Introductory Statistics

An updated and revised edition of the popular introduction to statistics for students of economics or business, suitable for a one- or two-semester course. Presents an approach that is generally available only in much more advanced texts, yet uses the simplest mathematics consistent with a sound presentation. This Fifth Edition includes a wealth of new problems and examples (many of them real-life problems drawn from the literature) to support the theoretical discussion. Emphasizes the regression model, including nonlinear and multiple regression. Topics covered include randomization to eliminate bias, exploratory data analysis, graphs, expected value in bidding, the bootstrap, path analysis, robust estimation, maximum likelihood estimation and Bayesian estimation and decisions.

Thomas H. Wonnacott is the author of Introductory Statistics, 5th Edition, published by Wiley.

Ronald Johnston Wonnacott OC FRSC was a Canadian economist. Wonnacott received his bachelor's and master's degrees from the University of Western Ontario, then earned a doctorate from Harvard University. He taught at Western from 1958 to 1996, and served as William G. Davis Professor of International Trade.

PART I BASIC PROBABILITY AND STATISTICS

1

(186)

The Nature of Statistics

3

(22)

Random Sampling: A Political Poll

4

(6)

Randomized Experiments: Testing a Hospital Routine

10

(4)

Observational Studies vs. Randomized Experiments

14

(6)

Brief Outline of the Book

20

(5)

Summary

20

(5)

Descriptive Statistics

25

(44)

Frequency Tables and Graphs

26

(6)

Center of a Distribution

32

(7)

Spread of a Distribution

39

(7)

Statistics by Computer

46

(1)

Linear Transformations

47

(5)

Calculations Using Relative Frequencies

52

(1)

The Use and Misuse of Graphs

53

(16)

Summary

64

(5)

Probability

69

(40)

Introduction

70

(3)

Probability Models

73

(6)

Compound Events

79

(6)

Conditional Probability

85

(4)

Independence

89

(4)

Bayes Theorem: Tree Reversal

93

(6)

Other Views of Probability

99

(10)

Summary

103

(6)

Probability Distributions

109

(44)

Discrete Random Variables

110

(3)

Mean and Variance

113

(3)

The Binomial Distribution

116

(8)

Continuous Distributions

124

(3)

The Normal Distribution

127

(7)

A Function of a Random Variable

134

(7)

Expected Value in Bidding

141

(12)

Summary

146

(7)

Two Random Variables

153

(34)

Distributions

154

(7)

A Function of Two Random Variables

161

(3)

Covariance

164

(6)

Linear Combination of Two Random Variables

170

(17)

Summary

176

(6)

Review Problems

182

(5)

PART II INFERENCE FOR MEANS AND PROPORTIONS

187

(168)

Sampling

189

(42)

Random Sampling

190

(6)

Moments of the Sample Mean

196

(3)

The Shape of the Sampling Distribution

199

(8)

Proportions (Percentages)

207

(8)

Small-Population Sampling

215

(3)

Monte Carlo

218

(13)

Summary

225

(6)

Point Estimation

231

(22)

Populations and Samples

232

(1)

Efficiency of Unbiased Estimators

232

(7)

Efficiency of Biased and Unbiased Estimators

239

(5)

Consistent Estimators

244

(9)

Summary

248

(5)

Confidence Intervals

253

(34)

A Single Mean

254

(7)

Small-Sample t

261

(4)

Difference in Two Means, Independent Samples

265

(3)

Difference in Two Means, Matched Samples

268

(5)

Proportions

273

(4)

The Bootstrap

277

(10)

Summary

281

(6)

Hypothesis Testing

287

(37)

Hypothesis Testing Using Confidence Intervals

288

(5)

p-Value (One-Sided)

293

(7)

Classical Hypothesis Tests

300

(6)

Classical Tests Reconsidered

306

(4)

Operating Characteristics Curve (OCC)

310

(4)

Two-Sided Tests

314

(10)

Summary

320

(4)

Analysis of Variance (ANOVA)

324

(31)

One-Way ANOVA

325

(11)

Two-Way ANOVA

336

(7)

Confidence Intervals

343

(12)

Summary

346

(4)

Review Problems

350

(5)

PART III REGRESSION: RELATING TWO OR MORE VARIABLES

355

(160)

Fitting a Line

357

(14)

Introduction

358

(2)

Ordinary Least Squares (OLS)

360

(6)

Advantages of OLS and WLS

366

(5)

Summary

368

(3)

Simple Regression

371

(25)

The Regression Model

372

(3)

Sampling Variability

375

(4)

Confidence Intervals and Tests for β

379

(4)

Predicting Y at a Given Level of X

383

(6)

Extending the Model

389

(7)

Summary

390

(6)

Multiple Regression

396

(38)

Why Multiple Regression?

397

(3)

The Regression Model and Its OLS Fit

400

(6)

Confidence Intervals and Statistical Tests

406

(4)

Regression Coefficients as Multiplication Factors

410

(7)

Simple and Multiple Regression Compared

417

(7)

Path Analysis

424

(10)

Summary

428

(6)

Regression Extensions

434

(40)

Dummy (0-1) Variables

435

(10)

Analysis of Variance (ANOVA) by Regression

445

(4)

Simplest Nonlinear Regression

449

(3)

Nonlinearity Removed by Logs

452

(9)

Diagnosis by Residual Plots

461

(13)

Summary

466

(8)

Correlation

474

(41)

Simple Correlation

475

(7)

Correlation and Regression

482

(7)

The Two Regression Lines

489

(7)

Correlation in Multiple Regression

496

(5)

Multicollinearity

501

(14)

Summary

506

(6)

Review Problems

512

(3)

PART IV TOPICS IN CLASSICAL AND BAYESIAN INFERENCE

515

(122)

Nonparametric and Robust Statistics

517

(32)

Introduction: Mean or Median?

518

(1)

Sign Test for the Median

518

(4)

Confidence Interval for the Median

522

(3)

Wilcoxon Rank Test

525

(3)

Rank Tests in General

528

(5)

Runs Test for Independence

533

(3)

Robust Statistics: Trimming and Weighting

536

(13)

Summary

545

(4)

Chi-Square Tests

549

(15)

χ2 Tests for Multinomials: Goodness of Fit

550

(5)

χ2 Tests for Independence: Contingency Tables

555

(9)

Summary

561

(3)

Maximum Likelihood Estimation

564

(18)

Introduction

565

(1)

MLE for Some Familiar Cases

566

(7)

MLE for the Uniform Distribution

573

(3)

MLE in General

576

(6)

Summary

579

(3)

Bayesian Inference

582

(38)

Posterior Distributions

583

(5)

The Population Proportion

588

(10)

The Mean μ in a Normal Model

598

(7)

The Slope β in Normal Regression

605

(3)

Bayesian Shrinkage Estimates

608

(7)

Classical and Bayesian Estimates Compared

615

(5)

Summary

615

(5)

Bayesian Decision Theory

620

(17)

Maximizing Gain (or Minimizing Loss)

621

(6)

Point Estimation as a Decision

627

(6)

Classical and Bayesian Statistics Compared

633

(4)

Summary

635

(2)

Appendixes

637

(26)

2-2 Careful Approximation of the Median

638

(1)

2-5 Effects of a Linear Transformation: Proofs

638

(1)

3-7 Probability as Axiomatic Mathematics

638

(1)

4-2 Easier Formula for σ2: Proof

639

(1)

4-3 Binomial Formula: Proof

639

(2)

4-4 Calculus for Continuous Distributions

641

(1)

5-3 Independent Implies Uncorrelated: Proof

642

(1)

5-4 Linear Combinations: Proofs

642

(1)

6-3 Central Limit Theorem

643

(1)

6-4 Continuity Correction: Graphical Explanation

643

(1)

7-2 Standard Error of X

643

(1)

7-4 Consistency: Careful Definition

644

(1)

8-3 Standard Error of (X1 - X2): Proof

645

(1)

8-5 Confidence Interval for π Derivation of Graph

645

(1)

9-2 A More Exact p-Value for Proportions

646

(1)

10-1 Breakdown of Total SS: Proof

647

(1)

10-2 Two-Way ANOVA, Breakdown of Total SS: Proof

647

(1)

10-3 ANOVA Is Much More Than Just Testing H0

648

(1)

11-1 Lines and Planes

648

(2)

11-2 Least-Squares Formulas: Proofs

650

(1)

12-2 The Moments of b: Proofs and Discussion

651

(2)

12-3 A One-sided or Two-sided Test?

653

(1)

12-4 Confidence Intervals above X0: Proofs

654

(1)

13-2 Solution of a Set of Simultaneous Equations

655

(1)

13-5 Direct Plus Indirect Relation: Proof

656

(1)

14-4 Log Regression Handles a Multiplicative Error Term

656

(1)

15-1 Correlation in Chapter 15 Agrees with Chapter 5

657

(1)

15-2 ANOVA and r2: Proofs

657

(1)

18-2 MLE for Some Familiar Cases: Proofs

658

(2)

19-2 Bayesian Confidence Interval for π Proof

660

(1)

19-3 Posterior Distribution of μ in a Normal Model: Proof

661

(1)

19-4 Posterior Distribution of β in Normal Regression: Proof

661

(1)

19-5 Bayesian Shrinkage Confidence Intervals

662

(1)

Tables

663

(16)

References

679

(6)

Answers to Odd-Numbered Problems

685

(14)

Glossary of Common Symbols

699

(4)

Index of Examples and Problems

703

(2)

Index

705

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Introductory Statistics

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Table of Contents

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Summary

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