Social Statistics For A Diverse SocietyPDF电子书下载

1 The What and the Why of Statistics 2

Introduction 2

The Research Process 3

Asking Research Questions 4

The Role of Theory 6

Formulating the Hypotheses 7

Independent and Dependent Variables：Causality 10

Independent and Dependent Variables：Guidelines 13

Collecting Data 14

Levels of Measurement 14

Nominal Level of Measurement 15

Ordinal Level of Measurement 15

Interval-Ratio Level of Measurement 16

Cumulative Property of Levels of Measurement 17

Levels of Measurement of Dichotomous Variables 19

Discrete and Continuous Variables 20

Analyzing Data and Evaluating the Hypotheses 21

Descriptive and Inferential Statistics：Principles 21

Descriptive and Inferential Statistics：Illustration 23

Organization of Information：Frequency Distributions 23

Graphic Presentation 23

Measures of Central Tendency 24

Measures of Variability 24

Bivariate Methods 24

Statistical Inference 24

Evaluating the Hypotheses 25

Looking at Social Differences 26

Box 1.1 A Tale of Simple Arithmetic：How Culture May Influence How We Count 26

Box 1.2 Are You Anxious About Statistics？ 28

MAIN POINTS 29

KEY TERMS 30

SPSS DEMONSTRATIONS 30

EXERCISES 32

GROUP PROBLEMS 34

2 Organization of Information：Frequency Distributions 38

Introduction 38

Frequency Distributions 38

Proportions and Percentages 40

Percentage Distributions 43

Comparisons 43

Statistics in Practice：Labor Force Participation of Native Americans 45

The Construction of Frequency Distributions 47

Frequency Distributions for Nominal Variables 49

Frequency Distributions for Ordinal Variables 50

Frequency Distributions for Interval-Ratio Variables 52

Cumulative Distributions 55

Box 2.1 Real Limits，Stated Limits，and Midpoints of Class Intervals 56

Rates 60

Statistics in Practice：Marriage and Divorce Rates over Time 62

Reading the Research Literature：Statistical Tables 63

Basic Principles 63

Tables with a Different Format 66

Conclusion 68

MAIN POINTS 68

KEY TERMS 69

SPSS DEMONSTRATIONS 69

EXERCISES 74

SPSS PROBLEMS 85

GROUP PROBLEMS 86

3 Graphic Presentation 90

Introduction 90

The Pie Chart：The Race and Ethnicity of the Elderly 91

The Bar Graph：The Living Arrangements and Labor Force Participation of the Elderly 93

The Statistical Map：The Geographic Distribution of the Elderly 96

The Histogram 99

Statistics in Practice：The “Graying” of America 101

The Frequency Polygon 103

The Stem and Leaf Plot 105

Time Series Charts 108

Distortions in Graphs 110

Shrinking and Stretching the Axes：Visual Confusion 110

Distortions with Picture Graphs 112

Statistics in Practice：Diversity at a Glance 113

MAIN POINTS 117

KEY TERMS 117

SPSS DEMONSTRATIONS 118

EXERCISES 122

SPSS PROBLEMS 129

GROUP PROBLEMS 130

4 Measures of Central Tendency 134

Introduction 134

The Mode：Foreign Languages Spoken in the United States 135

The Median：Worries About Health Care 138

Finding the Median in Sorted Data 139

An Odd Number of Cases 139

An Even Number of Cases 141

Finding the Median in Frequency Distributions 142

Box 4.1 Finding the Median in Grouped Data 144

Statistics in Practice：Opinions About National Defense Spending 145

Statistics in Practice：Changes in Age at First Marriage 146

Locating Percentiles in a Frequency Distribution 146

Box 4.2 Finding Percentiles in Grouped Data 149

The Mean：Murder Rates in Fifteen American Cities 149

Using a Formula to Calculate the Mean 151

Understanding Some Important Properties of the Arithmetic Mean 152

Box 4.3 Finding the Mean in a Frequency Distribution 153

Interval-Ratio Level of Measurement 156

Center of Gravity 156

Sensitivity to Extremes 157

The Shape of the Distribution：The Experience of Traumatic Events 158

The Symmetrical Distribution 160

The Positively Skewed Distribution 160

The Negatively Skewed Distribution 162

Guidelines for Identifying the Shape of a Distribution 162

Considerations for Choosing a Measure of Central Tendency 163

Level of Measurement 164

Box 4.4 Statistics in Practice：Median Annual Earnings Among Subgroups 165

Skewed Distribution 166

Symmetrical Distribution 166

MAIN POINTS 166

KEY TERMS 167

SPSS DEMONSTRATIONS 167

EXERCISES 171

SPSS PROBLEMS 176

GROUP PROBLEMS 178

5 Measures of Variability 180

Introduction 180

The Importance of Measuring Variability 180

The Index of Qualitative Variation（IQV） 183

Steps for Calculating the IQV 184

Calculating the Total Number o f Differences 185

Calculating the Maximum Possible Differences 186

Computing the Ratio 188

Expressing the IQV as a Percentage 189

Calculating the IQV from Percentage or Proportion Distributions 189

Box 5.1 The IQV Formula：What’s Going On Here？ 190

Statistics in Practice：Diversity in U.S.Society 191

Box 5.2 Statistics in Practice：Diversity at Berkeley Through the Years 192

The Range 196

Box 5.3 Using the IQV：American Attitudes About Spending 197

The Interquartile Range：Increases in Elderly Populations 199

The Box Plot 202

The Variance and the Standard Deviation：Changes in the Nursing Home Population 204

Calculating the Deviation from the Mean 207

Calculating the Variance and the Standard Deviation 209

Box 5.4 Computational Formula for the Variance and Standard Deviation 213

Considerations for Choosing a Measure of Variation 214

Reading the Research Literature：Gender Differences in Caregiving 216

MAIN POINTS 219

KEY TERMS 220

SPSS DEMONSTRATIONS 220

EXERCISES 224

SPSS PROBLEMS 232

GROUP PROBLEMS 233

6 Relationships Between Two Variables：Cross-Tabulation 236

Introduction 236

Independent and Dependent Variables 238

The Bivariate Table：Safety in Cities 240

How to Construct a Bivariate Table：Race and Home Ownership 242

How to Compute Percentages in a Bivariate Table 244

Calculating Percentages Within Each Category of the Independent Variable 245

Comparing the Percentages Across Different Categories of the Independent Variable 246

How to Deal with Ambiguous Relationships Between Variables 246

BOX 6.1 Percentaging a Bivariate Table 247

Reading the Research Literature：Medicaid Use Among the Elderly 250

The Properties of a Bivariate Relationship 255

The Existence of the Relationship 255

The Strength of the Relationship 257

The Direction of the Relationship 258

Elaboration 260

Testing for Nonspuriousness：Firefighters and Property Damage 261

An Intervening Relationship：Religion and Attitude Toward Abortion 265

Conditional Relationships：More on Abortion 271

The Limitations of Elaboration 274

Statistics in Practice：Family Support for the Transition from High School 275

MAIN POINTS 279

KEY TERMS 280

SPSS DEMONSTRATIONS 280

EXERCISES 284

SPSS PROBLEMS 292

GROUP PROBLEMS 294

7 Measures of Association for Nominal and Ordinal Variables 298

Introduction 298

Proportional Reduction of Error 300

PRE and Degree of Association 302

A General Formula for PRE Measures 302

Lambda：A Measure of Associationfor Nominal Variables 304

A Method for Calculating Lambda 304

Statistics in Practice：Home Ownership，Financial Satisfaction，and Race 306

Some Guidelines for Calculating Lambda 309

Gamma and Somers’d：Ordinal Measures of Association 310

Analyzing the Association Between Ordinal Variables：Job Security and Job Satisfaction 311

Comparison of Pairs 313

Types o f Pairs 314

Uses for Information About Pairs 316

Counting Pairs 316

Box 7.1 A Martian’s Eye View of Job Security and Job Satisfaction 317

Same Order Pairs（Ns） 317

Inverse Order Pairs（Nd） 319

Pairs Tied on the Dependent Variable（Nty） 319

Calculating Gamma 322

Positive and Negative Gamma 322

Gamma as a PRE Measure 323

Statistics in Practice：Trauma by Social Class 324

Calculating Somers’d 326

Tied Pairs and Somers’d 326

Somers’d Compared with Gamma 327

Using Ordinal Measures with Dichotomous Variables 328

Box 7.2 What Is Strong？What Is Weak？A Guide to Interpretation 329

Reading the Research Literature：Worldview and Abortion Beliefs 329

Examining the Data 331

Interpreting the Data 332

MAIN POINTS 333

KEY TERMS 334

SPSS DEMONSTRATION 335

EXERCISES 337

SPSS PROBLEMS 345

GROUP PROBLEMS 346

8 Bivariate Regression and Correlation 350

Introduction 350

The Scatter Diagram 352

Linear Relations and Prediction Rules 355

Constructing Straight Line Graphs 357

Finding the Best-Fitting Line 360

Defining Error 361

The Sum of Squared Error（∑e2） 361

The Least-Squares Line 361

Review 362

Computing a and b for the Prediction Equation 362

Interpreting a and bYx 365

Box 8.1 Understanding the Covariance 367

Calculating bYx Using a Computational Formula 367

Box 8.2 A Note on Nonlinear Relationships 368

Statistics in Practice：GNP and Willingness to Volunteer Time for Environmental Protection 370

Methods for Assessing the Accuracy of Predictions 373

Prediction Errors 374

The Coefficient of Determination（r2）as a PRE Measure 376

Calculating r2 377

Pearson’s Correlation Coefficient（r） 378

Characteristics of Pearson’s r 379

Calculating r Using a Computational Formula 380

Statistics in Practice：Comparable Worth Discrimination 381

Computing a and b for the Prediction Equation 383

Computing r and r2 386

Statistics in Practice：The Marriage Penalty in Earnings 386

MAIN POINTS 388

KEY TERMS 389

SPSS DEMONSTRATIONS 389

EXERCISES 396

SPSS PROBLEMS 404

GROUP EXERCISES 405

9 Organization of Information and Measurement of Relationships：A Review of Descriptive Data Analysis 408

Introduction 408

Descriptive Data Analysis for Nominal Variables 410

Statistics in Practice：Gender and Local Political Party Activism 411

Organize the Data into a Frequency Distribution 412

Display the Data in a Graph 413

Describe What Is Average or Typical o f a Distribution 414

Describe Variability Within a Distribution 415

Describe the Relationship Between Two Variables 415

Descriptive Data Analysis for Ordinal Variables 416

Gender and Local Political Party Activism：Continuing Our Research Example 416

Organize the Data into a Frequency Distribution 417

Display the Data in a Graph 419

Describe What Is Average or Typical of a Distribution 421

Describe Variability Within a Distribution 421

Describe the Relationship Between Two Variables 421

Descriptive Data Analysis for Interval-Ratio Variables 425

Statistics in Practice：Education and Income 425

Organize the Data into a Frequency Distribution 425

Display the Data in a Graph 427

Describe What Is Average or Typical of a Distribution 427

Describe Variability Within a Distribution 428

Describe the Relationship Between Two Variables 429

A Final Note 432

EXERCISES 432

SPSS PROBLEMS 439

10 The Normal Distribution 442

Introduction 442

Properties of the Normal Distribution 443

Empirical Distributions Approximating the Normal Distribution 444

An Example：Final Grades in Statistics 444

Areas Under the Normal Curve 446

Interpreting the Standard Deviation 447

Standard（Z）Scores 447

Transforming a Raw Score into a Z Score 448

Transforming a Z Score into a Raw Score 450

The Standard Normal Distribution 451

The Standard Normal Table 452

The Structure of the Standard Normal Table 452

Transforming Z Scores into Proportions（or Percentages） 454

Finding the Area Between the Mean and a Specified Positive Z Score 454

Finding the Area Between the Mean and a Specified Negative Z Score 454

Finding the Area Between Two Z Scores on the Same Side of the Mean 455

Finding the Area Between Two Z Scores on Opposite Sides of the Mean 456

Finding the Area Above a Positive Z Score or Below a Negative Z Score 456

Transforming Proportions（or Percentages）into Z Scores 458

Finding a Z Score Bounding an Area Above It 458

Finding a Z Score Bounding an Area Below It 459

Working with Percentiles 460

Finding the Percentile Rank of a Score Higher Than the Mean 461

Finding the Percentile Rank of a Score Lower Than the Mean 461

Finding the Raw Score Associated with a Percentile Higher Than 50 462

Finding the Raw Score Associated with a Percentile Lower Than 50 464

A Final Note 465

MAIN POINTS 465

KEY TERMS 465

SPSS DEMONSTRATIONS 465

EXERCISES 470

SPSS PROBLEMS 476

GROUP PROBLEMS 477

11 Building Blocks of Inference：Sampling and Sampling Distributions 480

Introduction 480

Aims of Sampling 481

Some Basic Principles of Probability 483

Probability Sampling 484

The Simple Random Sample 485

The Systematic Random Sample 487

The Stratified Random Sampling 488

Box 11.1 Disproportionate Stratified Samples and Diversity 490

The Concept of Sampling Distribution 492

The Population 492

The Sample 493

The Dilemma 494

The Sampling Distribution 495

The Sampling Distribution of the Mean 495

An Illustration 495

Review 498

The Population 498

The Sample 498

The Sampling Distribution of the Mean 498

The Mean of the Sampling Distribution 500

The Standard Error of the Mean 501

The Central Limit Theorem 501

The Size of the Sample 504

The Significance of the Sampling Distribution and the Central Limit Theorem 504

MAIN POINTS 506

KEY TERMS 507

SPSS DEMONSTRATION 508

EXERCISES 511

GROUP PROBLEMS 514

12 Estimation 518

Introduction 518

Estimation Defined 519

Reasons for Estimation 520

Point and Interval Estimation 520

Confidence Intervals for Means 522

Rationale for Confidence Intervals 522

Box 12.1 Estimation as a Type of Inference 523

Procedures for Estimating Means 526

Calculating the Standard Error of the Mean 527

Deciding on the Level of Confidence and Finding the Corresponding Z Value 527

Calculating the Confidence Interval 527

Interpreting the Results 528

Reducing Risk 528

Estimating Sigma 529

Calculating the Standard Error of the Mean 530

Deciding on the Level of Confidence and Finding the Corresponding Z Value 530

Calculating the Confidence Interval 530

Interpreting the Results 530

Sample Size and Confidence Intervals 530

Box 12.2 What Affects Confidence Interval Width？A Summary 534

Statistics in Practice：Hispanic Migration and Earnings 534

Confidence Intervals for Proportions 536

The Sampling Distribution of Proportions 537

Procedures for Estimating Proportions 538

Calculating the Standard Error of the Proportion 539

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value 539

Calculating the Confidence Interval 540

Interpreting the Results 540

Increasing the Sample Size 541

Example 3 Revisited：Raising the Minimum Wage 542

Calculating the Standard Error of the Proportion 542

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value 542

Calculating the Confidence Interval 542

Interpreting the Results 542

Statistics in Practice：Opinions About the Death Penalty 542

Statistics in Practice：More on the Death Penalty 543

Calculating the Standard Error of the Proportion 544

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value 544

Calculating the Confidence Interval 544

Interpreting the Results 545

MAIN POINTS 545

KEY TERMS 546

SPSS DEMONSTRATION 546

EXERCISES 549

SPSS PROBLEM 552

GROUP PROBLEMS 553

13 Testing Hypotheses：The Basics 556

Introduction 556

Elements of Statistical Hypothesis Testing 557

The Research Hypothesis（H1） 558

The Null Hypothesis（H0） 558

Assumptions of Statistical Hypothesis Testing 559

The Test Statistic and the P Value 560

Determining What Is Sufficiently Improbable 563

The Critical Value of the Test Statistic 564

One-and Two-Tailed Tests 565

Making a Decision and Interpreting the Result 569

The Six Steps in Hypothesis Testing：A Summary 570

1.Making Assumptions 571

2.Stating the Research and the Null Hypotheses 571

3.Selecting the Sampling Distribution and Specifying the Test Statistic 571

4.Choosing Alpha（α）and Establishing the Region of Rejection 572

5.Computing the Test Statistics 572

6.Making a Decision and Interpreting the Results 572

Statistics in Practice：The Earnings of White Women 572

Applying the Six-Step Model 573

Comparing One-and Two-Tailed Tests 574

Errors in Hypothesis Testing 574

MAIN POINTS 575

KEY TERMS 576

SPSS DEMONSTRATION 576

EXERCISES 578

SPSS PROBLEMS 581

GROUP PROBLEM 582

14 Testing Hypotheses About Two Samples 584

Introduction 584

The Structure of Hypothesis Testing with Two Samples 585

The Assumption of Independent Samples 585

Stating the Research and the Null Hypotheses 586

The Sampling Distribution of the Difference Between Means 587

Estimating the Standard Error 588

The t Statistic 588

Calculating the Estimated Standard Error 589

The Population Variances Are Assumed Equal 589

The Population Variances Are Assumed Unequal 589

Comparing the t and the Z Statistics 589

The t Distribution and the Degrees of Freedom（df） 590

Determining the Degrees of Freedom 590

Adjusting for Unequal Variances 590

The Shape of the t Distribution 591

Critical Values of the t Distribution 591

Review 593

Hypotheses About Differences Between Means：Illustrations 593

The Population Variances Are Assumed Equal：The Earnings of Asian American Men 593

The Population Variances Are Assumed Unequal：The Ratings of Ross Perot 599

Testing the Significance of the Difference Between Two Sample Proportions（with Large Samples：N1＋N2＞100） 602

An Illustration：Public Opinion About the Environment 602

Statistics in Practice：Gender and Abortion Attitudes 605

Reading the Research Literature：Reporting the Results of Statistical Hypothesis Testing 606

MAIN POINTS 609

KEY TERMS 609

SPSS DEMONSTRATION 610

EXERCISES 613

SPSS PROBLEMS 617

GROUP PROBLEMS 618

15 The Chi-Square Test 620

Introduction 620

The Concept of Chi-Square as a Statistical Test 623

The Concept of Statistical Independence 623

The Structure of Hypothesis Testing with Chi-Square 624

The Assumptions 625

Stating the Research and the Null Hypotheses 625

The Concept of Expected Frequencies 625

Calculating the Expected Frequencies 625

Calculating the Obtained Chi-Square 627

The Sampling Distribution of Chi-Square 629

Determining the Degrees of Freedom 630

Critical Values of the Chi-Square Distribution 631

Review 632

The Limitations of the Chi-Square Test：Sample Size and Statistical Significance 634

Box 15.1 Comparing Chi-Square with Tests of Differences Between Proportions 636

Statistics in Practice：Social Class and Health 638

Reading the Research Literature：AIDS Risks Among Women 641

MAIN POINTS 644

KEY TERMS 645

SPSS DEMONSTRATION 645

EXERCISES 647

SPSS PROBLEMS 658

GROUP PROBLEMS 659

16 Reviewing Inferential Statistics 662

Introduction 662

Normal Distributions 663

Sampling：The Case of AIDS 664

Estimation 666

Statistics in Practice：The War on Drugs 668

Box 16.1 Interval Estimation for Peers as a Maior Influence on the Drug Attitudes of the Young 671

The Process of Statistical Hypothesis Testing 672

Step 1：Making Assumptions 673

Step 2：Stating the Research and the Null Hypotheses 673

Step 3：Selecting a Sampling Distribution and a Test Statistic 674

Step 4：Choosing Alpha and Establishing the Region of Rejection 674

Box 16.2 Possible Hypotheses for Comparing Two Samples 675

Box 16.3 Criteria for Statistical Tests When Comparing Two Samples 676

Finding the Critical Value of Z 677

Finding the Critical Value of t 678

Finding the Critical Value of Chi-Square 678

Step 5：Computing the Test Statistic 679

Step 6：Making a Decision and Interpreting the Results 679

Statistics in Practice：Affirmative Action 679

Box 16.4 Formulas for Z，t，and X2 680

Box 16.5 Affirmative Action：The Process of Statistical Hypothesis Testing，Using a Z test for Proportions 684

Statistics in Practice：Attitudes Toward Illegal Immigrants 685

Box 16.6 Attitudes Toward Illegal Immigrants：The Process of Statistical Hypothesis Testing，Using a t Test 687

Statistics in Practice：Education and Employment 688

Sampling Technique and Sample Characteristics 689

Comparing Ratings of the Major Between Sociology and Other Social Science Alumni 691

Ratings of Foundational Skills in Sociology：Changes over Time 692

Box 16.7 Education and Employment：The Processof Statistical Hypothesis Testing，Using Chi-Square 694

Gender Differences in Ratings of Foundational Skills，Occupational Prestige，and Income 696

Box 16.8 Occupational Prestige of Male and Female Sociology Alumni：Another Example Using a t Test 698

Conclusion 699

EXERCISES 700

SPSS PROBLEMS 706

Appendix A Table of Random Numbers 709

Appendix B The Standard Normal Table 713

Appendix C Distribution of t 718

Appendix D Distribution of Chi-Square 720

Appendix E How to Use a Statistical Package 721

Appendix F The General Social Survey 738

Appendix G A Basic Math Review 739

Appendix H How to Use the GSS Data Files and Lotus ScreenCam 741

Answers to Odd-Numbered Exercises/Answers-1 749

Index/Glossary/Index-1 774