Statistical Design and Inference for the Social Sciences

Donald Vandegrift is a Professor of Economics at The College of New Jersey in Ewing, NJ where he teaches courses in statistics and economics. He received a BA from the College of William and Mary and a Ph.D. from the University of Connecticut. His primary areas of research are urban issues and experimental/behavioral economics. His urban research considers the amenity value and economic development effects of large institutions, crime and policing, and the economic effects of transport projects and land-use regulation. This research has appeared in Landscape and Urban Planning, Journal of Quantitative Criminology, Urban Affairs Review, Journal of Regional Science, Annals of Regional Science, Health & Place, and Research in Transportation Economics, among others. His experimental/behavioral research considers the effect of compensation schemes on risk taking, unproductive activities (i.e., sabotage), decisions to compete, and behavioral norms. This research has appeared in Journal of Economic Behavior and Organization, Experimental Economics, Labour Economics, Journal of Neuroscience, Psychology, and Economics, Journal of Research in Personality, and Journal of Institutional and Theoretical Economics. Grants from the National Science Foundation, the Lincoln Institute of Land Policy, and the Institute for Humane Studies have supported his research.

A soup to nuts introduction to statistics for the social researcher grounded in theory, real-life application, and critical analysis.

• PrefaceAcknowledgmentsForewardChapter 1: Making the Right Comparison: Understanding the Rules and Limitations of Quantitative ReasoningPositive and Normative StatementsDeduction and InductionUsing Deduction and Induction TogetherCause and AssociationLinking Deduction with Induction – Measurement ValidityA Note of Caution on MeasurementLinking Deduction with Induction – Measurement ReliabilityExercisesChapter 2: Making the Right Comparison: Observations, Variable Types, Data Displays, and Data ConversionsData Sets and Variable TypesVariable Types and Data DisplaysChoice of Divisor in Creating RatiosOther Types of Data Conversions: Adjusting for InflationOther Types of Data Conversions: Adjusting for SeasonalityOther Types of Data Conversions: Adjusting for NoiseExercisesChapter 3: Using Stata and Excel to Create Line, Bar, and Scatter DiagramsUsing StataUsing ExcelExercisesChapter 4: Summarizing Variables using Measures of Central Tendency and DispersionMeasures of Central Tendency – The MeanMeasures of Central Tendency – The MedianMeasures of Central Tendency – The ModeMeasures of Dispersion – The RangeMeasures of Dispersion – The Mean Absolute DeviationMeasures of Dispersion – The Variance and Standard DeviationPopulations and SamplesAppendixMeasures of Central Tendency and Dispersion Using Statistical SoftwareMeasures of Central Tendency and Dispersion in StataHistograms in StataMeasures of Central Tendency and Dispersion in ExcelHistograms in ExcelExercisesChapter 5: Research Design and Statistical FallaciesRandom Assignment and Wellness ProgramsBroader Lessons from Comparing Studies on the Effectiveness of Wellness ProgramsInferring Cause When RCTs Are Not PossibleWrongly Inferring Association: Regression Fallacy and MaturationWrongly Inferring Association: Ecological and Reductionist FallaciesWrongly Inferring Association: Simpson’s ParadoxWrongly Inferring Association: Cherry PickingWrongly Inferring Cause: Selection Bias and Sample MortalityWrongly Inferring Cause: Bidirectional CausalityExercisesChapter 6: Constructing Informative Comparisons and Inferring CauseJohn Snow’s EvidenceJohn Snow, Cholera, and General Rules for Quantitative ComparisonsDescriptive, Correlational, and Causal ResearchThe Difficulty of Establishing Cause Varies with ContextSorting Data and Making Comparisons to Produce Evidence on CauseData Sorting and Cause: An ExampleDifference-in-Differences AnalysisDifference-in-Differences: An ExampleDiscontinuity AnalysisDiscontinuity Analysis: An ExampleExercisesChapter 7: Sampling Distributions and Statistical InferenceBasic ProbabilityRandom Variables and Their Probability DistributionsDiscrete Probability FunctionsProbability Density FunctionsThe Uniform Probability DistributionThe Normal Probability DistributionThe Sampling Distribution and the Central Limit TheoremConfidence IntervalsConfidence Intervals for Means Using the z Distribution (s Known)Confidence Intervals for Proportions Using the z DistributionConfidence Intervals for Means Using the t Distribution (s Unknown)Choosing the Right Procedure to Calculate a Confidence IntervalExercisesChapter 8: One-Sample Hypothesis TestsThe Basic Structure of Hypothesis TestsThe Null and the Alternative HypothesesOne-Tailed and Two-Tailed Hypothesis TestsType I and Type II ErrorsOne- and Two-Sample Hypothesis TestsSampling Distributions and the Structure of One-Sample Hypothesis TestsUnderstanding Test Statistics for One-Sample Hypothesis TestsExecuting One-Sample Hypothesis Tests for a Population Mean Using the z DistributionExecuting One-Sample Hypothesis Tests for a Population Proportion Using the z DistributionExecuting One-Sample Hypothesis Tests for a Population Mean Using the t DistributionSummarizing the Steps for One-Sample Hypothesis TestsHypothesis Tests and Confidence IntervalsAppendixConfidence Intervals and Hypothesis Tests Using Statistical SoftwareConfidence Intervals and Hypothesis Tests in Stata Using Univariate MeasuresConfidence Intervals and Hypothesis Tests in Stata Using Sample ObservationsConfidence Intervals and Hypothesis Tests in Excel Using Sample ObservationsExercisesChapter 9: Two-Sample Hypothesis Tests of MeansTwo-Sample Hypothesis Tests and CauseUndefined Populations and External ValidityDependent and Independent SamplesOne-Sample Hypothesis Tests and Two-Sample Hypothesis TestsTwo-Sample Hypothesis Tests of Means: Independent SamplesTwo-Sample Hypothesis Test of Means: Dependent SamplesExecuting Two-Sample Hypothesis Tests on Means: MurdersSummarizing the Two-Sample Hypothesis Tests of MeansAppendixTwo-Sample Hypothesis Tests of Means Using Statistical SoftwareTwo-Sample Hypothesis Tests of Means in Stata Using Univariate MeasuresTwo-Sample Hypothesis Tests of Means in Stata Using Sample ObservationsTwo-Sample Hypothesis Tests of Means in Excel Using Sample ObservationsExercisesChapter 10: Two-Sample Hypothesis Tests of ProportionsTwo-Sample Hypothesis Test for Proportions: Independent SamplesTwo-Sample Hypothesis Test for Proportions: Dependent SamplesSummarizing the Two-Sample Hypothesis Tests of ProportionsAppendixTwo-Sample Hypothesis Tests of Proportions Using Statistical SoftwareTwo-Sample Hypothesis Tests of Proportions in Stata Using Univariate MeasuresTwo-Sample Hypothesis Tests of Proportions in Stata Using Sample ObservationsTwo-Sample Hypothesis Tests of Proportions in Excel Using Sample ObservationsExercisesChapter 11: Correlation and Simple Linear RegressionCorrelationCalculating the Correlation Coefficient and Testing the Hypothesis ? = 0Simple Linear RegressionSimple Linear Regression as Estimating Relationships Using (x, y) CoordinatesCalculating Coefficients in a Simple Linear RegressionTesting Coefficients of a Simple Linear RegressionCalculating R^2AppendixCorrelation and Simple Linear Regression Using Statistical SoftwareCorrelation in StataSimple Linear Regression in StataCorrelation in ExcelSimple Linear Regression in ExcelExercisesChapter 12: Simple Linear Regression: Assumptions and ExtensionsAssumptions of Simple Linear RegressionNonlinear Relationships and Log Transformation in Simple Linear RegressionDichotomous Independent Variables in Simple Linear RegressionDetecting and Correcting Serial AutocorrelationDetecting and Correcting HeteroskedasticityTransforming Variables to Support Causal Claims: Time Lags and ChangesAppendixSimple Linear Regression Procedures Using Statistical SoftwareExecuting Log-Transform Simple Linear Regression in StataDetecting and Correcting Serial Autocorrelation in StataDetecting and Correcting Heteroskedasticity in StataUsing Stata to Transform Variables and Generate Evidence on CauseExecuting Log-Transform Simple Linear Regression in ExcelDetecting Serial Correlation in ExcelDetecting Heteroskedasticity in ExcelUsing Excel to Transform Variables and Generate Evidence on CauseExercisesGlossary