Mind on statistics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
Cengage Learning Custom Press
2020
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| Ausgabe: | 6. ed., student ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| ISBN: | 1337793604 9781337793605 |
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Datensatz im Suchindex
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| adam_text | Contents Preface xii Statistics Success Stories and Cautionary Tales 1.1 1.2 What Is Statistics? 3 Eight Statistical Stories with Morals 1.3 The Common Elements in the Eight Stories Key Terms Exercises 3 4 10 11 12 Turning Data into Information 17 2.1 2.2 Raw Data 17 Types of Variables 2.3 Summarizing One orTwo Categorical Variables 22 2.4 2.5 Exploring Features of Quantitative Data with Pictures 26 Numerical Summaries of Quantitative Variables 39 2.6 2.7 How to Handle Outliers 47 Bell-Shaped Distributions and Standard Deviations Key Terms 19 In Summary Boxes 55 Simulations for Further Exploration Exercises 48 54 55 56 Relationships Between Quantitative Variables 71 3.1 3.2 Looking for Patterns with Scatterplots 72 Describing Linear Patterns with a Regression Line 3.3 Measuring Strength and Direction with Correlation 85 3.4 3.5 Regression and Correlation Difficulties and Disasters Correlation Does Not Prove Causation 97 Key Terms 101 In Summary Boxes 101 Simulations for Further Exploration Exercises 102 101 76 92
4 Relationships Between Categorical Variables 4.1 Displaying Relationships Between Categorical Variables 117 4.2 Risk, Relative Risk, and Misleading Statistics About Risk 122 4.3 The Effect of a Third Variable and Simpson s Paradox 4.4 Assessing the Relationship in a 2 X 2 Table: Hypothesis Testing 128 4.5 Randomization Test for a 2 x 2 Table Key Terms 143 In Summary Boxes Exercises 159 5.1 Collecting and Using Sample Data Wisely 5.2 Margin of Error, Confidence Intervals, and Sample Size 5.3 5.4 Choosing a Simple Random Sample 167 Additional Probability Sampling Methods 5.5 Difficulties and Disasters in Sampling Pitfalls In Asking Survey Questions Exercises 159 163 169 178 183 191 In Summary Boxes 191 Simulations for Further Exploration 191 191 Gathering Useful Data for Examining Relationships 203 6.1 6.2 Speaking the Language of Research Studies Designing a Good Experiment 208 6.3 6.4 Designing a Good Observational Study 217 Difficulties and Disasters in Experiments and Observational Studies 219 Key Terms 224 In Summary Boxes Exercises 224 7 144 144 Key Terms 6 139 Sampling: Surveys and How to Ask Questions 5.6 127 144 Simulations for Further Exploration 5 117 Probability 203 224 233 7.1 7.2 7.3 Random Circumstances 233 Interpretations of Probability 235 Probability Definitions and Relationships 7.4 7.5 Basic Rules for Finding Probabilities 245 Conditional Probabilities and Bayes Rule 252 7.6 7.7 Using Simulation to Estimate Probabilities 259 Flawed Intuitive Judgments About Probability 261 Key Terms 240 268 In Summary Boxes 268 J
Contents Simulations for Further Exploration Exercises 8 Random Variables 281 8.1 What Is a Random Variable? 8.2 8.3 Discrete Random Variables 284 Expectations for Random Variables 8.4 8.5 Binomial Random Variables 294 Continuous Random Variables 299 8.6 Normal Random Variables 301 Approximating Binomial Distribution Probabilities 8.7 8.8 281 289 312 Linear Combinations and Linear Transformations of Random Variables 316 Key Terms 323 In Summary Boxes 323 Simulations for Further Exploration Exercises 9 268 269 323 324 Understanding Sampling Distributions: Statistics as Random Variables 337 9.1 Parameters, Statistics, and Statistical Inference 9.2 9.3 From Curiosity to Questions About Parameters 340 SD Module 0: An Overview of Sampling Distributions 9.4 SD Module 1 : Sampling Distribution for One Sample Proportion 348 SD Module 2: Sampling Distribution for the Difference in Two Sample Proportions 353 SD Module 3: Sampling Distribution for One Sample Mean 357 SD Module 4: Sampling Distribution for the Sample Mean of Paired Differences 361 SD Module 5: Sampling Distribution for the Difference in Two Sample Means 364 Preparing for Statistical Inference: Standardized Statistics 367 9.5 9.6 9.7 9.8 9.9 337 345 Lesson 1 : Standardized Statistics for Sampling Distributions Lesson 2: Standardized Statistics for Proportions Lesson 3: Standardized Statistics for Means 9.10 Generalizations Beyond the Big Five Key Terms 378 In Summary Boxes 378 Simulations for Further Exploration Exercises 371 379 379 368 367 367 vii
10 Estimating Proportions with Confidence 10.1 397 Cl Module 0: An Overview of Confidence Intervals Lesson 1:The Basic Idea of a Confidence Interval 397 397 Lesson 2: Computing Confidence Intervals for the Big Five Parameters 10.2 400 Cl Module 1 : Confidence Intervals for Population Proportions 403 Lesson 1 : Details of How to Compute a Confidence Interval for a Population Proportion 403 Lesson 2: Understanding the Formula 406 Lesson 3: Reconciling and Understanding Different Margin of Error Formulas 409 10.3 Cl Module 2: Confidence Intervals for the Difference In Two Population Proportions 412 10.4 Using Simulation to Calculate Confidence Intervals: Bootstrapping 416 Using Confidence Intervals to Guide Decisions 422 10.5 Key Terms 426 In Summary Boxes 427 Simulations for Further Exploration Exercises 11 427 427 Estimating Means with Confidence 11.1 11.2 441 Introduction to Confidence Intervals for Means 441 Cl Module 3: Confidence Intervals for One Population Mean 449 Lesson 1: Finding a Confidence Interval for a Mean for Any Sample Size and Any Confidence Level 449 Lesson 2: Special Case: Approximate 95% Confidence Intervals for Large Samples 11.3 і 11.4 ֊ 455 Cl Module 4: Confidence Intervals for the Population Mean of Paired Differences 457 Cl Module 5: Confidence Intervals for the Difference in Two Population Means (Independent Samples) Lesson 1 : The General (Unpooled) Case 462 462 Lesson 2: The Equal Variance Assumption and the Pooled Standard Error 11.5 11.6 468 Using Simulation to Calculate Confidence Intervals: Bootstrapping for Means and Other Parameters 472
Understanding Any Confidence Interval 479 Key Terms 482 In Summary Boxes 482 Simulations for Further Exploration Exercises 483 482
Contents 12 Testing Hypotheses About Proportions 12.1 497 HT Module 0: An Overview of Hypothesis Testing Lesson 1: Formulating Hypothesis Statements 498 498 Lesson 2: Test Statistic, p-Value, and Deciding Between the Hypotheses 501 Lesson 3: What Can Go Wrong: The Two Types of Errors and Their Probabilities 508 12.2 HT Module 1 :Testing Hypotheses About a Population Proportion 512 12.3 HT Module 2: Testing Hypotheses About the Difference in Two Population Proportions 524 Using Resampling to Estimate the p-Value for Testing Hypotheses About Two Proportions 529 12.4 12.5 12.6 Sample Size, p-Values, and Power 533 Understanding and Addressing Criticisms of Significance Testing 538 Key Terms 548 In Summary Boxes 548 Simulations for Further Exploration Exercises 13 548 549 Testing Hypotheses About Means 567 13.1 Introduction to Hypothesis Tests for Means 13.2 HT Module 3:Testing Hypotheses About One Population Mean 569 HT Module 4: Testing Hypotheses About the Population Mean of Paired Differences 575 HT Module 5: Testing Hypotheses About the Difference in Two Population Means (Independent Samples) 579 13.3 13.4 Lesson 1 : The General (Unpooled) Case 567 579 Lesson 2: The Pooled Two-Sample f֊Test 585 Lesson 3: Randomization Test for Comparing Two Means The Relationship Between Significance Tests and Confidence Intervals 591 13.6 Choosing an Appropriate Inference Procedure 13.7 Effect Size 13.8 Evaluating Statistical Results in Research Reports Key Terms 607 608 608 Inference About Simple Regression 14.1 14.2 603 607 In Summary Boxes Exercises 594 598 Simulations for Further
Exploration 14 588 13.5 623 Sample and Population Regression Models 624 Estimating the Standard Deviation for Regression 631 ix
14.3 Inference About the Slope ofa Linear Regression 635 14.4 Predicting y and Estimating Mean y at a Specific x 638 14.5 Checking Conditions for Using Regression Models for Inference 644 Key Terms 650 In Summary Boxes 650 Simulations for Further Exploration Exercises 15 More About Inference for Categorical Variables 15.1 The Chi-Square Test for Two-Way Tables 15.2 Methods for Analyzing 2 X 2Tables 15.3 Testing Hypotheses About One Categorical Variable: Goodness-of-Fit 680 Key Terms 686 In Summary Boxes Analysis of Variance 661 673 686 701 16.1 Comparing Means with an ANOVA f-Test 16.2 Details of One-Way Analysis of Variance 702 710 16.3 Other Methods for Comparing Populations 16.4 Two-Way Analysis of Variance Key Terms 724 In Summary Boxes 724 724 724 17 Turning Information into Wisdom 17.1 Beyond the Data I 17.2 17.3 17.4 17.5 Transforming Uncertainty into Wisdom Making Personal Decisions 738 Controlling Societal Risks 740 Understanding Our World 742 Getting to Know You 17.7 Words to the Wise 745 In Summary Boxes 746 738 743 746 Appendix of Tables References 735 735 17.6 Exercises 716 720 Simulations for Further Exploration Exercises 751 759 Answers to Selected Odd-Numbered Exercises Index 790 661 686 Simulations for Further Exploration Exercises 687 16 650 651 765
Conients Instructors: The Supplemental Topics are available on the book companion website, http://www.cengage.com/statistics/Utts6e. supplemental topic 1 Additional Discrete Random Variables 51.1 51.2 Hypergeometric Distribution Poisson Distribution 51.3 Multinomial Distribution 51.4 Negative Binomial and Geometric Distributions Key Terms Exercises supplemental тож 2 Nonparametric Tests of Hypotheses 52.1 The Sign Test 52.2 52.3 The Two-Sample Rank-Sum Test TheWilcoxon Signed-RankTest 52.4 The Kruskal-Wallis Test Key Terms Exercises supplemental topic 3 Multiple Regression 53.1 53.2 The Multiple Linear Regression Model Inference About Multiple Regression Models 53.3 Checking Conditions for Multiple Linear Regression Key Terms Exercises supplemental topic 4 Two-Way Analysis ofVariance 54.1 54.2 Assumptions and Models for Two-Way ANOVA Testing for Main Effects and Interactions Key Terms Exercises supplemental topic 5 Ethics 55.1 Ethical Treatment of Human and Animal Participants 55.2 Assurance of Data Quality 55.3 55.4 Appropriate Statistical Analyses Fair Reporting of Results Key Terms Exercises
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| adam_txt |
Contents Preface xii Statistics Success Stories and Cautionary Tales 1.1 1.2 What Is Statistics? 3 Eight Statistical Stories with Morals 1.3 The Common Elements in the Eight Stories Key Terms Exercises 3 4 10 11 12 Turning Data into Information 17 2.1 2.2 Raw Data 17 Types of Variables 2.3 Summarizing One orTwo Categorical Variables 22 2.4 2.5 Exploring Features of Quantitative Data with Pictures 26 Numerical Summaries of Quantitative Variables 39 2.6 2.7 How to Handle Outliers 47 Bell-Shaped Distributions and Standard Deviations Key Terms 19 In Summary Boxes 55 Simulations for Further Exploration Exercises 48 54 55 56 Relationships Between Quantitative Variables 71 3.1 3.2 Looking for Patterns with Scatterplots 72 Describing Linear Patterns with a Regression Line 3.3 Measuring Strength and Direction with Correlation 85 3.4 3.5 Regression and Correlation Difficulties and Disasters Correlation Does Not Prove Causation 97 Key Terms 101 In Summary Boxes 101 Simulations for Further Exploration Exercises 102 101 76 92
4 Relationships Between Categorical Variables 4.1 Displaying Relationships Between Categorical Variables 117 4.2 Risk, Relative Risk, and Misleading Statistics About Risk 122 4.3 The Effect of a Third Variable and Simpson's Paradox 4.4 Assessing the Relationship in a 2 X 2 Table: Hypothesis Testing 128 4.5 Randomization Test for a 2 x 2 Table Key Terms 143 In Summary Boxes Exercises 159 5.1 Collecting and Using Sample Data Wisely 5.2 Margin of Error, Confidence Intervals, and Sample Size 5.3 5.4 Choosing a Simple Random Sample 167 Additional Probability Sampling Methods 5.5 Difficulties and Disasters in Sampling Pitfalls In Asking Survey Questions Exercises 159 163 169 178 183 191 In Summary Boxes 191 Simulations for Further Exploration 191 191 Gathering Useful Data for Examining Relationships 203 6.1 6.2 Speaking the Language of Research Studies Designing a Good Experiment 208 6.3 6.4 Designing a Good Observational Study 217 Difficulties and Disasters in Experiments and Observational Studies 219 Key Terms 224 In Summary Boxes Exercises 224 7 144 144 Key Terms 6 139 Sampling: Surveys and How to Ask Questions 5.6 127 144 Simulations for Further Exploration 5 117 Probability 203 224 233 7.1 7.2 7.3 Random Circumstances 233 Interpretations of Probability 235 Probability Definitions and Relationships 7.4 7.5 Basic Rules for Finding Probabilities 245 Conditional Probabilities and Bayes'Rule 252 7.6 7.7 Using Simulation to Estimate Probabilities 259 Flawed Intuitive Judgments About Probability 261 Key Terms 240 268 In Summary Boxes 268 J
Contents Simulations for Further Exploration Exercises 8 Random Variables 281 8.1 What Is a Random Variable? 8.2 8.3 Discrete Random Variables 284 Expectations for Random Variables 8.4 8.5 Binomial Random Variables 294 Continuous Random Variables 299 8.6 Normal Random Variables 301 Approximating Binomial Distribution Probabilities 8.7 8.8 281 289 312 Linear Combinations and Linear Transformations of Random Variables 316 Key Terms 323 In Summary Boxes 323 Simulations for Further Exploration Exercises 9 268 269 323 324 Understanding Sampling Distributions: Statistics as Random Variables 337 9.1 Parameters, Statistics, and Statistical Inference 9.2 9.3 From Curiosity to Questions About Parameters 340 SD Module 0: An Overview of Sampling Distributions 9.4 SD Module 1 : Sampling Distribution for One Sample Proportion 348 SD Module 2: Sampling Distribution for the Difference in Two Sample Proportions 353 SD Module 3: Sampling Distribution for One Sample Mean 357 SD Module 4: Sampling Distribution for the Sample Mean of Paired Differences 361 SD Module 5: Sampling Distribution for the Difference in Two Sample Means 364 Preparing for Statistical Inference: Standardized Statistics 367 9.5 9.6 9.7 9.8 9.9 337 345 Lesson 1 : Standardized Statistics for Sampling Distributions Lesson 2: Standardized Statistics for Proportions Lesson 3: Standardized Statistics for Means 9.10 Generalizations Beyond the Big Five Key Terms 378 In Summary Boxes 378 Simulations for Further Exploration Exercises 371 379 379 368 367 367 vii
10 Estimating Proportions with Confidence 10.1 397 Cl Module 0: An Overview of Confidence Intervals Lesson 1:The Basic Idea of a Confidence Interval 397 397 Lesson 2: Computing Confidence Intervals for the Big Five Parameters 10.2 400 Cl Module 1 : Confidence Intervals for Population Proportions 403 Lesson 1 : Details of How to Compute a Confidence Interval for a Population Proportion 403 Lesson 2: Understanding the Formula 406 Lesson 3: Reconciling and Understanding Different Margin of Error Formulas 409 10.3 Cl Module 2: Confidence Intervals for the Difference In Two Population Proportions 412 10.4 Using Simulation to Calculate Confidence Intervals: Bootstrapping 416 Using Confidence Intervals to Guide Decisions 422 10.5 Key Terms 426 In Summary Boxes 427 Simulations for Further Exploration Exercises 11 427 427 Estimating Means with Confidence 11.1 11.2 441 Introduction to Confidence Intervals for Means 441 Cl Module 3: Confidence Intervals for One Population Mean 449 Lesson 1: Finding a Confidence Interval for a Mean for Any Sample Size and Any Confidence Level 449 Lesson 2: Special Case: Approximate 95% Confidence Intervals for Large Samples 11.3 і 11.4 ֊ 455 Cl Module 4: Confidence Intervals for the Population Mean of Paired Differences 457 Cl Module 5: Confidence Intervals for the Difference in Two Population Means (Independent Samples) Lesson 1 : The General (Unpooled) Case 462 462 Lesson 2: The Equal Variance Assumption and the Pooled Standard Error 11.5 11.6 468 Using Simulation to Calculate Confidence Intervals: Bootstrapping for Means and Other Parameters 472
Understanding Any Confidence Interval 479 Key Terms 482 In Summary Boxes 482 Simulations for Further Exploration Exercises 483 482
Contents 12 Testing Hypotheses About Proportions 12.1 497 HT Module 0: An Overview of Hypothesis Testing Lesson 1: Formulating Hypothesis Statements 498 498 Lesson 2: Test Statistic, p-Value, and Deciding Between the Hypotheses 501 Lesson 3: What Can Go Wrong: The Two Types of Errors and Their Probabilities 508 12.2 HT Module 1 :Testing Hypotheses About a Population Proportion 512 12.3 HT Module 2: Testing Hypotheses About the Difference in Two Population Proportions 524 Using Resampling to Estimate the p-Value for Testing Hypotheses About Two Proportions 529 12.4 12.5 12.6 Sample Size, p-Values, and Power 533 Understanding and Addressing Criticisms of Significance Testing 538 Key Terms 548 In Summary Boxes 548 Simulations for Further Exploration Exercises 13 548 549 Testing Hypotheses About Means 567 13.1 Introduction to Hypothesis Tests for Means 13.2 HT Module 3:Testing Hypotheses About One Population Mean 569 HT Module 4: Testing Hypotheses About the Population Mean of Paired Differences 575 HT Module 5: Testing Hypotheses About the Difference in Two Population Means (Independent Samples) 579 13.3 13.4 Lesson 1 : The General (Unpooled) Case 567 579 Lesson 2: The Pooled Two-Sample f֊Test 585 Lesson 3: Randomization Test for Comparing Two Means The Relationship Between Significance Tests and Confidence Intervals 591 13.6 Choosing an Appropriate Inference Procedure 13.7 Effect Size 13.8 Evaluating Statistical Results in Research Reports Key Terms 607 608 608 Inference About Simple Regression 14.1 14.2 603 607 In Summary Boxes Exercises 594 598 Simulations for Further
Exploration 14 588 13.5 623 Sample and Population Regression Models 624 Estimating the Standard Deviation for Regression 631 ix
14.3 Inference About the Slope ofa Linear Regression 635 14.4 Predicting y and Estimating Mean y at a Specific x 638 14.5 Checking Conditions for Using Regression Models for Inference 644 Key Terms 650 In Summary Boxes 650 Simulations for Further Exploration Exercises 15 More About Inference for Categorical Variables 15.1 The Chi-Square Test for Two-Way Tables 15.2 Methods for Analyzing 2 X 2Tables 15.3 Testing Hypotheses About One Categorical Variable: Goodness-of-Fit 680 Key Terms 686 In Summary Boxes Analysis of Variance 661 673 686 701 16.1 Comparing Means with an ANOVA f-Test 16.2 Details of One-Way Analysis of Variance 702 710 16.3 Other Methods for Comparing Populations 16.4 Two-Way Analysis of Variance Key Terms 724 In Summary Boxes 724 724 724 17 Turning Information into Wisdom 17.1 Beyond the Data I 17.2 17.3 17.4 17.5 Transforming Uncertainty into Wisdom Making Personal Decisions 738 Controlling Societal Risks 740 Understanding Our World 742 Getting to Know You 17.7 Words to the Wise 745 In Summary Boxes 746 738 743 746 Appendix of Tables References 735 735 17.6 Exercises 716 720 Simulations for Further Exploration Exercises 751 759 Answers to Selected Odd-Numbered Exercises Index 790 661 686 Simulations for Further Exploration Exercises 687 16 650 651 765
Conients Instructors: The Supplemental Topics are available on the book companion website, http://www.cengage.com/statistics/Utts6e. supplemental topic 1 Additional Discrete Random Variables 51.1 51.2 Hypergeometric Distribution Poisson Distribution 51.3 Multinomial Distribution 51.4 Negative Binomial and Geometric Distributions Key Terms Exercises supplemental тож 2 Nonparametric Tests of Hypotheses 52.1 The Sign Test 52.2 52.3 The Two-Sample Rank-Sum Test TheWilcoxon Signed-RankTest 52.4 The Kruskal-Wallis Test Key Terms Exercises supplemental topic 3 Multiple Regression 53.1 53.2 The Multiple Linear Regression Model Inference About Multiple Regression Models 53.3 Checking Conditions for Multiple Linear Regression Key Terms Exercises supplemental topic 4 Two-Way Analysis ofVariance 54.1 54.2 Assumptions and Models for Two-Way ANOVA Testing for Main Effects and Interactions Key Terms Exercises supplemental topic 5 Ethics 55.1 Ethical Treatment of Human and Animal Participants 55.2 Assurance of Data Quality 55.3 55.4 Appropriate Statistical Analyses Fair Reporting of Results Key Terms Exercises |
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