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1 The What and the Why of Statistics2

Introduction2

The Research Process3

Asking Research Questions4

The Role of Theory6

Formulating the Hypotheses7

Independent and Dependent Variables：Causality10

Independent and Dependent Variables：Guidelines13

Collecting Data14

Levels of Measurement14

Nominal Level of Measurement15

Ordinal Level of Measurement15

Interval-Ratio Level of Measurement16

Cumulative Property of Levels of Measurement17

Levels of Measurement of Dichotomous Variables19

Discrete and Continuous Variables20

Analyzing Data and Evaluating the Hypotheses21

Descriptive and Inferential Statistics：Principles21

Descriptive and Inferential Statistics：Illustration23

Organization of Information：Frequency Distributions23

Graphic Presentation23

Measures of Central Tendency24

Measures of Variability24

Bivariate Methods24

Statistical Inference24

Evaluating the Hypotheses25

Looking at Social Differences26

Box 1.1 A Tale of Simple Arithmetic：How Culture May Influence How We Count26

Box 1.2 Are You Anxious About Statistics？28

MAIN POINTS29

KEY TERMS30

SPSS DEMONSTRATIONS30

EXERCISES32

GROUP PROBLEMS34

2 Organization of Information：Frequency Distributions38

Introduction38

Frequency Distributions38

Proportions and Percentages40

Percentage Distributions43

Comparisons43

Statistics in Practice：Labor Force Participation of Native Americans45

The Construction of Frequency Distributions47

Frequency Distributions for Nominal Variables49

Frequency Distributions for Ordinal Variables50

Frequency Distributions for Interval-Ratio Variables52

Cumulative Distributions55

Box 2.1 Real Limits，Stated Limits，and Midpoints of Class Intervals56

Rates60

Statistics in Practice：Marriage and Divorce Rates over Time62

Reading the Research Literature：Statistical Tables63

Basic Principles63

Tables with a Different Format66

Conclusion68

MAIN POINTS68

KEY TERMS69

SPSS DEMONSTRATIONS69

EXERCISES74

SPSS PROBLEMS85

GROUP PROBLEMS86

3 Graphic Presentation90

Introduction90

The Pie Chart：The Race and Ethnicity of the Elderly91

The Bar Graph：The Living Arrangements and Labor Force Participation of the Elderly93

The Statistical Map：The Geographic Distribution of the Elderly96

The Histogram99

Statistics in Practice：The “Graying” of America101

The Frequency Polygon103

The Stem and Leaf Plot105

Time Series Charts108

Distortions in Graphs110

Shrinking and Stretching the Axes：Visual Confusion110

Distortions with Picture Graphs112

Statistics in Practice：Diversity at a Glance113

MAIN POINTS117

KEY TERMS117

SPSS DEMONSTRATIONS118

EXERCISES122

SPSS PROBLEMS129

GROUP PROBLEMS130

4 Measures of Central Tendency134

Introduction134

The Mode：Foreign Languages Spoken in the United States135

The Median：Worries About Health Care138

Finding the Median in Sorted Data139

An Odd Number of Cases139

An Even Number of Cases141

Finding the Median in Frequency Distributions142

Box 4.1 Finding the Median in Grouped Data144

Statistics in Practice：Opinions About National Defense Spending145

Statistics in Practice：Changes in Age at First Marriage146

Locating Percentiles in a Frequency Distribution146

Box 4.2 Finding Percentiles in Grouped Data149

The Mean：Murder Rates in Fifteen American Cities149

Using a Formula to Calculate the Mean151

Understanding Some Important Properties of the Arithmetic Mean152

Box 4.3 Finding the Mean in a Frequency Distribution153

Interval-Ratio Level of Measurement156

Center of Gravity156

Sensitivity to Extremes157

The Shape of the Distribution：The Experience of Traumatic Events158

The Symmetrical Distribution160

The Positively Skewed Distribution160

The Negatively Skewed Distribution162

Guidelines for Identifying the Shape of a Distribution162

Considerations for Choosing a Measure of Central Tendency163

Level of Measurement164

Box 4.4 Statistics in Practice：Median Annual Earnings Among Subgroups165

Skewed Distribution166

Symmetrical Distribution166

MAIN POINTS166

KEY TERMS167

SPSS DEMONSTRATIONS167

EXERCISES171

SPSS PROBLEMS176

GROUP PROBLEMS178

5 Measures of Variability180

Introduction180

The Importance of Measuring Variability180

The Index of Qualitative Variation（IQV）183

Steps for Calculating the IQV184

Calculating the Total Number o f Differences185

Calculating the Maximum Possible Differences186

Computing the Ratio188

Expressing the IQV as a Percentage189

Calculating the IQV from Percentage or Proportion Distributions189

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

Statistics in Practice：Diversity in U.S.Society191

Box 5.2 Statistics in Practice：Diversity at Berkeley Through the Years192

The Range196

Box 5.3 Using the IQV：American Attitudes About Spending197

The Interquartile Range：Increases in Elderly Populations199

The Box Plot202

The Variance and the Standard Deviation：Changes in the Nursing Home Population204

Calculating the Deviation from the Mean207

Calculating the Variance and the Standard Deviation209

Box 5.4 Computational Formula for the Variance and Standard Deviation213

Considerations for Choosing a Measure of Variation214

Reading the Research Literature：Gender Differences in Caregiving216

MAIN POINTS219

KEY TERMS220

SPSS DEMONSTRATIONS220

EXERCISES224

SPSS PROBLEMS232

GROUP PROBLEMS233

6 Relationships Between Two Variables：Cross-Tabulation236

Introduction236

Independent and Dependent Variables238

The Bivariate Table：Safety in Cities240

How to Construct a Bivariate Table：Race and Home Ownership242

How to Compute Percentages in a Bivariate Table244

Calculating Percentages Within Each Category of the Independent Variable245

Comparing the Percentages Across Different Categories of the Independent Variable246

How to Deal with Ambiguous Relationships Between Variables246

BOX 6.1 Percentaging a Bivariate Table247

Reading the Research Literature：Medicaid Use Among the Elderly250

The Properties of a Bivariate Relationship255

The Existence of the Relationship255

The Strength of the Relationship257

The Direction of the Relationship258

Elaboration260

Testing for Nonspuriousness：Firefighters and Property Damage261

An Intervening Relationship：Religion and Attitude Toward Abortion265

Conditional Relationships：More on Abortion271

The Limitations of Elaboration274

Statistics in Practice：Family Support for the Transition from High School275

MAIN POINTS279

KEY TERMS280

SPSS DEMONSTRATIONS280

EXERCISES284

SPSS PROBLEMS292

GROUP PROBLEMS294

7 Measures of Association for Nominal and Ordinal Variables298

Introduction298

Proportional Reduction of Error300

PRE and Degree of Association302

A General Formula for PRE Measures302

Lambda：A Measure of Associationfor Nominal Variables304

A Method for Calculating Lambda304

Statistics in Practice：Home Ownership，Financial Satisfaction，and Race306

Some Guidelines for Calculating Lambda 309

Gamma and Somers’d：Ordinal Measures of Association310

Analyzing the Association Between Ordinal Variables：Job Security and Job Satisfaction311

Comparison of Pairs313

Types o f Pairs314

Uses for Information About Pairs316

Counting Pairs316

Box 7.1 A Martian’s Eye View of Job Security and Job Satisfaction317

Same Order Pairs（Ns）317

Inverse Order Pairs（Nd）319

Pairs Tied on the Dependent Variable（Nty）319

Calculating Gamma322

Positive and Negative Gamma322

Gamma as a PRE Measure 323

Statistics in Practice：Trauma by Social Class324

Calculating Somers’d326

Tied Pairs and Somers’d326

Somers’d Compared with Gamma 327

Using Ordinal Measures with Dichotomous Variables328

Box 7.2 What Is Strong？What Is Weak？A Guide to Interpretation329

Reading the Research Literature：Worldview and Abortion Beliefs329

Examining the Data331

Interpreting the Data332

MAIN POINTS333

KEY TERMS334

SPSS DEMONSTRATION335

EXERCISES337

SPSS PROBLEMS345

GROUP PROBLEMS346

8 Bivariate Regression and Correlation350

Introduction350

The Scatter Diagram352

Linear Relations and Prediction Rules355

Constructing Straight Line Graphs357

Finding the Best-Fitting Line360

Defining Error361

The Sum of Squared Error（∑e2）361

The Least-Squares Line361

Review362

Computing a and b for the Prediction Equation362

Interpreting a and bYx365

Box 8.1 Understanding the Covariance367

Calculating bYx Using a Computational Formula367

Box 8.2 A Note on Nonlinear Relationships368

Statistics in Practice：GNP and Willingness to Volunteer Time for Environmental Protection370

Methods for Assessing the Accuracy of Predictions373

Prediction Errors374

The Coefficient of Determination（r2）as a PRE Measure376

Calculating r2377

Pearson’s Correlation Coefficient（r）378

Characteristics of Pearson’s r379

Calculating r Using a Computational Formula380

Statistics in Practice：Comparable Worth Discrimination381

Computing a and b for the Prediction Equation383

Computing r and r2386

Statistics in Practice：The Marriage Penalty in Earnings386

MAIN POINTS388

KEY TERMS389

SPSS DEMONSTRATIONS389

EXERCISES396

SPSS PROBLEMS404

GROUP EXERCISES405

9 Organization of Information and Measurement of Relationships：A Review of Descriptive Data Analysis408

Introduction408

Descriptive Data Analysis for Nominal Variables410

Statistics in Practice：Gender and Local Political Party Activism411

Organize the Data into a Frequency Distribution412

Display the Data in a Graph413

Describe What Is Average or Typical o f a Distribution414

Describe Variability Within a Distribution415

Describe the Relationship Between Two Variables415

Descriptive Data Analysis for Ordinal Variables416

Gender and Local Political Party Activism：Continuing Our Research Example416

Organize the Data into a Frequency Distribution417

Display the Data in a Graph419

Describe What Is Average or Typical of a Distribution421

Describe Variability Within a Distribution421

Describe the Relationship Between Two Variables421

Descriptive Data Analysis for Interval-Ratio Variables425

Statistics in Practice：Education and Income425

Organize the Data into a Frequency Distribution425

Display the Data in a Graph427

Describe What Is Average or Typical of a Distribution427

Describe Variability Within a Distribution428

Describe the Relationship Between Two Variables429

A Final Note432

EXERCISES432

SPSS PROBLEMS439

10 The Normal Distribution442

Introduction442

Properties of the Normal Distribution443

Empirical Distributions Approximating the Normal Distribution444

An Example：Final Grades in Statistics444

Areas Under the Normal Curve446

Interpreting the Standard Deviation447

Standard（Z）Scores447

Transforming a Raw Score into a Z Score448

Transforming a Z Score into a Raw Score450

The Standard Normal Distribution451

The Standard Normal Table452

The Structure of the Standard Normal Table452

Transforming Z Scores into Proportions（or Percentages）454

Finding the Area Between the Mean and a Specified Positive Z Score454

Finding the Area Between the Mean and a Specified Negative Z Score454

Finding the Area Between Two Z Scores on the Same Side of the Mean455

Finding the Area Between Two Z Scores on Opposite Sides of the Mean456

Finding the Area Above a Positive Z Score or Below a Negative Z Score456

Transforming Proportions（or Percentages）into Z Scores458

Finding a Z Score Bounding an Area Above It458

Finding a Z Score Bounding an Area Below It459

Working with Percentiles460

Finding the Percentile Rank of a Score Higher Than the Mean461

Finding the Percentile Rank of a Score Lower Than the Mean461

Finding the Raw Score Associated with a Percentile Higher Than 50462

Finding the Raw Score Associated with a Percentile Lower Than 50464

A Final Note465

MAIN POINTS465

KEY TERMS465

SPSS DEMONSTRATIONS465

EXERCISES470

SPSS PROBLEMS476

GROUP PROBLEMS477

11 Building Blocks of Inference：Sampling and Sampling Distributions480

Introduction480

Aims of Sampling481

Some Basic Principles of Probability483

Probability Sampling484

The Simple Random Sample485

The Systematic Random Sample487

The Stratified Random Sampling488

Box 11.1 Disproportionate Stratified Samples and Diversity490

The Concept of Sampling Distribution492

The Population492

The Sample493

The Dilemma494

The Sampling Distribution495

The Sampling Distribution of the Mean495

An Illustration495

Review498

The Population498

The Sample498

The Sampling Distribution of the Mean498

The Mean of the Sampling Distribution500

The Standard Error of the Mean501

The Central Limit Theorem501

The Size of the Sample 504

The Significance of the Sampling Distribution and the Central Limit Theorem504

MAIN POINTS506

KEY TERMS507

SPSS DEMONSTRATION508

EXERCISES511

GROUP PROBLEMS514

12 Estimation518

Introduction518

Estimation Defined519

Reasons for Estimation520

Point and Interval Estimation520

Confidence Intervals for Means522

Rationale for Confidence Intervals522

Box 12.1 Estimation as a Type of Inference523

Procedures for Estimating Means526

Calculating the Standard Error of the Mean527

Deciding on the Level of Confidence and Finding the Corresponding Z Value527

Calculating the Confidence Interval527

Interpreting the Results528

Reducing Risk528

Estimating Sigma529

Calculating the Standard Error of the Mean530

Deciding on the Level of Confidence and Finding the Corresponding Z Value530

Calculating the Confidence Interval530

Interpreting the Results530

Sample Size and Confidence Intervals530

Box 12.2 What Affects Confidence Interval Width？A Summary534

Statistics in Practice：Hispanic Migration and Earnings534

Confidence Intervals for Proportions536

The Sampling Distribution of Proportions537

Procedures for Estimating Proportions538

Calculating the Standard Error of the Proportion539

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value539

Calculating the Confidence Interval540

Interpreting the Results540

Increasing the Sample Size541

Example 3 Revisited：Raising the Minimum Wage542

Calculating the Standard Error of the Proportion542

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value542

Calculating the Confidence Interval542

Interpreting the Results542

Statistics in Practice：Opinions About the Death Penalty542

Statistics in Practice：More on the Death Penalty543

Calculating the Standard Error of the Proportion544

Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value544

Calculating the Confidence Interval544

Interpreting the Results545

MAIN POINTS545

KEY TERMS546

SPSS DEMONSTRATION546

EXERCISES549

SPSS PROBLEM552

GROUP PROBLEMS553

13 Testing Hypotheses：The Basics556

Introduction556

Elements of Statistical Hypothesis Testing557

The Research Hypothesis（H1）558

The Null Hypothesis（H0）558

Assumptions of Statistical Hypothesis Testing559

The Test Statistic and the P Value560

Determining What Is Sufficiently Improbable563

The Critical Value of the Test Statistic564

One-and Two-Tailed Tests565

Making a Decision and Interpreting the Result569

The Six Steps in Hypothesis Testing：A Summary570

1.Making Assumptions571

2.Stating the Research and the Null Hypotheses571

3.Selecting the Sampling Distribution and Specifying the Test Statistic571

4.Choosing Alpha（α）and Establishing the Region of Rejection572

5.Computing the Test Statistics572

6.Making a Decision and Interpreting the Results572

Statistics in Practice：The Earnings of White Women572

Applying the Six-Step Model573

Comparing One-and Two-Tailed Tests574

Errors in Hypothesis Testing574

MAIN POINTS575

KEY TERMS576

SPSS DEMONSTRATION576

EXERCISES578

SPSS PROBLEMS581

GROUP PROBLEM582

14 Testing Hypotheses About Two Samples584

Introduction584

The Structure of Hypothesis Testing with Two Samples585

The Assumption of Independent Samples585

Stating the Research and the Null Hypotheses586

The Sampling Distribution of the Difference Between Means587

Estimating the Standard Error588

The t Statistic588

Calculating the Estimated Standard Error589

The Population Variances Are Assumed Equal589

The Population Variances Are Assumed Unequal589

Comparing the t and the Z Statistics589

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

Determining the Degrees of Freedom590

Adjusting for Unequal Variances590

The Shape of the t Distribution591

Critical Values of the t Distribution591

Review593

Hypotheses About Differences Between Means：Illustrations593

The Population Variances Are Assumed Equal：The Earnings of Asian American Men593

The Population Variances Are Assumed Unequal：The Ratings of Ross Perot599

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

An Illustration：Public Opinion About the Environment602

Statistics in Practice：Gender and Abortion Attitudes605

Reading the Research Literature：Reporting the Results of Statistical Hypothesis Testing606

MAIN POINTS609

KEY TERMS609

SPSS DEMONSTRATION610

EXERCISES613

SPSS PROBLEMS617

GROUP PROBLEMS618

15 The Chi-Square Test620

Introduction620

The Concept of Chi-Square as a Statistical Test623

The Concept of Statistical Independence623

The Structure of Hypothesis Testing with Chi-Square624

The Assumptions625

Stating the Research and the Null Hypotheses625

The Concept of Expected Frequencies625

Calculating the Expected Frequencies625

Calculating the Obtained Chi-Square627

The Sampling Distribution of Chi-Square629

Determining the Degrees of Freedom630

Critical Values of the Chi-Square Distribution631

Review632

The Limitations of the Chi-Square Test：Sample Size and Statistical Significance634

Box 15.1 Comparing Chi-Square with Tests of Differences Between Proportions636

Statistics in Practice：Social Class and Health638

Reading the Research Literature：AIDS Risks Among Women641

MAIN POINTS644

KEY TERMS645

SPSS DEMONSTRATION645

EXERCISES647

SPSS PROBLEMS658

GROUP PROBLEMS659

16 Reviewing Inferential Statistics662

Introduction662

Normal Distributions663

Sampling：The Case of AIDS664

Estimation666

Statistics in Practice：The War on Drugs668

Box 16.1 Interval Estimation for Peers as a Maior Influence on the Drug Attitudes of the Young671

The Process of Statistical Hypothesis Testing672

Step 1：Making Assumptions673

Step 2：Stating the Research and the Null Hypotheses673

Step 3：Selecting a Sampling Distribution and a Test Statistic674

Step 4：Choosing Alpha and Establishing the Region of Rejection674

Box 16.2 Possible Hypotheses for Comparing Two Samples675

Box 16.3 Criteria for Statistical Tests When Comparing Two Samples676

Finding the Critical Value of Z677

Finding the Critical Value of t678

Finding the Critical Value of Chi-Square678

Step 5：Computing the Test Statistic679

Step 6：Making a Decision and Interpreting the Results679

Statistics in Practice：Affirmative Action679

Box 16.4 Formulas for Z，t，and X2680

Box 16.5 Affirmative Action：The Process of Statistical Hypothesis Testing，Using a Z test for Proportions684

Statistics in Practice：Attitudes Toward Illegal Immigrants685

Box 16.6 Attitudes Toward Illegal Immigrants：The Process of Statistical Hypothesis Testing，Using a t Test687

Statistics in Practice：Education and Employment688

Sampling Technique and Sample Characteristics689

Comparing Ratings of the Major Between Sociology and Other Social Science Alumni691

Ratings of Foundational Skills in Sociology：Changes over Time692

Box 16.7 Education and Employment：The Processof Statistical Hypothesis Testing，Using Chi-Square694

Gender Differences in Ratings of Foundational Skills，Occupational Prestige，and Income696

Box 16.8 Occupational Prestige of Male and Female Sociology Alumni：Another Example Using a t Test698

Conclusion699

EXERCISES700

SPSS PROBLEMS706

Appendix A Table of Random Numbers709

Appendix B The Standard Normal Table713

Appendix C Distribution of t718

Appendix D Distribution of Chi-Square720

Appendix E How to Use a Statistical Package721

Appendix F The General Social Survey738

Appendix G A Basic Math Review739

Appendix H How to Use the GSS Data Files and Lotus ScreenCam741

Answers to Odd-Numbered Exercises/Answers-1749

Index/Glossary/Index-1774