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[ Pobierz całość w formacie PDF ]Gettingthe
Information
YouNeed
PART
CHAPTER1
DataCollection
Statisticsisaprocess—aseriesofstepsthatleadtoagoal.
Thistextisdividedintofourpartstohelpthereadersee
theprocessofstatistics.
Thefirststepintheprocessistodeterminethere-
searchobjectiveorquestiontobeanswered.Then,infor-
mationisobtainedtoanswerthequestionsstatedinthe
researchobjective.
DataCollection
CHAPTER
Outline
1.1
IntroductiontothePracticeofStatistics
1.2
ObservationalStudies,Experiments,andSimple
RandomSampling
1.3
OtherEffectiveSamplingMethods
1.4
SourcesofErrorsinSampling
1.5
TheDesignofExperiments
"
ChapterReview
"
CaseStudy:ChrysalisesforCash(onCD)
DECISIONS
ItisMondaymorningandalreadyyouarethinkingabout
Fridaynight—movienight.Youdon’ttrustthemoviereviews
publishedbyprofessionalcritics,soyoudecidetosurvey
“regular”peopleyourself.Youneedtodesignaquestionnaire
thatcanbeusedtohelpyoumakeaninformeddecisionabout
whethertoattendaparticularmovie.SeetheDecisionActivity
onpage37.
PuttingItAllTogether
Formostofyou,thisisyourfirststatisticscourse.Taking
astatisticscourseisdifferentfromtakingamathematics
course.Whilethereareformulasandmathematicalsym-
bolsinthecourse,statisticsisnotmathematics.So,
whetheryouhavestruggledorhadsuccessinpriormath-
ematicscourses,youcansucceedinstatistics.
Beforeyoubeginthecourse,read“HowtoUseThis
Book”ontheinsidefrontcoverofthetext.
Section1.1IntroductiontothePracticeofStatistics
3
1.1
IntroductiontothePracticeofStatistics
Objectives
Definestatisticsandstatisticalthinking
Understandtheprocessofstatistics
Distinguishbetweenqualitativeandquantitative
variables
Distinguishbetweendiscreteandcontinuousvariables
DefineStatisticsandStatisticalThinking
Whatisstatistics?Whenaskedthisquestion,manypeoplerespondthatstatis-
ticsisnumbers.Thisresponseisonlypartiallycorrect.
Definition
Statistics
isthescienceofcollecting,organizing,summarizing,andana-
lyzinginformationtodrawconclusionsoranswerquestions.
Itishelpfultoconsiderthisdefinitioninthreeparts.Thefirstpartofthedef-
initionstatesthatstatisticsinvolvesthecollectionofinformation.Thesecond
referstotheorganizationandsummarizationofinformation.Finally,thethird
statesthattheinformationisanalyzedtodrawconclusionsoranswerspecific
questions.
Whatistheinformationreferredtointhedefinition?Theinformationis
data
.Accordingtothe
AmericanHeritageDictionary
,
data
are“afactorpropo-
sitionusedtodrawaconclusionormakeadecision.”Datacanbenumerical,as
inheight,ortheycanbenonnumerical,asingender.Ineithercase,datade-
scribecharacteristicsofanindividual.Thereasonthatdataareimportantinsta-
tisticscanbeseeninthisdefinition:dataareusedtodrawaconclusionormake
adecision.
Analysisofdatacanleadtopowerfulresults.Datacanbeusedtooffsetan-
ecdotalclaims,suchasthesuggestionthatcellulartelephonescausebraincan-
cer.Aftercarefullycollecting,summarizing,andanalyzingdataregardingthis
phenomenon,itwasdeterminedthatthereisnolinkbetweencellphoneusage
andbraincancer.
Becausedataarepowerful,theycanbedangerouswhenmisused.Themis-
useofdatausuallyoccurswhendataareincorrectlyobtainedoranalyzed.For
example,radioortelevisiontalkshowsregularlyaskpollquestionsinwhichre-
spondentsmustcallinorusetheInternettosupplytheirvote.Theonlyindivid-
ualswhoaregoingtocallinarethosethathaveastrongopinionaboutthe
topic.Thisgroupisnotlikelytoberepresentativeofpeopleingeneral,sothe
resultsofthepollarenotmeaningful.Wheneverwelookatdata,weshouldbe
mindfulofwherethedatacomefrom.
Evenwhendatatellusthatarelationexists,weneedtoinvestigate.Forex-
ample,astudyshowedthatbreast-fedchildrenhavehigherIQsthanthosewho
werenotbreast-fed.Doesthisstudymeanthatmothersshouldbreast-feedtheir
children?Notnecessarily.ItmaybethatsomeotherfactorcontributestotheIQ
ofthechildren.Inthiscase,itturnsoutthatmotherswhobreast-feedgenerally
havehigherIQsthanthosewhodonot.Therefore,itmaybegeneticsthatleads
tothehigherIQ,notbreast-feeding.Thisillustratesanideainstatisticsknown
asthe
lurkingvariable
.Instatistics,wemustconsiderthelurkingvariablesbe-
causetwovariablesmostoftenareinfluencedbyathirdvariable.Agoodstatis-
ticalstudywillhaveawayofdealingwiththelurkingvariable.
Anotherkeyaspectofdataisthattheyvary.Tohelpunderstandthisvari-
ability,considerthestudentsinyourclassroom.Iseveryonethesameheight?
No.Doeseveryonehavethesamecolorhair?No.So,amongagroupofindivid-
ualsthereisvariation.Nowconsideryourself.Doyoueatthesameamountof
foodeachday?No.Doyousleepthesamenumberofhourseachday?No.So,
InOtherWords
Anecdotal
meansthattheinformation
beingconveyedisbasedoncasual
observation,notscientificresearch.
4
Chapter1DataCollection
evenlookingatanindividualthereisvariation.Datavary.Thegoalofstatistics
istodescribeandunderstandthesourcesofvariation.
Becauseofthisvariabilityindata,theresultsthatweobtainusingdatacan
vary.Thisisaverydifferentideathanwhatyoumaybeusedtofromyourmath-
ematicsclasses.Inmathematics,ifBobandJaneareaskedtosolve
theywillbothobtain asthesolution,iftheyusethecorrect
procedures.Instatistics,ifBobandJaneareaskedtoestimatetheaveragecom-
mutetimeforworkersinDallas,Texas,theywilllikelygetdifferentanswers,
eventhoughtheybothusethecorrectprocedure.Thedifferentanswersoccur
becausetheylikelysurveyeddifferentindividuals,andtheseindividualshave
differentcommutetimes.Note:TheonlywayBobandJanewouldgetthesame
resultisiftheybothasked
all
commutersorthesamecommutershowlongit
takestogettowork,buthowlikelyisthis?
So,inmathematicswhenaproblemissolvedcorrectly,theresultscanbere-
portedwith100%certainty.Instatistics,whenaproblemissolved,theresults
donothave100%certainty.Instatistics,wemightsaythatweare95%confi-
dentthattheaveragecommutetimeinDallas,Texasis21.5minutes.Whileun-
certainresultsmaysounddisturbingnow,itwillbecomemoreapparentwhat
thismeansasweproceedthroughthecourse.
Withoutcertainty,howcanstatisticsbeuseful?Statisticscanprovideanun-
derstandingoftheworldaroundusbecauserecognizingwherevariabilityindata
comesfromcanhelpustocontrolit.Understandingthetechniquespresentedin
thistextwillprovideyouwithpowerfultoolsthatwillgiveyoutheabilitytoan-
alyzeandcritiquemediareports,makeinvestmentdecisions(suchaswhatmutu-
alfundtoinvestin),orconductresearchonmajorpurchases(suchaswhattype
ofcaryoushouldbuy).Thiswillhelptomakeyouaninformedconsumerofin-
formationandguideyouinbecomingacriticalandstatisticalthinker.
=
11,
UnderstandtheProcessofStatistics
Thedefinitionofstatisticsimpliesthatthemethodsofstatisticsfollowa
process.
TheProcessofStatistics
1.
Identifytheresearchobjective
.Aresearchermustdeterminetheques-
tion(s)heorshewantsanswered.Thequestion(s)mustbedetailedsothat
itidentifiesagroupthatistobestudiedandthequestionsthataretobe
answered.Thegrouptobestudiediscalledthe
population
.An
individual
isapersonorobjectthatisamemberofthepopulationbeingstudied.For
example,aresearchermaywanttostudythepopulationofall2005model-
yearautomobiles.Theindividualsinthisstudywouldbethecars.
2.
Collecttheinformationneededtoanswerthequestionsposedin(1)
.Gain-
ingaccesstoanentirepopulationisoftendifficultandexpensive.Incon-
ductingresearch,wetypicallylookatasubsetofthepopulation,calleda
sample
.Forexample,theU.S.populationofpeople18yearsorolderis
about218million.Manynationalstudiesconsistofsamplesofsize1,100.
Thecollection-of-informationstepisvitaltothestatisticalprocess,be-
causeiftheinformationisnotcollectedcorrectly,theconclusionsdrawn
aremeaningless.Donotoverlooktheimportanceofappropriatedata-
collectionprocesses.
3.
Organizeandsummarizetheinformation
.Thisstepintheprocessisre-
ferredtoas
descriptivestatistics
.
CAUTION
Manynonscientificstudiesare
basedon
conveniencesamples
,such
asInternetsurveysorphone-inpolls.
Theresultsofanystudyperformed
usingthistypeofsamplingmethod
arenotreliable.
Definition
Descriptivestatistics
consistsoforganizingandsummarizingthein-
formationcollected.
Descriptivestatisticsdescribetheinformationcollectedthroughnumeri-
calmeasurements,charts,graphs,andtables.Themainpurposeofde-
scriptivestatisticsistoprovideanoverviewoftheinformationcollected.
Section1.1IntroductiontothePracticeofStatistics
4.
Drawconclusionsfromtheinformation
.Inthissteptheinformationcol-
lectedfromthesampleisgeneralizedtothepopulation.
Definition
Inferentialstatistics
usesmethodsthattakeresultsobtainedfroma
sample,extendsthemtothepopulation,andmeasuresthereliabilityofthe
result.
Forexample,ifaresearcherisconductingastudybasedonthepopula-
tionofAmericansaged18yearsorolder,shemightobtainasampleof
1,100Americansaged18yearsorolder.Theresultsobtainedfromthe
samplewouldbegeneralizedtothepopulation.Thereisalwaysuncer-
taintywhenusingsamplestodrawconclusionsregardingapopulation
becausewecan’tlearneverythingaboutapopulationbylookingata
sample.Therefore,statisticianswillreportalevelofconfidenceintheir
conclusions.Thislevelofconfidenceisawayofrepresentingthereliabili-
tyofresults.Iftheentirepopulationisstudied,theninferentialstatisticsis
notnecessary,becausedescriptivestatisticswillprovidealltheinforma-
tionthatweneedregardingthepopulation.
Thefollowingexamplewillillustratetheprocessofastatisticalstudy.
EXAMPLE1
EffectivenessofAntihypertensiveDrugs
Accordingtoresearchers,littleinformationexistsontheeffectsthatantihyper-
tensivedrugshaveonpatientswhohaveheartdiseaseandnormalbloodpres-
sure.*Bloodpressureistheforceofbloodagainstthewallsofarteriesandis
presentedastwonumbers:thesystolicpressure(astheheartbeats)overthedi-
astolicpressure(astheheartrelaxesbetweenbeats).Abloodpressuremeas-
urementof120/80mmHg(millimetersofmercury)isnormal.Hypertensionor
highbloodpressureexistsinindividualswithasystolicbloodpressureabove
160mmHgoradiastolicbloodpressureabove100mmHg.ResearchersSteven
E.Nissanandhisassociateswantedtodeterminetheeffectivenessofanantihy-
pertensivedrug**onpreventingcardiovasculareventssuchascongestiveheart
failure,stroke,orotherheart-relatedproblems.Thefollowingstatisticalprocess
allowedtheresearcherstomeasuretheeffectivenessofthedrug:
Group1Group2
1.
Identifytheresearchobjective
.Researcherswishedtodeterminetheef-
fectivenessofthedrugonpreventingcardiovasculareventsinpatients
whohaveheartdiseaseandnormalbloodpressure.
2.
Collecttheinformationneededtoanswerthequestions
.Theresearchers
divided1,317patientswithheartdiseaseanddiastolicbloodpressureless
than100mmHgintotwogroups.Group1had663patientsandgroup2
had654patients.Thepatientsingroup1received10mgdailyoftheanti-
hypertensivedrug.Thepatientsingroup2receiveda
placebo
.A
placebo
isaninnocuousdrugsuchasasugartablet.Group1iscalledthe
experi-
mentalgroup
.Group2iscalledthe
controlgroup
.Neitherthedoctorad-
ministeringthedrugnorthepatientknewwhetherheorshewasinthe
experimentalorcontrolgroup.Thisisreferredtoasa
double-blind
ex-
periment.After24monthsoftreatment,eachpatient’sbloodpressure
wasrecorded.Inaddition,thenumberofpatientsineachgroupwhoex-
periencedacardiovasculareventwascounted.
3.
Organizeandsummarizetheinformation
.Beforeadministeringanydrugs,
itwasdeterminedthatbothgroupshadsimilarbloodpressure.Afterthe
*ThediscussionisbasedonastudydonebyStevenE.Nissan,E.MuratTuzcu,PeterLibby,PaulD.
Thompson,MagdiGhali,DahliaGarza,LanceBerman,HarryShi,EthelBuebendorf,andEric
Topolpublishedinthe
JournaloftheAmericanMedicalAssociation
,Vol.292,No.18.
**Thedrugusedinthestudywas10mgofamlodipine.
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