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