Introduction To Statistics - Harvard University

Introduction to StatisticsKosuke ImaiDepartment of PoliticsPrinceton UniversityFall 2011Kosuke Imai (Princeton University)IntroductionPOL345 Lectures1 / 15

Descriptive and Statistical InferenceDescriptive inference:123Summarize the observed dataTables with statistics, Data visualization through graphsStatistic a function of dataStatistical inference:1234Learning about unknown parameters from observed dataStatistical models: All models are false but some are usefulUncertainty: How confident are you about your inference?Statistical tests: Does smoking cause cancer?Research design:123What data to collect and how?Designing experiments, sample surveys, etc.Mimicking experiments in observational studiesKosuke Imai (Princeton University)IntroductionPOL345 Lectures2 / 15

Examples of Statistical InferenceInference typesParametersDataForecastingfuture data pointspast dataSample surveyfeatures of population random sampleCausal inferencecounter-factualsfactualsKosuke Imai (Princeton University)IntroductionPOL345 Lectures3 / 15

Causal InferenceWhat does “A causes B” mean?Counterfactuals: “what if” questionsWhat we don’t observe: counterfactual outcomeWhat we observe: factual outcomeQuantity of interest: differences between the factual(observed) and counterfactual (unobserved) outcomesDoes the minimum wage increase the unemployment rate?Factual: observed unemployment rate given the enactedminimum wage increaseCounterfactual: (unobserved) unemployment rate that wouldhave been realized had the minimum wage increase notoccurredNo causation without manipulation: immutablecharacteristicsDoes race affect your job prospect?Kosuke Imai (Princeton University)IntroductionPOL345 Lectures4 / 15

Statistical Framework of Causal Inference“Treatment”: Contacted or notObserved outcome: TurnoutPre-treatment variables: e.g., Age, Party IDPotential outcomes:Voters ContactTurnoutAgeTreated esNo?62Party IDDRR.DCausal effect: Difference between two potential outcomesFundamental problem of causal inferenceKosuke Imai (Princeton University)IntroductionPOL345 Lectures5 / 15

How to Figure Out the Counterfactuals?Association is not causationFind a similar unit!Outcome: voter turnoutTreatment: get-out-the vote phone callsQuestion: How much does a GOTV call increase turnout?Find an observation with same voting history, partisanship,age, gender, job, income, education, etc.Match on observed confounders that are systematicallyrelated to both treatment and outcomeBut, we cannot match on everythingSelection bias due to unobserved confounding inobservational studiesKosuke Imai (Princeton University)IntroductionPOL345 Lectures6 / 15

Randomized ExperimentsRandomize!Key idea: Randomization of the treatment makes thetreatment and control groups “identical” on averageThe two groups are similar in terms of all (both observedand unobserved) characteristicsCan attribute the average differences in outcome to thedifference in the treatmentRandomized experiments as the gold standardPlacebo effects and double-blind experimentsR EADING : FPP Chapter 1Kosuke Imai (Princeton University)IntroductionPOL345 Lectures7 / 15

Example 1: Get-Out-the-Vote ExperimentsWhat methods and messages work best for which voters?Selection bias: campaigns target certain votersRandomize the message each voter receivesHundreds of GOTV field experiments by political scientistsCivic duty message:Kosuke Imai (Princeton University)IntroductionPOL345 Lectures8 / 15

Social pressure message:Gerber, Green, and Larimer. (2008). American Political ScienceReview.Turnout: 31.5% (civic duty), 37.8% (social pressure)Kosuke Imai (Princeton University)IntroductionPOL345 Lectures9 / 15

Example 2: Employment DiscriminationDoes race affect employment prospect?Selection bias: African Americans and Whites are differentin terms of qualifications (e.g., education levels)Randomize applicant names in their resumeOutcome: call-back rateWhite female Black femaleWhite maleBlack maleEmily7.9 Aisha2.2 Todd5.9 Rasheed 3.0Anne8.3 Keisha 3.8 Neil6.6 Tremayne 4.3Jill8.4 Tamika 5.5 Geoffrey 6.8 Kareem4.7Allison 9.5 Lakisha 5.5 Brett6.8 Darnell4.8Laurie9.7 Latoya 5.8 Brendan 7.7 Tyrone5.3Bertrand and Mullainathan. (2004). American Economic ReviewKosuke Imai (Princeton University)IntroductionPOL345 Lectures10 / 15

Experimental vs. Observational StudiesR EADING : FPP Chapter 2Hormone-Replacement Therapy (HRT)Estrogen to replace the hormonesNurses’ Health Study (1985; observational study):HRT reduced the risk of heart disease by two thirdsIn 2001, 15 million women were filling HRT prescriptionsTwo randomized clinical trials:12Heart and Estrogen-progestin Replacement Study (1998)Women’s Health Initiative (2002)HRT increases the risk of heart disease, stroke, blood clots,breast cancer, etc.Where did this stark difference come from?Kosuke Imai (Princeton University)IntroductionPOL345 Lectures11 / 15

Possible Explanations1Selection bias: Healthy-user bias and prescriber effects2Different populations:RCTs: older women after menopauseNurses’ Study: younger women near the onset ofmenopauseNew hypothesis: HRT may protect younger women againstheart disease while being harmful for older womenKosuke Imai (Princeton University)IntroductionPOL345 Lectures12 / 15

Potential Objections to Experiments1CostMove-to-Opportunity experiment; 70million, 350,000 people2Ethical concernsExperiments affecting the real worldDenying control units access to beneficial treatmentsTreatments with potential harm3Internal vs. external validityGeneralizability: laboratory vs. field experimentsSample selectionHawthorne effects4Black boxCausal mechanisms: “why” rather than “whether”Kosuke Imai (Princeton University)IntroductionPOL345 Lectures13 / 15

Designing Observational StudiesWe still need observational studies: we often can’t dorandomized experiments for ethical and practical reasonsThe main problem: internal validitySelection bias: lack of randomized treatmentsStrategy: Find a situation where treated units are similar tocontrol unitsNatural experiments: treatments are haphazardlydeterminedKosuke Imai (Princeton University)IntroductionPOL345 Lectures14 / 15

Example: Effect of Raising Minimum WageBefore-and-after designIn 1992, NJ raises minimum wage from 4.25/hr to 5.05/hrIn (eastern) PA, the minimum wage remained at 4.25/hrNo evidence found for negative effectsCard and Krueger (1994). American Economic ReviewKosuke Imai (Princeton University)IntroductionPOL345 Lectures15 / 15

Introduction to Statistics Kosuke Imai Department of Politics Princeton University Fall 2011 Kosuke Imai (Princeton University) Introduction POL345 Lectures 1 / 15. Descriptive and Statistical Inference . HRT increases the risk of heart disease, stroke, blood clots, breast cancer, etc.