Introduction to Statistics - Harvard University · Randomize applicant names in their resume...

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Introduction to Statistics Kosuke Imai Department of Politics Princeton University Fall 2011 Kosuke Imai (Princeton University) Introduction POL345 Lectures 1 / 15

Transcript of Introduction to Statistics - Harvard University · Randomize applicant names in their resume...

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Introduction to Statistics

Kosuke Imai

Department of PoliticsPrinceton University

Fall 2011

Kosuke Imai (Princeton University) Introduction POL345 Lectures 1 / 15

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Descriptive and Statistical Inference

Descriptive inference:1 Summarize the observed data2 Tables with statistics, Data visualization through graphs3 Statistic = a function of data

Statistical inference:1 Learning about unknown parameters from observed data2 Statistical models: All models are false but some are useful3 Uncertainty: How confident are you about your inference?4 Statistical tests: Does smoking cause cancer?

Research design:1 What data to collect and how?2 Designing experiments, sample surveys, etc.3 Mimicking experiments in observational studies

Kosuke Imai (Princeton University) Introduction POL345 Lectures 2 / 15

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Examples of Statistical Inference

Inference types Parameters DataForecasting future data points past dataSample survey features of population random sampleCausal inference counter-factuals factuals

Kosuke Imai (Princeton University) Introduction POL345 Lectures 3 / 15

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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 notoccurred

No causation without manipulation: immutablecharacteristicsDoes race affect your job prospect?

Kosuke Imai (Princeton University) Introduction POL345 Lectures 4 / 15

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Statistical Framework of Causal Inference

“Treatment”: Contacted or notObserved outcome: TurnoutPre-treatment variables: e.g., Age, Party IDPotential outcomes:

Voters Contact Turnout Age Party IDTreated Control

John Yes Yes ? 20 DNicole No ? No 55 RMark No ? Yes 40 R

......

......

......

Amy Yes No ? 62 D

Causal effect: Difference between two potential outcomesFundamental problem of causal inference

Kosuke Imai (Princeton University) Introduction POL345 Lectures 5 / 15

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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 studies

Kosuke Imai (Princeton University) Introduction POL345 Lectures 6 / 15

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Randomized Experiments

Randomize!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 experiments

READING: FPP Chapter 1

Kosuke Imai (Princeton University) Introduction POL345 Lectures 7 / 15

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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:

American Political Science Review Vol. 102, No. 1

APPENDIX A: MAILINGS

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Kosuke Imai (Princeton University) Introduction POL345 Lectures 8 / 15

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Social pressure message:

Gerber, Green, and Larimer. (2008). American Political ScienceReview.

Turnout: 31.5% (civic duty), 37.8% (social pressure)

Kosuke Imai (Princeton University) Introduction POL345 Lectures 9 / 15

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Example 2: Employment Discrimination

Does 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 rate

White female Black female White male Black maleEmily 7.9 Aisha 2.2 Todd 5.9 Rasheed 3.0Anne 8.3 Keisha 3.8 Neil 6.6 Tremayne 4.3Jill 8.4 Tamika 5.5 Geoffrey 6.8 Kareem 4.7Allison 9.5 Lakisha 5.5 Brett 6.8 Darnell 4.8Laurie 9.7 Latoya 5.8 Brendan 7.7 Tyrone 5.3

Bertrand and Mullainathan. (2004). American Economic Review

Kosuke Imai (Princeton University) Introduction POL345 Lectures 10 / 15

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Experimental vs. Observational Studies

READING: FPP Chapter 2

Hormone-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 prescriptions

Two randomized clinical trials:1 Heart and Estrogen-progestin Replacement Study (1998)2 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) Introduction POL345 Lectures 11 / 15

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Possible Explanations

1 Selection bias: Healthy-user bias and prescriber effects

2 Different 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 women

Kosuke Imai (Princeton University) Introduction POL345 Lectures 12 / 15

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Potential Objections to Experiments

1 CostMove-to-Opportunity experiment; $70million, 350,000 people

2 Ethical concernsExperiments affecting the real worldDenying control units access to beneficial treatmentsTreatments with potential harm

3 Internal vs. external validityGeneralizability: laboratory vs. field experimentsSample selectionHawthorne effects

4 Black boxCausal mechanisms: “why” rather than “whether”

Kosuke Imai (Princeton University) Introduction POL345 Lectures 13 / 15

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Designing Observational Studies

We still need observational studies: we often can’t dorandomized experiments for ethical and practical reasonsThe main problem: internal validitySelection bias: lack of randomized treatments

Strategy: Find a situation where treated units are similar tocontrol unitsNatural experiments: treatments are haphazardlydetermined

Kosuke Imai (Princeton University) Introduction POL345 Lectures 14 / 15

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Example: Effect of Raising Minimum Wage

Before-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 effects

Card and Krueger (1994). American Economic ReviewKosuke Imai (Princeton University) Introduction POL345 Lectures 15 / 15


Numbers Male Female

Numbers Male Female

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Male Female Discrimination

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male - female jobs

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202 0...Black African Coloured Indian or Asian White Total Male Female Total Male Female Total Male Female Total Male Female Total Male Female Total 0-4 2 502 2 439 4 941 242 235 476

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male or female

male or female

2012 WITTENBERG UNIVERSITY FACT BOOKMale: Female Male: Female Male: Female Male: Female Male: Female Male: Female Male: Female Male: Female Number of Applicants: 2,205 2,682: 2,040

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Reproductive Male Female

Reproductive Male Female

Male-Female Relationships

Male-Female Relationships

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