Chance Encounters A First Course in Data Analysis and Inference

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ISBN: 9780471329367 | 0471329363
Cover: Hardcover
Copyright: 11/30/1999

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This unique book combines lucid and engaging exposition, graphic and poignantly applied examples, and realistic exercises to take readers beyond the mechanics of statistical techniques. The result is a journey into the realm of practical data analysis and inference-based problem solving.

What Is Statistics?

(37)

Polls and Surveys

(16)

Random Sampling

(3)

Errors in Surveys

(6)

Unrepresentative Information Can Be Useful

(1)

Preparing for a Survey

(1)

Who Uses Survey Methods?

(2)

Experimentation

(6)

Observational Studies

(4)

Statistics: What Is It, and Who Uses It?

(3)

Summary

(6)

Review Exercises 1

(4)

Tools for Exploring Univariate Data

(64)

Introduction

(5)

Types of Variables

(3)

Presentation of Data

(4)

The Roles of Numbers

(1)

Guidelines for Tabular Presentation

(3)

Simple Plots for Continuous Variables

(14)

Dot Plots

(2)

Stem-and-Leaf Plots

(6)

Histograms

(3)

Interpreting Stem-and-Leaf Plots and Histograms

(3)

Numerical Summaries for Continuous Variables

(14)

Locating the Center of the Data

(5)

The Five-Number Summary

(4)

Measuring the ``Spread'' of the Data

(3)

Plotting Data Summaries: The Box Plot

(2)

Repeated and Grouped Data

(6)

Repeated Data (Discrete Variables)

(5)

Grouped Data (Continuous Variables)

(1)

Qualitative Variables

(8)

Other Forms of Graphs

(1)

Choosing between Types of Graphs

(1)

Pareto Chart

(3)

Summary

(12)

Numbers and Tables of Data

(1)

Plotting

(1)

Review Exercises 2

(10)

Exploratory Tools for Relationships

101

(38)

Two Quantitative Variables

102

(15)

Plotting the Data

102

(5)

Modeling the Relationship

107

(7)

The Prediction Problem

114

(2)

Other Patterns

116

(1)

Quantitative versus Qualitative Variables

117

(7)

Using Dot Plots

120

(1)

Using Stem-and-Leaf Plots

120

(2)

Using Box Plots

122

(1)

An Organized Approach to Comparing Groups

123

(1)

Two Qualitative Variables

124

(4)

Are the Patterns You See Real or Random?

128

(2)

Summary

130

(9)

Review Exercises 3

131

(8)

Probabilities and Proportions

139

(58)

Introduction

139

(2)

Coin Tossing and Probability Models

141

(2)

Where Do Probabilities Come From?

143

(6)

Probabilities from Models

144

(1)

Probabilities from Data

145

(1)

Subjective Probabilities

146

(1)

Manipulation of Probabilities

147

(2)

Simple Probability Models

149

(9)

Sample Spaces

149

(1)

Events

150

(2)

Combining Events

152

(1)

Probability Distributions

153

(4)

Probabilities and Proportions

157

(1)

Probability Rules

158

(5)

Addition Rule for More Than Two Mutually Exclusive Events

160

(3)

Conditional Probability

163

(14)

Definition

163

(4)

Multiplication Rule

167

(2)

More-Complicated Calculations Using Conditional Probabilities

169

(8)

Statistical Independence

177

(7)

Two Events

177

(3)

Positive and Negative Association

180

(1)

Mutual Independence of More Than Two Events

181

(3)

Summary

184

(13)

Summary of Concepts

184

(1)

Summary of Useful Formulas

185

(1)

Review Exercises 4

186

(11)

Discrete Random Variables

197

(34)

Random Variables

197

(1)

Probability Functions

198

(6)

The Binomial Distribution

204

(10)

Sampling from a Finite Population

204

(1)

The Binomial Assumptions

205

(5)

Sampling from a Finite Population Revisited

210

(4)

Expected Values

214

(8)

Formula and Terminology

214

(5)

Population Standard Deviation

219

(1)

The Effect of Rescaling Random Variables

220

(2)

Summary

222

(9)

Review Exercises 5

223

(8)

Continuous Random Variables

231

(46)

Introduction

231

(6)

Proportions as Areas: The Standardized Histogram

231

(2)

Probabilities and Density Curves

233

(1)

Some Comparisons with the Discrete Case

234

(3)

The Normal Distribution

237

(10)

Introducing the Normal Distribution

237

(2)

Obtaining Probabilities

239

(5)

The Inverse Problem: Percentiles and Quantiles

244

(2)

Central Ranges

246

(1)

Working in Standard Units

247

(5)

The z-Score

247

(2)

Central Ranges and Extremes Using z-Scores

249

(2)

Obtaining Normal-Distribution Probabilities from Tables

251

(1)

Sums and Differences of Random Quantities

252

(14)

Variation and Its Propagation

252

(3)

Investigating the Behavior of a Sum and a Difference

255

(3)

Working with Sums and Differences

258

(5)

Application to Random Samples

263

(3)

Summary

266

(11)

Continuous Variables and Density Curves

266

(1)

The Normal Distribution

267

(1)

Combining Random Quantities

267

(1)

Review Exercises 6

268

(9)

Sampling Distributions of Estimates

277

(50)

Parameters and Estimates

278

(2)

Capital Letters and Small Letters: Estimates and Estimators

279

(1)

Sampling Distribution of the Sample Mean

280

(12)

Means of Random Samples

280

(4)

The Central Limit Effect

284

(6)

Introducing the Standard Error

290

(2)

Sampling Distribution of the Sample Proportion

292

(5)

Sample Proportions and Their Standard Errors

292

(4)

Some Asides about Polling

296

(1)

Estimates That Are Approximately Normal

297

(4)

Bias, Precision, and Accuracy

298

(1)

Interval Estimates

299

(1)

How Many Significant Figures?

300

(1)

Standard Errors of Differences

301

(7)

Standard Error for a Difference (Independent Samples)

302

(2)

Interpreting an Interval for a Difference

304

(1)

Individual Two-Standard-Error Intervals and Differences

305

(3)

Student's t-Distribution

308

(5)

Introduction

308

(1)

The Usefulness of Student's t-Distribution

309

(1)

Upper-Tail Probabilities and Percentage Points

310

(3)

Summary

313

(14)

Sampling Distributions

313

(1)

Estimation

314

(1)

Student's t-Distribution

315

(1)

Review Exercises 7

315

(12)

Confidence Intervals

327

(40)

Introduction

327

(8)

Adjusting the Confidence Level

331

(2)

How Can We Make a Precise Statement with Confidence?

333

(1)

Conservative Confidence Levels

334

(1)

Means

335

(2)

Proportions

337

(1)

Comparing Two Means

338

(3)

Comparing Two Proportions

341

(10)

Independence Case

341

(2)

Other Common Comparisons

343

(6)

``Margins of Error'' in Media Reports

349

(2)

How Big Should My Study Be?

351

(3)

Proportions

351

(1)

Means

352

(2)

Summary

354

(13)

Review Exercises 8

355

(12)

Significance Testing: Using Data to Test Hypotheses

367

(42)

Getting Started

368

(6)

Examples

368

(3)

Measuring Distance in Numbers of Standard Errors

371

(1)

The Difference between Tests and Intervals

372

(2)

What Do We Test? Types of Hypotheses

374

(4)

We Cannot Prove That a Hypothesized Value Is True

374

(1)

The Research Hypothesis and the Null Hypothesis

375

(1)

The Alternative Hypothesis (H1)

376

(2)

Measuring the Evidence against a Null Hypothesis

378

(11)

t-Tests and P-Values

378

(5)

Further Examples

383

(6)

Hypothesis Testing as Decision Making

389

(2)

Why Tests Should Be Supplemented by Intervals

391

(5)

A Relationship between Tests and Intervals

391

(1)

Interpreting the Word Significant

392

(3)

How Do You Show That a Hypothesis Is True?

395

(1)

Detecting Differences When They Matter

396

(1)

The Test Statistic and the P-Value as General Ideas

397

(1)

Summary

398

(11)

Hypotheses

398

(1)

P-Values

399

(1)

Significance

399

(1)

Review Exercises 9

400

(9)

Data on a Continuous Variable

409

(58)

One-Sample Issues

410

(18)

Tests and Confidence Intervals for a Mean

410

(7)

Paired Comparisons

417

(6)

A Nonparametric Test

423

(3)

Inferences about Spread

426

(2)

Two Independent Samples

428

(6)

Questions of Study Design and Analysis

428

(3)

Comparing Two Means

431

(3)

More Than Two Samples

434

(11)

One-Way Analysis of Variance and the F-Test

434

(4)

The F-Test and the Analysis-of-Variance Table

438

(7)

Blocking, Stratification, and Related Samples

445

(5)

Pairing

445

(3)

More General Blocking and Stratification

448

(2)

Summary

450

(17)

Some General Ideas about Analyzing Data

450

(1)

Normal Theory Techniques

451

(1)

Study Design and Interpretation

452

(1)

Review Exercises 10

452

(15)

Tables of Counts

467

(36)

One-Dimensional Tables

468

(7)

The Chi-Square Test for Goodness of Fit

469

(4)

Tables for the Chi-Square Distribution

473

(2)

Two-Way Tables of Counts

475

(16)

Introduction

475

(6)

The Chi-Square Test of Homogeneity

481

(6)

The Chi-Square Test of Independence

487

(2)

2 X 2 Tables

489

(2)

The Validity of the Chi-Square Test

491

(1)

The Perils of Collapsing Tables

491

(2)

Summary

493

(10)

General Ideas about Chi-Square Tests

493

(1)

One-Dimensional Tables

493

(1)

Two-Way Tables

494

(1)

Review Exercises 11

495

(8)

Relationships between Quantitative Variables: Regression and Correlation

503

(54)

Why Do Regression?

504

(5)

Correlation versus Regression

504

(1)

Causal Relationships

504

(4)

Inferences about Theories

508

(1)

Introduction to Relationship Modeling

509

(6)

The Straight Line

511

(1)

Extensions

512

(1)

The Exponential Curve

512

(2)

Other Types of Trend Curves

514

(1)

Choosing the Best Line

515

(5)

What Line Fits the Data Best?

516

(2)

The Least-Squares Line

518

(2)

Formal Inference for the Simple Linear Model

520

(19)

The Simple Linear Model

520

(5)

Inferences about the Slope and Intercept

525

(7)

The Regression Model and Prediction

532

(3)

Model Checking

535

(4)

Correlation and Association

539

(6)

Two Regression Lines

539

(1)

The Correlation Coefficient

540

(5)

Summary

545

(12)

Concepts

545

(1)

Linear Relationships

546

(1)

Review Exercises 12

546

(11)

Control Charts See web site

Time Series See web site

APPENDIXES Statistical Tables

557

(12)

A1 Random Numbers

558

(1)

A2 Binomial Distribution (Individual Terms)

559

(3)

A3 Minimum Sample Sizes

562

(1)

A4 Standard Normal Distribution

563

(2)

A5 Additional Standard Normal Tables

565

(1)

A6 Student's t-Distribution

566

(1)

A7 Chi-Square Distribution

567

(2)

References

569

(6)

Answers to Selected Problems

575

(30)

Index

605

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Chance Encounters A First Course in Data Analysis and Inference

Summary

Author Biography

Table of Contents

Supplemental Materials