Statistics and Data Analysis From Elementary

Introducing the concepts and methods of modern statistics with an emphasis on computer assisted data analysis, the book focuses on interpretation of results rather than their computation. Review of probability, collecting data, summarizing and exploring data, sampling distributions of statistics, basic concepts of inference, linear regression and correlation, analysis of single factor and multifactor Experiments.

Preface

ix

Introduction

1

(6)

What Is Statistics?

1

(1)

The Nature of Statistics?

2

(2)

What Is This Book About?

4

(1)

Advice to the Student

5

(2)

Review of Probability

7

(75)

Basic Ideas

8

(7)

Conditional Probability and Independence

15

(5)

Random Variables and Their Distributions

20

(4)

Expected Value, Variance, and Other Parameters of a Distribution

24

(6)

Jointly Distributed Random Variables

30

(10)

Chebyshev's Inequality and Weak Law of Large Numbers

40

(2)

Selected Discrete Distributions

42

(7)

Selected Continuous Distributions

49

(3)

Normal Distribution

52

(6)

*Transformations of Random Variables

58

(4)

Chapter Summary

62

(20)

Exercises

63

(19)

Collecting Data

82

(25)

Types of Statistical Studies

83

(2)

Observational Studies

85

(6)

Basic Sampling Designs

91

(4)

Experimental Studies

95

(5)

Chapter Summary

100

(7)

Exercises

101

(6)

Summarizing and Exploring Data

107

(60)

Types of Data

107

(2)

Summarizing Categorical Data

109

(1)

Summarizing Numerical Data

109

(19)

Summarizing Bivariate Data

128

(14)

Summarizing Time-Series Data

142

(7)

Chapter Summary

149

(18)

Exercises

150

(17)

Sampling Distributions of Statistics

167

(29)

Sampling Distribution of the Sample Mean

168

(7)

Sampling Distribution of the Sample Variance

175

(4)

Student's t-Distribution

179

(2)

Snedecor-Fisher's F-Distribution

181

(3)

*Sampling Distributions of Order Statistics

184

(3)

Chapter Summary

187

(9)

Exercises

188

(8)

Basic Concepts of Inference

196

(41)

Point Estimation

197

(6)

Confidence Interval Estimation

203

(5)

Hypothesis Testing

208

(19)

Chapter Summary

227

(10)

Exercises

228

(9)

Inferences for Single Samples

237

(32)

Inferences on Mean (Large Samples)

237

(12)

Inferences on Mean (Small Samples)

249

(5)

Inferences on Variance

254

(3)

*Prediction and Tolerance Intervals

257

(3)

Chapter Summary

260

(9)

Exercises

262

(7)

Inferences for Two Samples

269

(30)

Independent Samples and Matched Pairs Designs

269

(2)

Graphical Methods for Comparing Two Samples

271

(1)

Comparing Means of Two Populations

272

(14)

*Comparing Variances of Two Populations

286

(3)

Chapter Summary

289

(10)

Exercises

290

(9)

Inferences for Proportions and Count Data

299

(47)

Inferences on Proportion

299

(8)

Inferences for Comparing Two Proportions

307

(7)

Inferences for One-Way Count Data

314

(7)

Inferences for Two-Way Count Data

321

(8)

Chapter Summary

329

(17)

Exercises

330

(16)

Simple Linear Regression and Correlation

346

(55)

A Probabilistic Model for Simple Linear Regression

347

(1)

Fitting the Simple Linear Regression Model

348

(8)

Statistical Inference for Simple Linear Regression

356

(9)

Regression Diagnostics

365

(14)

*Correlation Analysis

379

(5)

Pitfalls of Regression and Correlation Analyses

384

(1)

Chapter Summary

385

(16)

Exercises

386

(15)

Multiple Linear Regression

401

(56)

A Probabilistic Model for Multiple Linear Regression

402

(1)

Fitting the Multiple Regression Model

403

(2)

*Multiple Regression Model in Matrix Notation

405

(2)

Statistical Inference for Multiple Regression

407

(6)

Regression Diagnostics

413

(2)

Topics in Regression Modeling

415

(12)

Variable Selection Methods

427

(10)

A Strategy for Building a Multiple Regression Model

437

(2)

Chapter Summary

439

(18)

Exercises

440

(17)

Analysis of Single Factor Experiments

457

(47)

Completely Randomized Design

457

(10)

Multiple Comparisons of Means

467

(13)

*Random Effects Model for a One-Way Layout

480

(2)

Randomized Block Design

482

(8)

Chapter Summary

490

(14)

Exercises

492

(12)

Analysis of Multifactor Experiments

504

(58)

Two-Factor Experiments with Fixed Crossed Factors

505

(17)

2k Factorial Experiments

522

(18)

Other Selected Types of Two-Factor Experiments

540

(7)

Chapter Summary

547

(15)

Exercises

548

(14)

Nonparametric Statistical Methods

562

(51)

Inferences for Single Samples

562

(11)

Inferences for Two Independent Samples

573

(7)

Inferences for Several Independent Samples

580

(3)

Inferences for Several Matched Samples

583

(3)

Rank Correlation Methods

586

(8)

*Resampling Methods

594

(9)

Chapter Summary

603

(10)

Exercises

604

(9)

Likelihood, Bayesian, and Decision Theory Methods

613

(56)

Maximum Likelihood Estimation

613

(18)

Likelihood Ratio Tests

631

(15)

Bayesian Inference

646

(4)

Decision Theory

650

(7)

Chapter Summary

657

(12)

Exercises

660

(9)

Appendix A Tables

669

(17)

Appendix B Abbreviated Answers to Selected Odd-Numbered Exercises

686

(27)

Index

713

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Statistics and Data Analysis From Elementary to Intermediate

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