1.The What and the Why of Statistics 1
The Research Process 2
Asking Research Questions 3
The Role of Theory 4
Formulating the Hypotheses 5
Independent and Dependent Variables：Causality 7
Independent and Dependent Variables：Guidelines 9
Collecting Data 10
Levels of Measurement 11
Nominal Level of Measurement 11
Ordinal Level of Measurement 12
Interval-Ratio Level of Measurement 12
Cumulative Property of Levels of Measurement 13
Levels of Measurement of Dichotomous Variables 13
Discrete and Continuous Variables 16
A Closer Look 1.1：A Cautionary Note：Measurement Error 16
Analyzing Data and Evaluating the Hypotheses 17
Descriptive and Inferential Statistics 17
Evaluating the Hypotheses 18
Looking at Social Differences 19
A Closer Look 1.2：A Tale of Simple Arithmetic：How Culture May Influence How We Count 20
A Closer Look 1.3：Are You Anxious About Statistics？ 21
2.Organization of Information：Frequency Distributions 27
Frequency Distributions 28
Proportions and Percentages 29
Percentage Distributions 31
Comparisons 32
Statistics in Practice：Labor Force Participation Among Foreign Born 33
The Construction of Frequency Distributions 35
Frequency Distributions for Nominal Variables 37
Frequency Distributions for Ordinal Variables 37
Frequency Distributions for Interval-Ratio Variables 38
Cumulative Distributions 43
A Closer Look 2.1：Real Limits，Stated Limits，and Midpoints ofClass Intervals 44
Rates 47
Statistics in Practice：Civilian Labor Force Participation Rates Over Time 48
Reading the Research Literature：Statistical Tables 48
Basic Principles 49
Tables With a Different Format 51
Conclusion 52
3.Graphic Presentation 65
The Pie Chart：Race and Ethnicity of the Elderly 66
The Bar Graph：Marital Status of the Elderly 68
The Statistical Map：The Geographic Distribution of the Elderly 70
The Histogram 71
Statistics in Practice：Gender and Age 73
The Line Graph 75
Time-Series Charts 77
A Closer Look 3.1：A Cautionary Note：Distortions in Graphs 79
Statistics in Practice：The Graphic Presentation of Education 81
4.Measures of Central Tendency 96
The Mode 97
The Median 100
Finding the Median in Sorted Data 101
An Odd Number of Cases 101
An Even Number of Cases 103
Finding the Median in Frequency Distributions 104
Statistics in Practice：Gendered Income Inequality 105
Locating Percentiles in a Frequency Distribution 106
The Mean 108
Calculating the Mean 109
A Closer Look 4.1：Finding the Mean in a Frequency Distribution 110
Understanding Some Important Properties of the Arithmetic Mean 113
Interval-Ratio Level of Measurement 113
Center of Gravity 113
Sensitivity to Extremes 113
The Shape of the Distribution：Television，Education，and Siblings 116
The Symmetrical Distribution 116
The Positively Skewed Distribution 117
The Negatively Skewed Distribution 119
Guidelines for Identifying the Shape of a Distribution 120
Considerations for Choosing a Measure of Central Tendency 121
Level of Measurement 121
Skewed Distribution 121
Symmetrical Distribution 122
A Closer Look 4.2：A Cautionary Note：Representing Income 122
5.Measures of Variability 135
The Importance of Measuring Variability 136
The Index of Qualitative Variation：A Brief Introduction 138
Steps for Calculating the IQV 139
A Closer Look 5.1：Statistics in Practice：Diversity at Berkeley Through the Years 140
Expressing the IQV as a Percentage 141
Statistics in Practice：Diversity in U.S.Society 142
The Range 143
The Interquartile Range：Increases in Elderly Population 145
The Box Plot 147
The Variance and the Standard Deviation：Changes in the Elderly Population 151
Calculating the Deviation From the Mean 152
Calculating the Variance and the Standard Deviation 154
Focus on Interpretation：GDP for Selected Countries 156
Considerations for Choosing a Measure of Variation 159
Reading the Research Literature：Differences in College Aspirations and Expectations Among Latino Adolescents 160
6.The Normal Distribution 177
Properties of the Normal Distribution 178
Empirical Distributions Approximating the Normal Distribution 178
An Example：Final Grades in Statistics 179
Areas Under the Normal Curve 180
Interpreting the Standard Deviation 181
Standard （Z） Scores 182
Transforming a Raw Score Into a Z Score 182
Transforming a Z Score Into a Raw Score 184
The Standard Normal Distribution 185
The Standard Normal Table 185
The Structure of the Standard Normal Table 186
Transforming Z Scores Into Proportions （or Percentages） 187
Finding the Area Between the Mean and a Specified Positive Z Score 188
Finding the Area Between the Mean and a Specified Negative Z Score 188
Finding the Area Above a Positive Z Score or Below a Negative Z Score 189
Transforming Proportions （or Percentages） Into Z Scores 190
Finding a Z Score Bounding an Area Above It 191
Finding a Z Score Bounding an Area Below It 192
Working With Percentiles in a Normal Distribution 193
Finding the Percentile Rank of a Score Higher Than the Mean 193
Finding the Percentile Rank of a Score Lower Than the Mean 194
Finding the Raw Score Associated With a Percentile Higher Than 50 195
Finding the Raw Score Associated With a Percentile Lower Than 50 196
A Final Note 197
7.Sampling and Sampling Distributions 206
Aims of Sampling 207
Some Basic Principles of Probability 209
Probability Defined 209
The Relative Frequency Method 209
The Normal Distribution and Probabilities 210
Probability Sampling 211
The Simple Random Sample 211
The Systematic Random Sample 213
The Stratified Random Sample 214
A Closer Look 7.1：Disproportionate Stratified Samples and Diversity 215
The Concept of the Sampling Distribution 216
The Population 217
The Sample 218
The Dilemma 219
The Sampling Distribution 219
The Sampling Distribution of the Mean 219
An Illustration 219
Review 222
The Mean of the Sampling Distribution 222
The Standard Error of the Mean 223
The Central Limit Theorem 224
The Size of the Sample 227
The Significance of the Sampling Distribution and the Central Limit Theorem 227
Statistics in Practice：The Central Limit Theorem 229
8.Estimation 237
Estimation Defined 238
Reasons for Estimation 239
Point and Interval Estimation 239
Procedures for Estimating Confidence Intervals for Means 240
A Closer Look 8.1：Estimation as a Type of Inference 241
Determining the Confidence Interval 242
Calculating the Standard Error of the Mean 243
Deciding on the Level of Confidence and Finding theCorresponding Z Value 243
Calculating the Confidence Interval 243
Interpreting the Results 244
Reducing Risk 244
Estimating Sigma 246
Calculating the Estimated Standard Error of the Mean 247
Deciding on the Level of Confidence and Finding theCorresponding Z Value 247
Calculating the Confidence Interval 247
Interpreting the Results 247
Sample Size and Confidence Intervals 247
A Closer Look 8.2：What Affects Confidence IntervalWidth？Summary 249
Statistics in Practice：Hispanic Migration and Earnings 250
Confidence Intervals for Proportions 253
Procedures for Estimating Proportions 254
Calculating the Estimated Standard Error of the Proportion 255
Deciding on the Desired Level of Confidence and Findingthe Corresponding Z Value 255
Calculating the Confidence Interval 255
Interpreting the Results 255
Statistics in Practice：The 2012 Benghazi Terrorist Attack Investigation 256
Calculating the Estimated Standard Error of the Proportion 256
Deciding on the Desired Level of Confidence and Finding theCorresponding Z Value 257
Calculating the Confidence Interval 257
Interpreting the Results 257
A Closer Look 8.3：A Cautionary Note：The Margin of Error 258
9.Testing Hypotheses 267
Assumptions of Statistical Hypothesis Testing 268
Stating the Research and Null Hypotheses 269
The Research Hypothesis （H1） 269
The Null Hypothesis （H0） 269
More About Research Hypotheses：One- and Two-Tailed Tests 270
Determining What Is Sufficiently Improbable：Probability Values and Alpha 271
The Five Steps in Hypothesis Testing：A Summary 275
Errors in Hypothesis Testing 276
The t Statistic and Estimating the Standard Error 278
The t Distribution and Degrees of Freedom 278
Comparing the t and Z Statistics 279
Statistics in Practice：The Earnings of White Women 280
Testing Hypotheses About Two Samples 281
The Assumption of Independent Samples 282
Stating the Research and Null Hypotheses 282
The Sampling Distribution of the Difference Between Means 283
Estimating the Standard Error 284
Calculating the Estimated Standard Error 284
The t Statistic 285
Calculating the Degrees of Freedom for a Difference Between Means Test 285
A Closer Look 9.1：Calculating the Estimated Standard Error andthe Degrees of Freedom（df）When the Population VariancesAre Assumed to Be Unequal 285
The Five Steps in Hypothesis Testing About Difference Between Means：A Summary 286
Focus on Interpretation：Cigarette Use Among Teens 287
Testing the Significance of the Difference Between Two Sample Proportions 289
Statistics in Practice：Comparing First- and Second-GenerationHispanic Americans 289
Focus on Interpretation：First- and Second-Generation Asian Americans 291
A Closer Look 9.2：A Cautionary Note：Is There a Significant Difference？ 292
Reading the Research Literature：Reporting the Results ofStatistical Hypothesis Testing 292
10.Bivariate Tables 303
Independent and Dependent Variables 304
How to Construct a Bivariate Table：Race and Home Ownership 305
How to Compute Percentages in a Bivariate Table 307
Calculating Percentages Within Each Category of the Independent Variable 308
Comparing the Percentages Across Different Categories of theIndependent Variable 308
A Closer Look 10.1：Percentaging a Bivariate Table 309
How to Deal With Ambiguous Relationships Between Variables 310
Reading the Research Literature：Place of Death in America 312
The Properties of a Bivariate Relationship 315
The Existence of the Relationship 316
The Strength of the Relationship 317
The Direction of the Relationship 317
Elaboration 319
Testing for Nonspuriousness：Firefighters and Property Damage 320
An Intervening Relationship：Religion and Attitude Toward Abortion 323
Conditional Relationships：More on Abortion 328
The Limitations of Elaboration 330
Statistics in Practice：Family Support for the Transition From High School 331
11.The Chi-Square Test and Measures of Association 347
The Concept of Chi-Square as a Statistical Test 350
The Concept of Statistical Independence 350
The Structure of Hypothesis Testing With Chi-Square 351
The Assumptions 351
Stating the Research and the Null Hypotheses 351
The Concept of Expected Frequencies 352
Calculating the Expected Frequencies 352
Calculating the Obtained Chi-Square 354
The Sampling Distribution of Chi-Square 355
Determining the Degrees of Freedom 356
Making a Final Decision 357
Review 358
A Closer Look 11.1：A Cautionary Note：Sample Size and Statistical Significance for Chi-Square 359
Focus on Interpretation：Education and Health Assessment 360
Reading the Research Literature：Violent Offense Onset by Gender，Race，and Age 362
Proportional Reduction of Error：A Brief Introduction 363
A Closer Look 11.2：What Is Strong？What Is Weak？A Guide to Interpretation 366
Lambda：A Measure of Association for Nominal Variables 367
A Method for Calculating Lambda 368
Some Guidelines for Calculating Lambda 369
Cramer’s V：A Chi-Square-Related Measure of Association for Nominal Variables 370
Focus on Interpretation：Gamma and Kendall’s Tau-b 370
Using Ordinal Measures With Dichotomous Variables 372
Focus on Interpretation：The Gender Gap in Gun Control 373
12.Analysis of Variance 388
Understanding Analysis of Variance 389
The Structure of Hypothesis Testing With ANOVA 391
The Assumptions 391
Stating the Research and the Null Hypotheses and Setting Alpha 392
The Concepts of Between and Within Total Variance 392
A Closer Look 12.1：Decomposition of SST 394
The F Statistic 395
Making a Decision 397
The Five Steps in Hypothesis Testing：A Summary 397
A Closer Look 12.2：Assessing the Relationship Between Variables 399
Focus on Interpretation：Are Immigrants Good for America’s Economy？ 399
Reading the Research Literature：Self-Image and Ethnic Identification 400
Reading the Research Literature：Stresses and Strains Among Grandmother Caregivers 402
13.Regression and Correlation 413
The Scatter Diagram 415
Linear Relations and Prediction Rules 417
Constructing Straight-Line Graphs 420
Finding the Best-Fitting Line 422
Defining Error 423
The Residual Sum of Squares （∑e2） 423
The Least Squares Line 424
Review 424
Computing a and b for the Prediction Equation 424
Interpreting a and b 427
Statistics in Practice：Median Household Income and Criminal Behavior 429
A Closer Look 13.1：Understanding the Covariance 429
A Closer Look 13.2：A Note on Nonlinear Relationships 430
Methods for Assessing the Accuracy of Predictions 432
Prediction Errors 434
The Coefficient of Determination （r2） as a PRE Measure 437
Calculating r2 439
Testing the Significance of r2 Using ANOVA 441
Making a Decision 443
Pearson’s Correlation Coefficient （r） 443
Characteristics of Pearson’s r 444
Statistics in Practice：Teen Pregnancy and Social Inequality 445
Focus on Interpretation：The Marriage Penalty in Earnings 448
Multiple Regression 450
ANOVA for Multiple Linear Regression 453
A Closer Look 13.3：A Cautionary Note：Spurious Correlations and Confounding Effects 454
Appendix A.Table of Random Numbers 477
Appendix B.The Standard Normal Table 480
Appendix C.Distribution of t 484
Appendix D.Distribution of Chi-Square 486
Appendix E.Distribution of F 487
Appendix F.A Basic Math Review 489
Learning Check Solutions 494
Answers to Odd-Numbered Exercises 504
Glossary 546
Notes 551
Index 556