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PART Ⅰ: Data1

CHAPTER1Looking at Data-Distributions2

Introduction4

Variables4

1.1 Displaying Distributions with Graphs5

Graphs for categorical variables6

Measuring the speed of light7

Measurement8

Variation9

Stemplots10

Examining distributions13

Histograms14

Looking at data17

Time plots18

Beyond the basics: decomposing time series21

Section 1.1 Exercises23

1.2 Describing Distributions with Numbers40

Measuring center: the mean41

Measuring center: the median42

Mean versus median43

Measuring spread: the quartiles44

Measuring spread: the interquartile range46

The five-number summary and boxplots47

Comparing distributions50

Measuring spread: the standard deviation51

Properties of the standard deviation53

Choosing measures of center and spread54

Changing the unit of measurement55

Section 1.2 Exercises58

1.3 The Normal Distributions64

Density curves66

Measuring center and spread for density curves68

Normal distributions70

The 68-95-99.7 rule72

Standardizing observations73

The standard normal distribution74

Normal distribution calculations76

Normal quantile plots79

Beyond the basics: density estimation84

Section 1.3 Exercises85

Chapter 1 Exercises93

CHAPTER 2Looking at Data-Relationships102

Introduction104

Getting started104

2.1 Scatterplots106

Interpreting scatterplots107

Adding categorical variables to scatterplots108

More examples of scatterplots109

Beyond the basics: scatterplot smoothers112

Categorical explanatory variables115

Section 2.1 Exercises117

2.2 Correlation126

The correlation r126

Properties of correlation128

Section 2.2 Exercises131

2.3 Least-Squares Regression135

Fitting a line to data137

Prediction137

Least-squares regression139

Interpreting the regression line142

Correlation and regression142

Understanding r 2 145

Section 2.3 Exercises148

2.4 Cautions about Regression and Correlation153

Residuals154

Lurking variables156

Outliers and inuential observations160

Beyond the basics: regression diagnostics163

Beware the lurking variable166

Beware correlations based on averaged data167

The restricted-range problem168

Section 2.4 Exercises169

2.5 An Application: Exponential Growth and WorldOil Production181

The nature of exponential growth181

The logarithm transformation184

Residuals again185

Prediction in the exponential growth model188

Section 2.5 Exercises189

2.6 Relations in Categorical Data193

Marginal distributions194

Describing relationships196

Conditional distributions196

Simpson's paradox199

The perils of aggregation200

Section 2.6 Exercises201

2.7 The Question of Causation207

Explaining association: causation208

Explaining association: common response209

Explaining association: confounding209

Establishing causation210

Section 2.7 Exercises212

Chapter 2 Exercises214

CHAPTER 3Producing Data228

Introduction230

3.1 First Steps230

Where to find data: the libraryand the Internet231

Sampling233

Experiments234

Section 3.1 Exercises235

3.2 Design of Experiments237

Comparative experiments239

Randomization241

Randomized comparative experiments242

How to randomize243

Cautions about experimentation246

Matched pairs design246

Block designs247

Section 3.2 Exercises250

3.3 Sampling Design256

Simple random samples257

Stratified samples258

Multistage samples259

Cautions about sample surveys260

Section 3.3 Exercises262

3.4 Toward Statistical Inference267

Sampling variability268

Sampling distributions269

The bias of a statistic272

The variability of a statistic272

Bias and variability274

Why randomize?275

Beyond the basics: capture-recapture sampling275

Section 3.4 Exercises277

Chapter 3 Exercises281

PART Ⅱ: Probability and Inference287

CHAPTER 4Probability: The Study of Randomness288

4.1 Randomness290

The language of probability290

Thinking about randomness291

The uses of probability292

Section 4.1 Exercises293

4.2 Probability Models295

Sample spaces295

Intuitive probability297

Probability rules298

Assigning probabilities:nite number of outcomes299

Assigning probabilities: equally likely outcomes300

Independence and the multiplication rule301

Applying the probability rules304

Section 4.2 Exercises306

4.3 Random Variables312

Discrete random variables313

Continuous random variables317

Normal distributions as probability distributions320

Section 4.3 Exercises322

4.4 Means and Variances of Random Variables326

The mean of a random variable326

Statistical estimation and the law of large numbers328

Thinking about the law of large numbers331

Beyond the basics: more laws of large numbers333

Rules for means333

The variance of a random variable335

Rules for variances337

Section 4.4 Exercises340

4.5 General Probability Rules346

General addition rules347

Conditional probability350

General multiplication rules353

Tree diagrams354

Bayes's rule355

Independence again356

Decision analysis357

Section 4.5 Exercises359

Chapter 4 Exercises365

CHAPTER 5From Probability to Inference373

Introduction374

5.1 Sampling Distributions for Counts and Proportions375

The binomial distributions for sample counts375

Binomial distributions in statistical sampling377

Finding binomial probabilities: tables378

Binomial mean and standard deviation380

Sample proportions381

Normal approximation for counts and proportions382

The continuity correction386

Binomial formulas387

Section 5.1 Exercises390

5.2 The Sampling Distribution of a Sample Mean397

The mean and standard deviation of x398

The sampling distribution of x400

The central limit theorem401

Beyond the basics: Weibull distributions406

Section 5.2 Exercises408

5.3 Control Charts415

x control charts415

Statistical process control418

Using control charts419

Section 5.3 Exercises422

Chapter 5 Exercises428

CHAPTER 6Introduction to Inference432

Introduction434

6.1 Estimating with Confidence435

Statistical confidence435

Confidence intervals437

Confidence interval for a population mean439

How confidence intervals behave441

Choosing the sample size443

Some cautions444

Beyond the basics: the bootstrap445

Section 6.1 Exercises447

6.2 Tests of Significance453

The reasoning of signicance tests453

Stating hypotheses454

Test statistics456

P -values457

Statistical significance458

Tests for a population mean460

Two-sided significance tests and confidence intervals463

P -values versus fixed a466

Section 6.2 Exercises468

6.3 Use and Abuse of Tests475

Choosing a level of significance476

What statistical significance doesn't mean477

Don't ignore lack of significance478

Statistical inference is not valid for all sets of data479

Beware of searching for significance479

Section 6.3 Exercises481

6.4 Power and Inference as a Decision483

Power483

Increasing the power486

Inference as decision488

Two types of error488

Error probabilities490

The common practice of testing hypotheses492

Section 6.4 Exercises493

Chapter 6 Exercises496

CHAPTER 7Inference for Distributions502

7.1 Inference for the Mean of a Population504

The t distributions504

The one-sample t condence interval505

The one-sample t test507

Matched pairs t procedures513

Robustness of the t procedures515

The power of the t test517

Inference for nonnormal populations518

The sign test519

Section 7.1 Exercises523

7.2 Comparing Two Means537

The two-sample z statistic538

The two-sample t procedures540

The two-sample t signicance test541

The two-sample t condence interval544

Robustness of the two-sample procedures545

Inference for small samples546

Software approximation for the degrees of freedom549

The pooled two-sample t procedures550

Section 7.2 Exercises556

7.3 Optional Topics in Comparing Distributions566

Inference for population spread566

The F test for equality of spread567

Robustness of normal inference procedures570

The power of the two-sample t -test570

Section 7.3 Exercises573

Chapter 7 Exercises575

CHAPTER 8Inference for Proportions584

8.1 Inference for a Single Proportion586

Condence interval for a single proportion586

Significance test for a single proportion588

Confidence intervals provide additional information591

Choosing a sample size592

Section 8.1 Exercises596

8.2 Comparing Two Proportions601

Confidence intervals602

Significance tests604

Beyond the basics: relative risk607

Section 8.2 Exercises609

Chapter 8 Exercises615

PART Ⅲ: Topics in Inference621

CHAPTER 9Inference for Two-Way Tables622

9.1 Inference for Two-Way Tables624

The two-way table624

Describing relations in two-way tables626

The hypothesis: no association628

Expected cell counts629

The chi-square test629

The chi-square test and the z test632

Beyond the basics: meta-analysis632

9.2 Formulas and Models for Two-Way Tables634

Computations634

Computing conditional distributions635

Computing expected cell counts637

Computing the chi-square statistic638

Models for two-way tables639

Comparing several populations: the first model640

Testing independence: the second model641

Concluding remarks642

chapter9 Exercses643

CHAPTER 10Inference for Regression660

10.1 Simple Linear Regression662

Statistical model for linear regression662

Data for simple linear regression663

Estimating the regression parameters666

Confidence intervals and signicance tests671

Confidence intervals for mean response673

Prediction intervals676

Beyond the basics: nonlinear regression678

10.2 More Detail about Simple Linear Regression681

Analysis of variance for regression681

The ANOVA F684

Calculations for regression inference686

Preliminary calculations687

Inference for slope and intercept688

Confidence intervals for the mean response and predictionintervals for a future observation690

Inference for correlation691

chapter10Exercises695

CHAPTER 11Multiple Regression710

Population multiple regression equation712

Data for multiple regression713

Multiple linear regression model713

Estimation of the multiple regression parameters714

Confidence intervals and significance tests for regressioncoeficients715

ANOVA table for multiple regression717

Squared multiple correlation R 2718

A case study: preliminary analysis719

Relationships between pairs of variables721

Regression on high school grades722

Interpretation of results723

Residuals724

Refining the model724

Regression on SAT scores726

Regression using all variables726

Test for a collection of regression coefficients728

Beyond the basics: multiple logistic regression730

Chapter 11 Exercises732

CHAPTER 12One-Way Analysis of Variance742

Data for a one-way ANOVA744

Comparing means745

The two-sample t statistic747

ANOVA hypotheses747

The ANOVA model750

Estimates of population parameters751

Testing hypotheses in one-way ANOVA753

The ANOVA table757

The F test759

Contrasts762

Multiple comparisons769

Software773

Power775

Chapter 12 Exercises779

CHAPTER 13Two-Way Analysis of Variance798

Advantages of two-way ANOVA800

The two-way ANOVA model803

Main effects and interactions804

The ANOVA table for two-way ANOVA809

Chapter 13 Exercises815