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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
Page2
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?
Page3
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.
Page4
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.
Page5
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.
Page6
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.
Page7
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.
Page8
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.
Page9
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.
Page10
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.
Page11
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.
Page12
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;
Page13
thisinformationcouldprovideacandidatewithavaluablesourceofinsightconcerningwhichgroups
shouldbetargetedatcampaigneventsleadinguptotheelection.Thehistoricaltrendsintheweekly
pollsshowthatvotersaremorelikelytobeswayedatanearlierpointintime.AsElectionDaydraws
nearer,thestatisticsshowthatthereliabilityofpollsoflikelyvoterstendstoincreaseastheestimated
proportionsdrawclosertothetruevotingpatternsofAmericansonElectionDay.
Page14
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>
Page15
Appendix
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