The2008PresidentialElection:

StatisticalAnalysisofVotingTrends

AllisonDeal

RhyanJohnsonHillarySuperakSarahWong

ESE405–Reliability&QualityControl

December8,2008

Page1

Contents

I. Introduction ..................................................................................................... 2

II. Methodology&Assumptions ........................................................................... 3

III. Calculations,Graphs,andAnalysis ................................................................... 5

A. Gender .................................................................................................... 5

B. Age .......................................................................................................... 6

C. Race ........................................................................................................ 7

D. IncomeLevel ........................................................................................... 8

E. RaceandGender ..................................................................................... 9

V. Conclusions .................................................................................................... 12

References ........................................................................................................... 14

Appendix .............................................................................................................. 15

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I. Introduction

The2008presidentialelection,andtheassociatedcampaignevents,comprisedaperiodof

UnitedStatespoliticalactivitythatwillgodowninhistoryasoneofthemostconsequentialand

momentousoccasionsever.Voterturnoutreacheditshighestlevelofalltime,withover128million

votescast.Moreover,fundraisingforbothmajorpartiesreachedrecordhighamounts,leadingto

abundantadvertisingandmediacoverage.Theelection,whichwastrackedaroundtheglobe,trulyhad

aninternationalimpactbeyondthebordersoftheUnitedStates.

Oneoftheprimaryreasonsforthehistoricalnatureofthe2008presidentialelectionwasthe

backgroundsofthecandidates.TheDemocraticticketconsistedofBarackObama,asenatorfrom

Illinois,andhisrunning‐mate,JoeBiden,asenatorfromDelaware;theRepublicanticketconsistedof

JohnMcCain,asenatorfromArizona,andSarahPalin,thegovernorofAlaska.Obamawasthefirst

African‐Americancandidateforamajorpoliticalparty;Palin,ifelected,wouldhavebeenthefirstever

femalevice‐president.

Thepurposeofthisreportwastoanalyzethetrendsofvotersinthe2008presidentialelection.

Specifically,thefollowinganalysesinvestigatethevotingpatternsofvariousdemographicgroups.The

principalquestionofinterestwas:

Whichdemographicfactorshadthemostimpactonthecandidateselectedbyavoter?

Anothertopicofanalysiswastheaccuracyofpre‐electionpolls.Numerousmediasourcespublished

weeklypollsoftheopinionsoflikelyvotersintheweeksleadinguptoElectionDay.Clearly,the

proportionsofvotersleaningtowardsObamaorMcCainfluctuatedonaweeklybasis.Forthisanalysis,

thequestionofinterestwas:

Dopre‐electionpollsprovideamoreaccuratepredictionoftheactualelectionoutcomeasElectionDaydrawsnearer?

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II. Methodology&Assumptions

Thevotingtrendsofthe2008electionwereinvestigatedbycomparingtheoverallproportionof

thepopulationthatvotedforthewinningcandidate,BarackObama,totheproportionofvotersin

differentdemographicgroupswhofavoredObamaatthepolls.Aone‐proportionz‐testwasutilizedin

thecalculationofap‐valueforeachtest:

n

pp

ppz

)1(

ˆ

00

0

!

!=

Theteststatistic,z,wascalculatedbasedonp0,theoverallproportionofthepopulationthatvotedfor

Obama,and p̂ ,theproportionforthegivendemographicgroupthatvotedforObama.Thenumberof

individualsineachgroup,n,wascalculatedbymultiplyingthepercentageoftotalrespondentsinthe

givendemographicgroupbythetotalnumberofrespondents.Apositivez‐scoreindicatedthatthe

membersofthecertaindemographicvotedmorestronglyforObamathantheoverallAmerican

populationvoted.Thefollowinghypothesesweretestedforeachdemographicparameter:

NullHypothesis

H0:TheproportionofsurveyedvotersinthecategoryofinterestwhovotedforObamaisthesameastheoverallpopulationproportionofvoterswhofavoredObama.

p̂ = p0

AlternateHypothesis

HA:TheproportionofsurveyedvotersinthecategoryofinterestwhovotedforObamaisdifferentfromtheoverallpopulationproportionofvoterswhofavoredObama.

p̂ ≠ p0

Forthepre‐electionpollingdata,thesampleproportionfromeachpointintimewascompared

top0basedontheoverallelectiondata.Thez‐scoreswerecomputedandusedinthecomparisons.

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Negativez‐scoresindicatedthatfewervoterswereleaningtowardsObamainthepre‐electionpollthan

actuallyvotedforObama;positivez‐scoresindicatedthatmorevoterswereleaningtowardsObama.

Astandardsignificancelevelofα=0.05wasusedinallanalyses.Oncetheteststatisticwas

calculated,itwasusedtogeneratethep‐valueforthetest.Ifthep‐valuewaslessthan0.05,thenthe

variablebeingexaminedwasdeemedtobeasignificantfactorinvoters’decisions.

Inordertouseaone‐proportionz‐test,wemustworkundertheassumptionthatthesamples

aresimplerandomsamples.AlldatawereobtainedfromCNNNews.Thesamplingmethodology

employedbyCNNdoeslegitimatelyconstitutesimplerandomsampling.Thedataarebasedonexitpolls

fromrandomlyselectedprecinctsacrossthenation.Inotherwords,everyprecincthasanequalchance

ofbeingincludedinthesample;largerormoreimportantprecinctsarenotgivenextraweight.

Interviewersstandoutsidetheselectedpollinglocationsandquestioneverythirdorfifthvoter,

dependingonthesizeoftheprecinct.Votersareinterviewedthroughouttheentiredurationofthe

precinct’shours.Thisaspectofthesamplingmethodologyhelpsavoidbiasthatcouldpotentiallyariseif,

forexample,onlymorningoreveningvotersweresurveyed.Overall,themethodologyusedtoobtain

thedataforthisstudyiscreditablewithcreatingasimplerandomsample,sothisassumptionismet.

Theothermajorassumptionthatgoesintoaone‐proportionz‐testisthatthesamplesare

sufficientlylarge.Thisassumptionisrequiredforthenormalapproximationtobevalid.Specifically,the

samplemustmeettheconditionthatnp0>10andn(1‐p0)>10.Thevalueofp0,theproportionofthe

totalpopulationofvotersthatselectedObama,was0.527,or52.7%.Thetotalsamplesizeofallvoters

surveyedintheexitpollwas17,836.Therefore,withoutgoingthroughanycalculations,itisobvious

thatforanydemographicsubgroupofthissample,bothnp0andn(1‐p0)willgreatlyexceed10sincethe

overallsampleissolarge.

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III. Calculations,Graphs,andAnalysis

ThefollowinganalysesinvestigateseveralquestionsconcerningthehabitsofAmericanvoters.

Althoughalldataweredrawnfromthe2008Presidentialelection,conclusionscanbeextrapolatedto

otherlocalandnationalelectionsaswell.

A. Gender

IstheproportionofmaleswhovotedforObamasignificantlydifferentfromtheoverall

populationproportionofbothgenderswhovotedforObama?

Amongthe8,383male

voters(47%ofthetotal

population),49%voted

forObamaand48%

votedforMcCain(Fig.1)

n

pp

ppz

)1(

ˆ

00

0

!

!= =

)836,17(47.0

)473.0(527.0

527.049.0 !=‐6.785 p‐value≈0

Sincethep‐valueforthistestisapproximately0,thereisstrongevidencethatthe

proportionofmaleswhovotedforObamaissignificantlydifferentfromtheoverallpopulation

proportionwhovotedforObama.Specifically,sincethez‐scoreisnegative,asmallerproportion

ofmalesvotedforObamarelativetotheentirepopulation;malevoterstendedtofavorMcCain

morestronglythantheoverallpopulationofbothgenders.

Fig.1.Percentagesofmalevotersforeachcandidate.

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B. Age

Istheproportionofyoungvoters(age18‐44)favoringObamasignificantlydifferentfromthe

overallpopulationproportionofvotersofallageswhovotedforObama?

Amongthe8,383voters

betweentheagesof18and

44whoweresurveyed,

57.4%reportedvotingfor

Obama;only41.8%voted

forMcCain(Fig.2).

n

pp

ppz

)1(

ˆ

00

0

!

!= =

383,8

)473.0(527.0

527.0574.0 !=8.619 p‐value≈0

Thesamplesize,n,wascalculatedbypoolingtwogroupsofvotersfromthesampledata:

votersage18‐29(18%ofthesample)andvotersage30‐44(29%ofthesample).Bytakinga

weightedaverageoftheproportionsinthesetwogroupswhovotedforObama,theoverall

“youngvoter”statisticwasobtained.

Thep‐valueforthistestisapproximately0,indicatingthattheproportionofyoungvoters

whovotedforObamaissignificantlydifferentfromtheoverallpopulationproportionwhovoted

forObama.Specifically,sincethez‐scoreispositive,alargerproportionofyoungvotersfavored

ObamarelativetotheproportionoftheentirevotingpopulationwhofavoredObama.Thisisan

interestingfindingsinceamajorpartofObama’scampaignstrategywastotargetfirst‐time

voters,whotendtofallintothe18‐44agegroup.

Fig.2.Percentagesofyoungvotersforeachcandidate.

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C. Race

IstheproportionofAfricanAmericanvotersfavoringObamasignificantlydifferentfromthe

overallpopulationproportionofvotersofallethnicitieswhovotedforObama?

Amongthe2,319African

Americanvoters(13%of

thetotalpopulation),95%

votedforObamaand4%

votedforMcCain(Fig.3)

n

pp

ppz

)1(

ˆ

00

0

!

!= =

319,2

)473.0(527.0

527.095.0 !=40.800 p‐value≈0

Sincethep‐valueforthistestisapproximately0,thereisstrongevidencethatthe

proportionofAfricanAmericanswhovotedforObamaissignificantlydifferentfromtheoverall

populationproportionwhovotedforObama.Specifically,sincethez‐scoreispositiveandvery

large,amuchlargerproportionofAfricanAmericansvotedforObamarelativetotheentire

population.ItcanbeconcludedthatAfricanAmericanvoterstendedtofavorObamamore

stronglythantheoverallpopulationofallethnicities.

Fig.3.PercentagesofAfricanAmericanvotersforeachcandidate.

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D. IncomeLevel

Istheproportionofvoterswhomakelessthan$100,000ayearandvotedforObamasignificantly

differentfromtheoverallpopulationproportionofallincomeswhovotedforObama?

Amongthe13,199lower‐

incomevoters(74%of

thetotalsurveyed

population),55%voted

forObamaand43%

votedforMcCain(Fig.4)

n

pp

ppz

)1(

ˆ

00

0

!

!= =

199,13

)473.0(527.0

527.055.0 !=5.293 p‐value≈0

Thep‐valueforthistestisagainapproximately0,suggestingthereisstrongevidencethat

theproportionofvoterswhoearnlessthan$100,000peryearandwhovotedforObamais

significantlydifferentfromtheoverallpopulationproportionwhovotedforObama.Specifically,

sincethez‐scoreispositive,alargerproportionofthislower‐incomedemographicvotedfor

Obamarelativetotheentirepopulation;lower‐incomevoterstendedtofavorObamamore

stronglythantheoverallpopulationofallincomelevels.

Fig.4.Percentagesoflower‐incomevotersforeachcandidate.

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E. RaceandGender

IstheproportionofAfricanAmericanmalevoterswhovotedforObamasignificantlydifferent

fromtheoverallpopulationproportionofallvoterswhovotedforObama?

Amongthe892African

Americanmales(5%ofthe

totalsurveyedpopulation),

95%votedforObamaand5%

votedforMcCain(Fig.5)

n

pp

ppz

)1(

ˆ

00

0

!

!= =

892

)473.0(527.0

527.095.0 !=25.301 p‐value≈0

Thep‐valueforthistest–againapproximately0–indicatesstrongevidencethatthe

proportionofvoterswhoareAfricanAmericanmalesandwhovotedforObamaissignificantly

differentfromtheoverallpopulationproportionwhovotedforObama.Specifically,sincethez‐

scoreispositiveandverylarge,amuchlargerproportionofthisdemographicvotedforObama

relativetotheentirepopulation;AfricanAmericanmalevoterstendedtofavorObamamore

stronglythantheoverallpopulationofallbackgrounds.Thisisasignificantandexpectedtrend

becauseObamahimselfisthefirstAfricanAmericanmaletorun(andtobeelected)foroffice.It

isinterestingtonotethatalmostallmembersofthisdemographicseemedtovoteforsomeone

ofthesameraceandgenderasthemselves.

Fig.5.PercentagesofAfricanAmericanmalevotersforeachcandidate.

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Afterconsideringthevotingtrendsofseveraldemographics,anewquestionwasraised:Do

pre‐electionpollsprovideamoreaccuratepredictionoftheactualelectionoutcomeasElectionDay

drawsnearer?Newdatafromincrementalpollingperiodsweregatheredandthefollowinganalyses

wereperformed.

Table1showsthepercentageofvoterswhofavoredeachcandidateatvariouspointsintime

leadinguptotheelection.Table1includesdatafromapproximatelyonepollpermonthforthefive

monthspriortotheelection.

Asshown,thep‐valueswerenon‐zeroastheelectiondrewnearer.Inthepollsfurthestintime

fromtheelection,thesampledproportionsweresignificantlydifferentfromthetruepopulation

proportionsonElectionDay.ClosertoElectionDay,theproportionswerenotsignificantlydifferent.This

trendindicatesthatthepre‐electionpollsbecamemoreaccuratetothetrueelectionoutcomeover

time.Notably,thehighestp‐valuewasfromthepollclosesttoElectionDay.Theresultsofthisanalysis

showthatvotersbecamemoredecisiveabouttheirchoiceofcandidatesastheelectiondrewnearer.

DATE OBAMA z‐score p‐value MCCAIN

6/15/2008 0.470 ‐6.000 0 0.480

7/13/2008 0.490 ‐3.895 0 0.460

8/22/2008 0.490 ‐3.895 0 0.450

9/22/2008 0.520 ‐0.737 0.461 0.430

10/22/2008 0.540 1.368 0.171 0.430

11/2/2008 0.530 0.316 0.975 0.440

11/4/2004 0.527 0.459

Table1.Percentageofvotersfavoringeachcandidate,basedonpre‐electionpolls.

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Figure6onthefollowingpageshowsthetrendsofAmericanvoters,asindicatedbymonthly

pre‐electionpolls.Itshouldbenotedthatinitially,McCainappearedtoleadObamainthenational

polls.However,overtime,Obama’sleadgrewastheelectiondrewnearer.Thistrendmaybearesult

ofeventsleadinguptotheelection.ManypoliticalanalystsdeclaredObamavictoriousinthethree

debatesthattookplaceweeklyinlateSeptemberandearlyOctober.Figure6showsthatduringthis

periodoftime,Obama’sleadoverMcCaingrew.

Final%forObama

Final%forMcCain

%forObama

%forMcCain

11/02/2008

Fig.6.Percentagesofvotersforeachcandidateovertimeinpre‐electionpolls.

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V. Conclusions

BarackObama’svictoryinthepresidentialelectionwasagroundbreakingeventthatwillgo

downinhistoryforitspoliticalimplications.Analysisofdemographicfactorsprovidesagreatdealof

insightintothetrendsandpatternsofAmericans’votinghabitsingeneral.Whilethereareseemingly

limitlessdemographiccategoriesthatcanbeanalyzed,thisparticularstudyexaminedvotertrends

basedongender,age,incomelevel,race,andleaningsovertime.Performanceofatwo‐sidedone‐

proportionhypothesistestenabledacceptanceorrejectionofthenullhypothesisthateachcategoryof

interestwouldvoteinthesamemannerastheoverallvotingpopulation.

Theresultsofthehypothesistestsrevealedthatmoreimportantthanacceptanceorrejectionof

thenullhypothesisisthestrengthofthisdecision.Thisanalysissuggeststhatthedemographicsstudied

(gender,age,incomelevel,andrace)doinfacthavesignificanceinvoterleanings.However,some

categorieshavemorestrengththanothers.Forexample,thestrongestcorrelationwasfoundinAfrican‐

Americans’votesforObama,andparticularly,hisoverwhelmingwinoftheAfrican‐Americanmalevote.

Whileanalyseslikethesearehighlysimplified,itisinterestingtoseewhichdemographicgroups

hadthemostimpactonObama’swin.Thisstudysuggeststhatracewasthemostinfluentialfactor

followedbygender,age,andlastlyincomelevel.FromJunethroughSeptember,thereweresignificant

shiftsinObama’spopularity;itwasclearbeforeElectionDaythatthevotingpopulationwassettlingon

theirpreferenceforObama.Onetrendinthepre‐electionpollsthatdeservesnoticeisthatthez‐scores

tendedtogetcloserto0asElectionDaydrewnearer.Thistrendindicatesthatthepollsbecamemore

accuratetothetrueElectionDayproportionsovertime,meaningthattheyprovidedabetterindication

ofthetrueresultsofthepresidentialelection.

Thisanalysishasfascinatingimplicationsforthecampaigningpoliciesofpoliticiansinfuture

elections.Thereisstatisticalevidencethatcertaindemographicgroupstendtovoteincertainmanners;

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thisinformationcouldprovideacandidatewithavaluablesourceofinsightconcerningwhichgroups

shouldbetargetedatcampaigneventsleadinguptotheelection.Thehistoricaltrendsintheweekly

pollsshowthatvotersaremorelikelytobeswayedatanearlierpointintime.AsElectionDaydraws

nearer,thestatisticsshowthatthereliabilityofpollsoflikelyvoterstendstoincreaseastheestimated

proportionsdrawclosertothetruevotingpatternsofAmericansonElectionDay.

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References

ABCNewsOnline.“ElectionMap:PresidentialRace.”2008.Accessed18Nov.2008.

<http://abcnews.go.com/politics>

CNNPolitics.“ElectionCenter2008:ExitPolls.”2008.Accessed18Nov.2008.

<http://www.cnn.com/ELECTION/2008/results/polls/>

RealClearPolitics.“GeneralElection:McCainvs.Obama.”2008.Accessed18Nov.2008.

<http://www.realclearpolitics.com/epolls/2008/president.html>

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Appendix