTER 25 Nonparametric CHAPTER 11 Sampling Distributions 291 CHAPTER 26 Statistical CHAPTER 12 General Rules of Probability∗ 315 CHAPTER 27 CHAPTER 13 Binomial Distributions∗ 339 CHAPTER 28 More * Starred material is not required for later parts of the text Tests 25-1 Process Control 26-1 Multiple Regression about Analysis of Variance 27-1 28-1 iii C O N T E N T S Adding categorical variables to scatterplots / 103 Measuring linear association: correlation / 104 Facts about correlation / 106 To the Instructor: About This Book To the Student: Statistical Thinking CHAPTER PART I: Exploring Data | CHAPTER Picturing Distributions with Graphs Individuals and variables / Categorical variables: pie charts and bar graphs / Quantitative variables: histograms / 11 Interpreting histograms / 15 Quantitative variables: stemplots / 19 Time plots / 23 39 Two-Way Tables* Marginal distributions / 162 Conditional distributions / 164 Simpson’s paradox / 168 161 CHAPTER Exploring Data: Part I Review Part I Summary / 179 Review Exercises / 182 Supplementary Exercises / 191 177 PART II: From Exploration to Inference | 198 CHAPTER The Normal Distributions Density curves / 67 Describing density curves / 71 Normal distributions / 73 The 68-95-99.7 rule / 74 The standard Normal distribution / 77 Finding Normal proportions / 79 Using the standard Normal table / 81 Finding a value given a proportion / 83 125 CHAPTER CHAPTER Describing Distributions with Numbers Measuring center: the mean / 40 Measuring center: the median / 41 Comparing the mean and the median / 42 Measuring spread: the quartiles / 43 The five-number summary and boxplots / 45 Spotting suspected outliers∗ / 47 Measuring spread: the standard deviation / 49 Choosing measures of center and spread / 52 Using technology / 53 Organizing a statistical problem / 55 Regression Regression lines / 125 The least-squares regression line / 128 Using technology / 130 Facts about least-squares regression / 132 Residuals / 135 Influential observations / 139 Cautions about correlation and regression / 142 Association does not imply causation / 144 67 CHAPTER Producing Data: Sampling Population versus sample / 202 How to sample badly / 204 Simple random samples / 205 Inference about the population / 209 Other sampling designs / 210 Cautions about sample surveys / 212 The impact of technology / 214 201 CHAPTER CHAPTER Scatterplots and Correlation Explanatory and response variables / 96 Displaying relationships: scatterplots / 97 Interpreting scatterplots / 99 iv 95 Producing Data: Experiments Observation versus experiment / 223 Subjects, factors, treatments / 225 How to experiment badly / 228 Randomized comparative experiments / 229 223 * Starred material is not required for later parts of the text CONTENTS The logic of randomized comparative experiments / 232 Cautions about experimentation / 234 Matched pairs and other block designs / 236 Commentary: Data Ethics* Institutional review boards / 250 Informed consent / 251 Confidentiality / 252 Clinical trials / 253 Behavioral and social science experiments / 255 249 CHAPTER 10 Introducing Probability The idea of probability / 262 The search for randomness∗ / 264 Probability models / 266 Probability rules / 268 Discrete probability models / 271 Continuous probability models / 273 Random variables / 277 Personal probability∗ / 279 261 v Binomial mean and standard deviation / 346 The Normal approximation to binomial distributions / 348 CHAPTER 14 Introduction to Inference The reasoning of statistical estimation / 360 Margin of error and confidence level / 362 Confidence intervals for a population mean / 364 The reasoning of tests of significance / 368 Stating hypotheses / 371 P-value and statistical significance / 373 Tests for a population mean / 378 Significance from a table / 381 359 CHAPTER 15 Thinking about Inference 393 Conditions for inference in practice / 394 How confidence intervals behave / 397 How significance tests behave / 400 Planning studies: sample size for confidence intervals / 405 Planning studies: the power of a statistical test / 406 CHAPTER 16 CHAPTER 11 Sampling Distributions Parameters and statistics / 292 Statistical estimation and the law of large numbers / 293 Sampling distributions / 296 The sampling distribution of x¯ / 299 The central limit theorem / 301 291 421 PART III: Inference about Variables | 440 CHAPTER 12 General Rules of Probability∗ Independence and the multiplication rule / 316 The general addition rule / 320 Conditional probability / 322 The general multiplication rule / 324 Independence again / 326 Tree diagrams / 326 From Exploration to Inference: Part II Review Part II Summary / 423 Review Exercises / 427 Supplementary Exercises / 433 Optional Exercises / 437 315 CHAPTER 13 Binomial Distributions∗ 339 The binomial setting and binomial distributions / 339 Binomial distributions in statistical sampling / 341 Binomial probabilities / 342 Using technology / 344 CHAPTER 17 Inference about a Population Mean Conditions for inference about a mean / 443 The t distributions / 445 The one-sample t confidence interval / 447 The one-sample t test / 449 Using technology / 452 Matched pairs t procedures / 453 Robustness of t procedures / 457 443 CHAPTER 18 Two-Sample Problems Two-sample problems / 471 Comparing two population means / 472 471 vi CONTENTS The chi-square test statistic / 568 Cell counts required for the chi-square test / 569 Using technology / 570 Uses of the chi-square test / 575 The chi-square distributions / 577 The chi-square test for goodness of fit∗ / 579 Two-sample t procedures / 475 Using technology / 481 Robustness again / 483 Details of the t approximation∗ / 485 Avoid the pooled two-sample t procedures∗ / 487 Avoid inference about standard deviations∗ / 488 CHAPTER 19 CHAPTER 23 Inference about a Population Proportion 501 The sample proportion pˆ / 502 Large-sample confidence intervals for a proportion / 504 Accurate confidence intervals for a proportion / 507 Choosing the sample size / 510 Significance tests for a proportion / 512 Inference for Regression 595 Conditions for regression inference / 597 Estimating the parameters / 599 Using technology / 601 Testing the hypothesis of no linear relationship / 604 Testing lack of correlation / 606 Confidence intervals for the regression slope / 608 Inference about prediction / 610 Checking the conditions for inference / 614 CHAPTER 20 Comparing Two Proportions 523 Two-sample problems: proportions / 523 The sampling distribution of a difference between proportions / 524 Large-sample confidence intervals for comparing proportions / 525 Using technology / 527 Accurate confidence intervals for comparing proportions / 528 Significance tests for comparing proportions / 530 CHAPTER 24 One-Way Analysis of Variance: Comparing Several Means Comparing several means / 635 The analysis of variance F test / 635 Using technology / 638 The idea of analysis of variance / 641 Conditions for ANOVA / 644 F distributions and degrees of freedom / 648 Some details of ANOVA∗ / 650 633 CHAPTER 21 Inference about Variables: Part III Review Part III Summary / 545 Review Exercises / 546 Supplementary Exercises / 552 541 AND D ATA S OURCES 667 689 T ABLES TABLE A Standard Normal cumulative proportions / 690 TABLE B Random digits / 692 TABLE C t distribution critical values / 693 TABLE D Chi-square distribution critical values / 694 TABLE E Critical values of the correlation r / 695 PART I V: Inference about Relationships | 558 CHAPTER 22 Two Categorical Variables: The Chi-Square Test Two-way tables / 561 The problem of multiple comparisons / 564 Expected counts in two-way tables / 566 N OTES 561 A NSWERS I NDEX TO S ELECTED E XERCISES 697 725 CONTENTS Setting up control charts / 26-23 Comments on statistical control / 26-30 Don’t confuse control with capability! / 26-32 Control charts for sample proportions / 26-34 Control limits for p charts / 26-35 P ART V: Optional Companion Chapters (AVAILABLE ON THE BPS CD AND ONLINE) CHAPTER 25 Nonparametric Tests 25-1 Comparing two samples: the Wilcoxon rank sum test / 25-3 The Normal approximation for W / 25-6 Using technology / 25-8 What hypotheses does Wilcoxon test? / 25-11 Dealing with ties in rank tests / 25-12 Matched pairs: the Wilcoxon signed rank test / 25-17 The Normal approximation for W + / 25-20 Dealing with ties in the signed rank test / 25-22 Comparing several samples: the Kruskal-Wallis test / 25-25 Hypotheses and conditions for the Kruskal-Wallis test / 25-26 The Kruskal-Wallis test statistic / 25-26 CHAPTER 26 Statistical Process Control Processes / 26-2 Describing processes / 26-2 The idea of statistical process control / 26-6 x¯ charts for process monitoring / 26-8 s charts for process monitoring / 26-13 Using control charts / 26-20 vii 26-1 CHAPTER 27 Multiple Regression Parallel regression lines / 27-2 Estimating parameters / 27-5 Using technology / 27-11 Inference for multiple regression / 27-14 Interaction / 27-24 The general multiple linear regression model / 27-30 The woes of regression coefficients / 27-37 A case study for multiple regression / 27-39 Inference for regression parameters / 27-49 Checking the conditions for inference / 27-55 27-1 CHAPTER 28 More About Analysis of Variance Beyond one-way ANOVA / 28-1 Follow-up analysis: Tukey pairwise multiple comparisons / 28-5 Follow-up analysis: contrasts∗ / 28-10 Two-way ANOVA: conditions, main effects, and interaction / 28-14 Inference for two-way ANOVA / 28-21 Some details of two-way ANOVA∗ / 28-30 28-1 T O T H E I N S T R U C T O R About This Book Welcome to the fifth edition of The Basic Practice of Statistics (BPS) This book is the cumulation of 40 years of teaching undergraduates and 20 years of writing texts Previous editions have been very successful, and I think that this new edition is the best yet In this Preface I describe for instructors the nature and features of the book and the changes in this fifth edition BPS is designed to be accessible to college and university students with limited quantitative background—just “algebra” in the sense of being able to read and use simple equations It 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 Of course, graphs and calculations are less tedious with good technology, so I recommend making available to your students the most effective technology that circumstances permit Despite its rather low mathematical level, BPS is a “serious”text in the sense that it wants students to more than master the mechanics of statistical calculations and graphs Even quite basic statistics is very useful in many fields of study and in everyday life, but only if the student has learned to move from a real world setting to choose and carry out statistical methods and then carry conclusions back to the original setting These translations require some conceptual understanding of such issues as the distinction between data analysis and inference, the critical role of where the data come from, the reasoning of inference, and the conditions under which we can trust the conclusions of inference BPS tries to teach both the mechanics and the concepts needed for practical statistical work, at a level appropriate for beginners 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 to 7), then moving to data production (Chapters and 9), and then to probability (Chapters 10 to 13) and inference (Chapters 14 to 28) 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 viii TO THE INSTRUCTOR 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 (19 of the 28 chapters) but places it in the context of statistics as a whole 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 Exercises often ask for conclusions that are more than a number (or “reject H0 ”) 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 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 said 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 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 ∗ All notes are collected in the Notes and Data Sources section at the end of the book ix ... details of two-way ANOVA∗ / 28-30 28-1 T O T H E I N S T R U C T O R About This Book Welcome to the fifth edition of The Basic Practice of Statistics (BPS) This book is the cumulation of 40 years of. .. gives a full presentation of basic probability and inference (19 of the 28 chapters) but places it in the context of statistics as a whole Experience with data The study of statistics is supposed... 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