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Basic Mathematics Review
Chapter 1: Introduction
1.1 Why Study Statistics?
1.2 The Role of Statistics in Scientific Inquiry
1.3 The Goals of This Text
1.4 Descriptive and Inferential Statistics
1.5 Level of Measurement
PART I DESCRIPTIVE STATISTICS
Chapter 2: Basic Descriptive Statistics: Percentages, Ratios and Rates, Frequency Distributions
2.1 Percentages and Proportions
2.2 Ratios, Rates, and Percentage Change
2.3 Frequency Distributions: Introduction
2.4 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 Variables
2.7 Charts & Graphs


Chapter 3: Measures of Central Tendency / 85
4.1 Introduction / 85
4.2 The Mode / 85
4.3 The Median / 87 One Step at a Time: Finding the Median / 89
4.4 The Mean / 89 Application 4.1 / 90 One Step at a Time: Computing the Mean / 90
4.5 Three Characteristics of the Mean / 91 Becoming a Critical Consumer: Using an Appropriate Measure of Central Tendency / 94
4.6 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 / 122


Chapter 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 STATISTICS
Chapter 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 / 175


Chapter 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 / 226


Chapter 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 / 325


Chapter 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 / 361
Chapter 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: OVERVIEW
Chapter 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 STATISITCS
8. 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.
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