Mind on Statistics

Front Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Brief Contents......Page 8
Contents......Page 9
Preface......Page 17
1.1 What Is Statistics?......Page 31
1.2 Seven Statistical Stories with Morals......Page 32
1.3 The Common Elements in the Seven Stories......Page 37
Key Terms......Page 38
Exercises......Page 39
2.1 Raw Data......Page 43
2.2 Types of Variables......Page 45
2.3 Summarizing One or Two Categorical Variables......Page 49
2.4 Exploring Features of Quantitative Data with Pictures......Page 54
2.5 Numerical Summaries of Quantitative Variables......Page 66
2.6 How to Handle Outliers......Page 77
2.7 Features of Bell-Shaped Distributions......Page 79
2.8 Skillbuilder Applet: The Empirical Rule in Action......Page 86
Key Terms......Page 87
Exercises......Page 88
3.1 Collecting and Using Sample Data Wisely......Page 101
3.2 Margin of Error, Confidence Intervals, and Sample Size......Page 105
3.3 Choosing a Simple Random Sample......Page 110
3.4 Other Sampling Methods......Page 113
3.5 Difficulties and Disasters in Sampling......Page 119
3.6 How to Ask Survey Questions......Page 125
3.7 Skillbuilder Applet: Random Sampling in Action......Page 133
Exercises......Page 136
4.1 Speaking the Language of Research Studies......Page 147
4.2 Designing a Good Experiment......Page 154
4.3 Designing a Good Observational Study......Page 163
4.4 Difficulties and Disasters in Experiments and Observational Studies......Page 166
Key Terms......Page 171
Exercises......Page 172
Relationships Between Quantitative Variables......Page 181
5.1 Looking for Patterns with Scatterplots......Page 182
5.2 Describing Linear Patterns with a Regression Line......Page 187
5.3 Measuring Strength and Direction with Correlation......Page 195
5.4 Regression and Correlation Difficulties and Disasters......Page 201
5.5 Correlation Does Not Prove Causation......Page 206
5.6 Skillbuilder Applet: Exploring Correlation......Page 208
Exercises......Page 211
6.1 Displaying Relationships Between Categorical Variables......Page 223
6.2 Risk, Relative Risk, and Misleading Statistics About Risk......Page 228
6.3 The Effect of a Third Variable and Simpson's Paradox......Page 234
6.4 Assessing the Statistical Significance of a 2 x 2 Table......Page 236
Key Terms......Page 246
Exercises......Page 247
7.1 Random Circumstances......Page 259
7.2 Interpretations of Probability......Page 261
7.3 Probability Definitions and Relationships......Page 268
7.4 Basic Rules for Finding Probabilities......Page 273
7.5 Strategies for Finding Complicated Probabilities......Page 281
7.6 Using Simulation to Estimate Probabilities......Page 289
7.7 Flawed Intuitive Judgments About Probability......Page 291
Exercises......Page 299
8.1 What Is a Random Variable?......Page 309
8.2 Discrete Random Variables......Page 313
8.3 Expectations for Random Variables......Page 318
8.4 Binomial Random Variables......Page 324
8.5 Continuous Random Variables......Page 330
8.6 Normal Random Variables......Page 332
8.7 Approximating Binomial Distribution Probabilities......Page 341
8.8 Sums, Differences, and Combinations of Random Variables......Page 344
Key Terms......Page 350
Exercises......Page 351
9.1 Parameters, Statistics, and Statistical Inference......Page 361
9.2 From Curiosity to Questions About Parameters......Page 364
9.3 SD Module 0: An Overview of Sampling Distributions......Page 374
9.4 SD Module 1: Sampling Distribution for One Sample Proportion......Page 378
9.5 SD Module 2: Sampling Distribution for the Difference in Two Sample Proportions......Page 384
9.6 SD Module 3: Sampling Distribution for One Sample Mean......Page 387
9.7 SD Module 4: Sampling Distribution for the Sample Mean of Paired Differences......Page 392
9.8 SD Module 5: Sampling Distribution for the Difference in Two Sample Means......Page 395
9.9 Preparing for Statistical Inference: Standardized Statistics......Page 398
9.10 Generalizations Beyond the Big Five......Page 403
9.11 Skillbuilder Applet: Finding the Pattern in Sample Means......Page 409
Key Terms......Page 413
Exercises......Page 414
10.1 Introduction......Page 431
10.2 CI Module 0: An Overview of Confidence Intervals......Page 433
10.3 CI Module 1: Confidence Interval for a Population Proportion......Page 440
10.4 CI Module 2: Confidence Intervals for the Difference in Two Population Proportions......Page 453
10.5 Using Confidence Intervals to Guide Decisions......Page 458
Key Terms......Page 462
Exercises......Page 463
Estimating Means with Confidence......Page 473
11.1 Introduction to Confidence Intervals for Means......Page 474
11.2 CI Module 3: Confidence Intervals for One Population Mean......Page 482
11.3 CI Module 4: Confidence Interval for the Population Mean of Paired Differences......Page 491
11.4 CI Module 5: Confidence Interval for the Difference in Two Population Means......Page 496
11.5 Understanding Any Confidence Interval......Page 508
11.6 Skillbuilder Applet: The Confidence Level in Action......Page 510
Key Terms......Page 513
Exercises......Page 514
12.1 Introduction......Page 525
12.2 HT Module 0: An Overview of Hypothesis Testing......Page 526
12.3 HT Module 1: Testing Hypotheses About a Population Proportion......Page 541
12.4 HT Module 2: Testing Hypotheses About the Difference in Two Population Proportions......Page 557
12.5 Sample Size, Statistical Significance, and Practical Importance......Page 563
Exercises......Page 568
13.1 Introduction to Hypothesis Tests for Means......Page 581
13.2 HT Module 3: Testing Hypotheses About One Population Mean......Page 583
13.3 HT Module 4: Testing Hypotheses About the Population Mean of Paired Differences......Page 591
13.4 HT Module 5: Testing Hypotheses About the Difference in Two Population Means......Page 595
13.5 The Relationship Between Significance Tests and Confidence Intervals......Page 604
13.6 Choosing an Appropriate Inference Procedure......Page 606
13.7 Effect Size......Page 610
13.8 Evaluating Significance in Research Reports......Page 615
Key Terms......Page 617
Exercises......Page 618
Inference About Simple Regression......Page 629
14.1 Sample and Population Regression Models......Page 630
14.2 Estimating the Standard Deviation for Regression......Page 635
14.3 Inference About the Slope of a Linear Regression......Page 639
14.4 Predicting y and Estimating Mean y at a Specific x......Page 643
14.5 Checking Conditions for Using Regression Models for Inference......Page 649
Key Terms......Page 655
Exercises......Page 656
15.1 The Chi-Square Test for Two-Way Tables......Page 665
15.2 Analyzing 2 x 2 Tables......Page 676
15.3 Testing Hypotheses About One Categorical Variable: Goodness-of-Fit......Page 682
Exercises......Page 688
16.1 Comparing Means with an ANOVA F-Test......Page 699
16.2 Details of One-Way Analysis of Variance......Page 709
16.3 Other Methods for Comparing Populations......Page 715
16.4 Two-Way Analysis of Variance......Page 719
Exercises......Page 723
17.1 Beyond the Data......Page 735
17.3 Making Personal Decisions......Page 739
17.4 Control of Societal Risks......Page 743
17.5 Understanding Our World......Page 745
17.6 Getting to Know You......Page 748
17.7 Words to the Wise......Page 749
Exercises......Page 751
Appendix of Tables......Page 755
References......Page 763
Answers to Selected Exercises......Page 768
Credits......Page 781
Index......Page 783