Statistics for Social Understanding (eBook)

Nancy Whittier is Sophia Smith Professor of Sociology at Smith College. She has taught statistics and research methods for 25 years, and also teaches classes on gender, sexuality, and social movements. She is the author of Frenemies: Feminists, Conservatives, and Sexual Violence (Oxford University Press, 2018), The Politics of Child Sexual Abuse: Emotions, Social Movements, and the State (Oxford University Press, 2009) and numerous articles on social movements, gender, and sexual violence.Tina Wildhagen is Associate Professor of Sociology and Dean of the Sophomore Class at Smith College. She has taught statistics and quantitative research methods for more than a decade, and also teaches courses on privilege and power in American education, inequality in higher education.Howard J. Gold is Professor of Government at Smith College. He has taught statistics for 30 years, and also teaches courses on American elections, public opinion and the media, and political behavior. His research focuses on public opinion, partisanship, and voting behavior.

Preface About the AuthorsChapter 1 Introduction Why Study Statistics? Research Questions and the Research Process Pinning Things Down: Variables and Measurement Units of Analysis Measurement Error: Validity and Reliability Levels of Measurement Causation: Independent and Dependent Variables Getting the Data: Sampling and GeneralizingSampling Methods Sources of Secondary Data: Existing Data Sets, Reports, and “Big Data” Big DataGrowth Mindset and Math Anxiety Using This BookStatistical SoftwareChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 2 Getting to Know Your DataFrequency DistributionsPercentages and ProportionsCumulative Percentage and PercentilePercent ChangeRates and RatiosRatesRatiosWorking with Frequency Distribution TablesMissing ValuesSimplifying Tables by Collapsing CategoriesGraphical Displays of a Single Variable: Bar Graphs, Pie Charts, Histograms, Stem-and-Leaf Plots, and Frequency PolygonsBar Graphs and Pie Charts HistogramsStem-and-Leaf-PlotsFrequency PolygonsTime Series ChartsComparing Two Groups On the Same Variable Using Tables, Graphs, and ChartsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 3 Examining Relationships between Two VariablesCross-Tabulations and Relationships between VariablesIndependent and Dependent VariablesColumn, Row, and Total PercentagesInterpreting the Strength of RelationshipsInterpreting the Direction of RelationshipsGraphical Representations of Bivariate RelationshipsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 4 Typical Values in a GroupWhat Does It Mean to Describe What Is Typical?MeanMedianModeFinding the Mode, Median, and Mean in Frequency DistributionsChoosing the Appropriate Measure of Central TendencyMedian Versus Mean IncomeChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 5 The Diversity of Values in a GroupRangeInterquartile RangeStandard DeviationUsing the Standard Deviation to Compare DistributionsComparing Apples and OrangesSkewed Versus Symmetric DistributionsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 6 Probability and the Normal DistributionThe Rules of ProbabilityThe Addition RuleThe Complement RuleThe Multiplication Rule with IndependenceThe Multiplication Rule without IndependenceApplying the Multiplication Rule with Independence to the “Linda” and “Birth-Order” Probability ProblemsThe Normal DistributionStandardizing Variables and Calculating Z-ScoresChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 7 From Sample to PopulationRepeated Sampling, Sample Statistics, and the Population ParameterSampling DistributionsFinding the Probability of Obtaining A Specific Sample StatisticEstimating the Standard Error from a Known Population Standard DeviationFinding and Interpreting the Z-Score for Sample MeansFinding and Interpreting the Z-Score for Sample ProportionsThe Impact of Sample Size On the Standard ErrorChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 8 Estimating Population ParametersInferential Statistics and the Estimation of Population ParametersConfidence Intervals Manage Uncertainty Through Margins of ErrorCertainty and Precision of Confidence IntervalsConfidence Intervals for ProportionsConstructing a Confidence Interval for Proportions: ExamplesConfidence Intervals for MeansThe t-DistributionCalculating Confidence Intervals for Means: ExamplesThe Relationship Between Sample Size and Confidence Interval RangeThe Relationship Between Confidence Level and Confidence Interval RangeInterpreting Confidence IntervalsHow Big a Sample?Assumptions for Confidence IntervalsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 9 Differences between Samples and PopulationsThe Logic of Hypothesis TestingNull Hypotheses (H0) and Alternative Hypotheses (Ha)One-Tailed and Two-Tailed TestsHypothesis Tests for ProportionsThe Steps of the Hypothesis TestOne-Tailed and Two-Tailed TestsHypothesis Tests for MeansExample: Testing a Claim about a Population MeanError and Limitations: How Do We Know We are Correct?Type I and Type II ErrorsWhat Does Statistical Significance Really Tell Us? Statistical and Practical Significance Chapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 10 Comparing GroupsTwo-Sample Hypothesis TestsThe Logic of the Null Hypothesis and Alternative Hypothesis in Two-Sample TestsNotation for Two-Sample TestsThe Sampling Distribution for Two-Sample TestsHypothesis Tests for Differences Between MeansConfidence Intervals for Differences Between MeansHypothesis Tests for Differences Between ProportionsConfidence Intervals for Differences Between ProportionsStatistical and Practical Significance in Two-Sample TestsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 11 Testing Mean Differences among Multiple GroupsComparing Variation Within and Between GroupsHypothesis Testing Using AnovaAnalysis of Variance AssumptionsDetermining Which Means are Different: Post-Hoc TestsAnova Compared to RepeateD t-TestsChapter Summary Using StataUsing SPSSPractice ProblemsChapter 12 Testing the Statistical Significance of Relationships in Cross-TabulationsThe Logic of Hypothesis Testing with Chi-SquareThe Steps of a Chi-Square TestSize and Direction of Effects: Analysis of ResidualsExample: Gender and Perceptions of HealthAssumptions of Chi-SquareStatistical Significance and Sample SizeChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 13 Ruling Out Competing Explanations for Relationships between VariablesCriteria for Causal RelationshipsModeling Spurious RelationshipsModeling Non-Spurious RelationshipsChapter SummaryUsing StataUsing SPSSPractice ProblemsChapter 14 Describing Linear Relationships between VariablesCorrelation CoefficientsCalculating Correlation CoefficientsScatterplots: Visualizing CorrelationsRegression: Fitting a Line to a ScatterplotThe “Best-Fitting” LineSlope and InterceptCalculating the Slope and InterceptGoodness-of-Fit MeasuresR-Squared (r2)Standard Error of PredictionDichotomous (“Dummy”) Independent VariablesMultiple RegressionStatistical Inference for RegressionThe F-StatisticStandard Error of the SlopeAssumptions of RegressionChapter SummaryUsing StataUsing SPSSPractice ProblemsSolutions to Odd Numbered Practice ProblemsGlossaryAppendix A Normal TableAppendix B Table of t-ValuesAppendix C F-Table, for Alpha = .05Appendix D Chi-Square TableAppendix E Selected List of FormulasAppendix F Choosing Tests for Bivariate RelationshipsIndex