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 Basic Mathematics ReviewChapter 1: Introduction1.1 Why Study Statistics?1.2 The Role of Statistics in Scientific Inquiry1.3 The Goals of This Text1.4 Descriptive and Inferential Statistics1.5 Level of MeasurementPART I DESCRIPTIVE STATISTICSChapter 2: Basic Descriptive Statistics: Percentages, Ratios and Rates, Frequency Distributions2.1 Percentages and Proportions2.2 Ratios, Rates, and Percentage Change2.3 Frequency Distributions: Introduction2.4 Frequency Distributions for Variables Measured at the Nominal and Ordinal Levels / 39 2.5 Frequency Distributions for Variables Measured at the IntervalRatio Level 2.6 Constructing Frequency Distributions for Interval-Ratio Level Variables2.7 Charts & Graphs Chapter 3: Measures of Central Tendency / 854.1 Introduction / 854.2 The Mode / 854.3 The Median / 87 One Step at a Time: Finding the Median / 894.4 The Mean / 89 Application 4.1 / 90 One Step at a Time: Computing the Mean / 904.5 Three Characteristics of the Mean / 91 Becoming a Critical Consumer: Using an Appropriate Measure of Central Tendency / 944.6 Choosing a Measure of Central Tendency Chapter 5 / Measures of Dispersion / 105 5.1 Introduction / 105 5.2 The Range (R) and Interquartile Range (Q) / 106 5.3 Computing the Range and Interquartile Range / 107 5.4 The Standard Deviation and Variance / 108 Application 5.1 / 111 One Step at a Time: Computing the Standard Deviation / 112 Application 5.2 / 112 5.5 Computing the Standard Deviation: An Additional Example / 113 Application 5.3 / 114 5.6 Interpreting the Standard Deviation / 115 Becoming a Critical Consumer: Getting the Whole Picture / 116 SUMMARY / 118 • SUMMARY OF FORMULAS / 119 • GLOSSARY / 119 • PROBLEMS / 119 • YOU ARE THE RESEARCHER: The Typical American and U.S. Culture Wars Revisited / 122Chapter 6 / The Normal Curve / 127 6.1 Introduction / 127 6.2 Computing Z Scores / 130 One Step at a Time: Computing Z Scores / 130 6.3 The Normal Curve Table / 131 6.4 Finding Total Area Above and Below a Score / 132 One Step at a Time: Finding Areas Above and Below Positive and Negative Z Scores / 134 Application 6.1 / 135 6.5 Finding Areas Between Two Scores / 135 One Step at a Time: Finding Areas Between Z scores / 136 Application 6.2 / 137 6.6 Using the Normal Curve to Estimate Probabilities / 137 One Step at a Time: Finding Probabilities / 139 Becoming a Critical Consumer: Applying the Laws of Probability / 140 SUMMARY / 141 • SUMMARY OF FORMULAS / 141 • GLOSSARY / 142 • PROBLEMS / 142 DETAILED CONTENTS vii PART II INFERENTIAL STATISTICSChapter 7 / Introduction to Inferential Statistics, the Sampling Distribution, and Estimation / 146 7.1 Introduction / 146 7.2 Probability Sampling / 147 7.3 The Sampling Distribution / 148 7.4 The Sampling Distribution: An Additional Example / 152 7.5 Symbols and Terminology / 154 7.6 Introduction to Estimation / 155 7.7 Bias and Effi ciency / 155 7.8 Estimation Procedures: Introduction / 158 7.9 Interval Estimation Procedures for Sample Means (Large Samples) / 160 One Step at a Time: Constructing Confi dence Intervals for Sample Means / 162 Application 7.1 / 162 7.10 Interval Estimation Procedures for Sample Proportions (Large Samples) / 163 One Step at a Time: Constructing Confi dence Intervals for Sample Proportions / 164 Becoming a Critical Consumer: Public Opinion Polls, Election Projections, and Surveys / 165 Application 7.2 / 168 Application 7.3 / 168 7.11 A Summary of the Computation of Confi dence Intervals / 169 7.12 Controlling the Width of Interval Estimates / 169 SUMMARY / 171 • SUMMARY OF FORMULAS / 172 • GLOSSARY / 172 • PROBLEMS / 173 • YOU ARE THE RESEARCHER: Estimating the Characteristics of the Typical American / 175Chapter 8 / Hypothesis Testing I: The One-Sample Case / 177 8.1 Introduction / 177 8.2 An Overview of Hypothesis Testing / 178 8.3 The Five-Step Model for Hypothesis Testing / 183 viii DETAILED CONTENTS One Step at a Time: Testing the Signifi cance of the Difference Between a Sample Mean and a Population Mean: Computing Z(obtained) and Interpreting Results / 186 8.4 One-Tailed and Two-Tailed Tests of Hypothesis / 186 8.5 Selecting an Alpha Level / 191 8.6 The Student’s t Distribution / 192 One Step at a Time: Testing the Signifi cance of the Difference Between a Sample Mean and a Population Mean Using the Student’s t distribution: Computing t(obtained) and Interpreting Results / 196 Application 8.1 / 197 8.7 Tests of Hypotheses for Single-Sample Proportions (Large Samples) / 197 One Step at a Time: Testing the Signifi cance of the Difference Between a Sample Proportion and a Population Proportion: Computing Z(obtained) and Interpreting Results / 199 Application 8.2 / 200 SUMMARY / 201 • SUMMARY OF FORMULAS / 201 • GLOSSARY / 201 • PROBLEMS / 202 Chapter 9 / Hypothesis Testing II: The Two-Sample Case / 206 9.1 Introduction / 206 9.2 Hypothesis Testing with Sample Means (Large Samples) / 206 One Step at a Time: Testing the Difference in Sample Means for Signifi cance (Large Samples): Computing Z(obtained) and Interpreting Results / 210 Application 9.1 / 210 9.3 Hypothesis Testing with Sample Means (Small Samples) / 211 One Step at a Time: Testing the Difference in Sample Means for Signifi cance (Small Samples): Computing t(obtained) and Interpreting Results / 213 9.4 Hypothesis Testing with Sample Proportions (Large Samples) / 214 One Step at a Time: Testing the Difference in Sample Proportions for Signifi cance (Large Samples): Computing Z(obtained) and Interpreting Results Step-by-Step / 216 Application 9.2 / 216 9.5 The Limitations of Hypothesis Testing: Signifi cance versus Importance / 217 DETAILED CONTENTS ix Becoming a Critical Consumer: When Is a Difference a Difference? / 219 SUMMARY / 221 • SUMMARY OF FORMULAS / 221 • GLOSSARY / 222 • PROBLEMS / 222 • YOU ARE THE RESEARCHER: Gender Gaps and Support for Traditional Gender Roles / 226Chapter 10 / Hypothesis Testing III: The Analysis of Variance / 232 10.1 Introduction / 232 10.2 The Logic of the Analysis of Variance / 233 10.3 The Computation of ANOVA / 234 One Step at a Time: Computing ANOVA / 236 10.4 A Computational Example / 237 10.5 A Test of Signifi cance for ANOVA / 237 10.6 An Additional Example for Computing and Testing the Analysis of Variance / 239 Application 10.1 / 241 10.7 The Limitations of the Test / 242 Becoming a Critical Consumer: Reading the Professional Literature / 243 SUMMARY / 244 • SUMMARY OF FORMULAS / 245 • GLOSSARY / 245 • PROBLEMS / 245 • YOU ARE THE RESEARCHER: Why Are Some People Liberal (or Conservative)? Why Are Some People More Sexually Active? / 249 Chapter 11 / Hypothesis Testing IV: Chi Square / 256 11.1 Introduction / 256 11.2 Bivariate Tables / 256 11.3 The Logic of Chi Square / 258 11.4 The Computation of Chi Square / 259 One Step at a Time: Computing Chi Square / 261 11.5 The Chi Square Test for Independence / 261 One Step at a Time: Computing Column Percentages / 264 Application 11.1 / 264 11.6 The Chi Square Test: An Additional Example / 265 11.7 The Limitations of the Chi Square Test / 268 x DETAILED CONTENTS Becoming a Critical Consumer: Reading the Professional Literature / 269 SUMMARY / 270 • SUMMARY OF FORMULAS / 270 • GLOSSARY / 270 • PROBLEMS / 271 • YOU ARE THE RESEARCHER: Understanding Political Beliefs / 275 PART III MEASURES OF ASSOCIATION / 281 Chapter 12 / Introduction to Bivariate Association and Measures of Association for Variables Measured at the Nominal Level / 282 12.1 Statistical Signifi cance and Theoretical Importance / 282 12.2 Association Between Variables and Bivariate Tables / 283 12.3 Three Characteristics of Bivariate Associations / 285 Application 12.1 / 289 12.4 Introduction to Measures of Association / 290 12.5 Measures of Association for Variables Measured at the Nominal Level: Chi Square-Based Measures / 290 One Step at a Time: Calculating and Interpreting Phi and Cramer’s V / 293 Application 12.2 / 294 12.6 Lambda: A Proportional Reduction in Error Measure of Association for Nominal Level Variables / 295 One Step at a Time: Calculating and Interpreting Lambda / 298 Becoming a Critical Consumer: Reading Percentages / 299 SUMMARY / 300 • SUMMARY OF FORMULAS / 300 • GLOSSARY / 300 • PROBLEMS / 301 • YOU ARE THE RESEARCHER: Understanding Political Beliefs, Part II / 303 Chapter 14 / Association Between Variables Measured at the Ordinal Level / 308 13.1 Introduction / 308 13.2 Proportional Reduction in Error / 308 13.3 Gamma / 309 13.4 Determining the Direction of Relationships / 313 One Step at a Time: Computing and Interpreting Gamma / 316 Application 13.1 / 317 DETAILED CONTENTS xi 13.5 Spearman’s Rho (rs ) / 317 One Step at a Time: Computing and Interpreting Spearman’s Rho / 320 Application 13.2 / 321 SUMMARY / 321 • SUMMARY OF FORMULAS / 321 • GLOSSARY / 321 • PROBLEMS / 322 • YOU ARE THE RESEARCHER: Exploring Sexual Attitudes and Behavior / 325Chapter 14 / Association Between Variables Measured at the Interval-Ratio Level / 330 14.1 Introduction / 330 14.2 Scattergrams / 330 14.3 Regression and Prediction / 334 14.4 Computing a and b / 336 One Step at a Time: Computing the Slope ( b) / 338 One Step at a Time: Computing the Y Intercept ( a) / 338 One Step at a Time: Using the Regression Line to Predict Scores on Y / 339 14.5 The Correlation Coeffi cient (Pearson’s r) / 339 One Step at a Time: Computing Pearson’s r / 341 14.6 Interpreting the Correlation Coeffi cient: r 2 / 341 Application 14.1 / 344 14.7 The Correlation Matrix / 345 Becoming a Critical Consumer: Correlation, Causation, and Cancer / 347 14.8 Correlation, Regression, Level of Measurement, and Dummy Variables / 349 SUMMARY / 350 • SUMMARY OF FORMULAS / 351 • GLOSSARY / 351 • PROBLEMS / 352 • YOU ARE THE RESEARCHER: Who Surfs the Internet? Who Succeeds in Life? / 355 PART IV MULTIVARIATE TECHNIQUES / 361Chapter 15 / Partial Correlation and Multiple Regression and Correlation / 362 15.1 Introduction / 362 15.2 Partial Correlation / 362 xii DETAILED CONTENTS One Step at a Time: Computing and Interpreting Partial Correlations / 366 15.3 Multiple Regression: Predicting the Dependent Variable / 367 One Step at a Time: Computing and Interpreting Partial Slopes / 369 One Step at a Time: Computing the Y intercept / 370 One Step at a Time: Using the Multiple Regression Line to Predict Scores on Y / 371 15.4 Multiple Regression: Assessing the Effects of the Independent Variables / 371 One Step at a Time: Computing and Interpreting Beta-Weights ( b*) / 372 15.5 Multiple Correlation / 373 One Step at a Time: Computing and Interpreting the Coeffi cient of Multiple Determination ( R2 ) / 375 15.6 The Limitations of Multiple Regression and Correlation / 375 Becoming a Critical Consumer: Is Support for the Death Penalty Related to White Racism? / 376 Application 15.1 / 378 SUMMARY / 379 • SUMMARY OF FORMULAS / 380 • GLOSSARY / 380 • PROBLEMS / 381 • YOU ARE THE RESEARCHER: A Multivariate Analysis of Internet Use and Success / 384 Appendix A Area Under the Normal Curve / 389 Appendix B Distribution of t / 393 Appendix C Distribution of Chi Square / 394 Appendix D Distribution of F / 395 Appendix E Using Statistics: Ideas for Research Projects / 397 Appendix F An Introduction to SPSS for Windows / 402 Appendix G Code Book for the General Social Survey, 2006 / 409 Appendix H Glossary of Symbols / 416 Answers to Odd-Numbered Computational Problems / 418 Glossary / 428 Index / 434 Part I: OVERVIEWChapter 1. Statistics and Scientific Method.Part II: DESCRIPTIVE STATISTICS.2. Basic Mathematical and Measurement Concepts.3. Frequency Distributions.4. Measures of Central Tendency and Variability.5. The Normal Curve and Standard Scores.6. Correlation.7. Linear Regression.Part III: INFERENTIAL STATISITCS8. Random Sampling and Probability.9. Binomial Distribution.10. Introduction to Hypothesis Testing Using the Sign Test.11. Power.12. Sampling Distributions, Sampling Distribution of the Mean, the Normal Deviate (z) Test.13. Student's t-Test for Single Samples.14. Student's t-Test for Correlated and Independent Groups.15. Introduction to the Analysis of Variance.16. Introduction to Two-Way Analysis of Variance.17. Chi-Square and Other Nonparametric Tests.