![Page 1: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/1.jpg)
Stat 13, Intro. to Statistical Methods for the Life and Health Sciences.
1.FinishingupthebicyclesandcommutetimesandSIDSandBacktoSleepexamples.2.Comparing2means,breastfeedingandintelligenceexample.3.Paireddataandstudyingwithmusicexample.4.Simulationapproachwithpaireddataandbaseballexample.Readch7.
NOLECTURETHUNOV3!ReviewforthemidtermwillbeinclassNov1.RecallthereisalsonolectureorofficehourTueNov8.BringaPENCILandCALCULATORandanybooksornotesyouwanttothemidtermandfinal.HW3isdueTueNov1.4.CE.10,5.3.28,6.1.17,and6.3.14.In5.3.28d,usethetheory-basedformula.Youdonotneedtouseanapplet.Themidtermwillbeonch1-7.http://www.stat.ucla.edu/~frederic/13/F16.
1
![Page 2: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/2.jpg)
BicyclingtoWork• WecannotgeneralizebeyondGrovesandhistwobikes.
• Alimitationisthatthisstudyisnotdouble-blind• Theresearcherandthesubject(whichhappenedtobethesamepersonhere)werenotblindtowhichtreatmentwasbeingused.
• Dr.Grovesknewwhichbikehewasriding,andthismighthaveaffectedhisstateofmindorhischoiceswhileriding.How?
![Page 3: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/3.jpg)
• SIDS.Davies(1985)foundthatinHongKong,wherethecustomwasforchildrentosleepontheirbacks,theratesofSIDSwereverylow.
• 1992:BacktoSleepbeganintheUnitedStates.
![Page 4: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/4.jpg)
BreastfeedingandIntelligenceExample6.3
![Page 5: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/5.jpg)
BreastfeedingandIntelligence
• A1999studyin Pediatricsexaminedifchildrenwhowerebreastfedduringinfancydifferedfrombottle-fed.
• 323childrenrecruitedatbirthin1980-81fromfourWesternMichiganhospitals.
• Researchersdeemedtheparticipantsrepresentativeofthecommunityinsocialclass,maternaleducation,age,maritalstatus,andsexofinfant.
• Childrenwerefollowed-upatage4andassessedusingtheGeneral CognitiveIndex(GCI)• Ameasureofthechild’sintellectualfunctioning
• Researcherssurveyedparentsandrecordedifthechildhadbeenbreastfedduringinfancy.
![Page 6: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/6.jpg)
BreastfeedingandIntelligence
• Explanatoryandresponsevariables.• Explanatoryvariable:Whetherthebabywasbreastfed.(Categorical)
• Responsevariable: Baby’sGCIatage4.(Quantitative)
• Isthisanexperimentoranobservationalstudy?• Cancause-and-effectconclusionsbedrawninthisstudy?
![Page 7: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/7.jpg)
BreastfeedingandIntelligence
• Nullhypothesis: ThereisnorelationshipbetweenbreastfeedingduringinfancyandGCIatage4.
• Alternativehypothesis: ThereisarelationshipbetweenbreastfeedingduringinfancyandGCIatage4.
![Page 8: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/8.jpg)
BreastfeedingandIntelligence
• µbreastfed =AverageGCIatage4forbreastfedchildren• µnot =AverageGCIatage4forchildrennotbreastfed
• H0: µbreastfed =µnot• Ha: µbreastfed ≠µnot
![Page 9: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/9.jpg)
BreastfeedingandIntelligenceGroup Samplesize, n Samplemean Sample SDBreastfed 237 105.3 14.5NotBF 85 100.9 14.0
![Page 10: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/10.jpg)
BreastfeedingandIntelligence
Thedifferenceinmeanswas4.4.• IfbreastfeedingisnotrelatedtoGCIatage4:
• Isitpossible adifferencethislargecouldhappenbychancealone?Yes
• Isitplausible(believable,fairlylikely)adifferencethislargecouldhappenbychancealone?• Wecaninvestigatethiswithsimulations.• Alternatively,wecanusetheory-basedmethods.
![Page 11: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/11.jpg)
T-statistic• Tousetheory-basedmethodsinthemultiplemeansapplet,thet-statisticisused.
• Itissimplythenumberofstandarddeviationsourstatisticisaboveorbelowthemeanunderthenullhypothesis.
• 𝑡 = #$%$&#$&'()*+,$)-#&.-/1%23-45 = 6̅8(6̅9(:
;89
<8=;9
9
<9
�
• Here,t= ?:@.B(?::.C
(8E.F9
9GH =� 8E.I9
JF )
= 2.46.
• p-value~1.4or1.5%.[2*(1-pnorm(2.46))],orusept.
![Page 12: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/12.jpg)
BreastfeedingandIntelligence
Meaningofthep-value:• IfbreastfeedingwerenotrelatedtoGCIatage4,thentheprobabilityofobservingadifferenceof4.4ormoreor-4.4orlessjustbychanceisabout1.4%.
• A95%CIcanalsobeobtainedusingthet-
distribution.TheSEis (?O.@9
PBQ+
� ?O.:9
S@) =1.79.
SothemarginoferrorismultiplierxSE.
![Page 13: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/13.jpg)
BreastfeedingandIntelligence
• TheSEis (?O.@9
PBQ+
� ?O.:9
S@) =1.79.Themarginof
errorismultiplierxSE.• Themultipliershouldtechnicallybeobtainedusingthetdistribution,butforlargesamplesizesyougetalmostthesamemultiplierwithtandnormal.Use1.96fora95%CItoget4.40+/- 1.96x1.79=4.40+/- 3.51=(0.89,7.91).
• Thebookuses2insteadof1.96,andtheappletuses1.9756fromthet-distribution.Justuse1.96forthisclass.
![Page 14: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/14.jpg)
BreastfeedingandIntelligence
• Wehavestrongevidenceagainstthenullhypothesisandcanconcludetheassociationbetweenbreastfeedingandintelligence hereisstatisticallysignificant.
• BreastfedbabieshavestatisticallysignificantlyhigheraverageGCIscoresatage4.
• Wecanseethisinboththesmallp-value(0.015)andtheconfidenceintervalthatsaysthemeanGCIforbreastfedbabiesis0.89to7.91pointshigherthanthatfornon-breastfedbabies.
![Page 15: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/15.jpg)
BreastfeedingandIntelligence
• Towhatlargerpopulation(s)wouldyoubecomfortablegeneralizingtheseresults?• TheparticipantswereallchildrenborninWesternMichigan.
• Thislimitsthepopulationtowhomwecangeneralizetheseresults.
![Page 16: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/16.jpg)
BreastfeedingandIntelligence
• CanyouconcludethatbreastfeedingimprovesaverageGCIatage4?• No.Thestudywasnotarandomizedexperiment.• Wecannotconcludeacause-and-effectrelationship.
• TheremightbealternativeexplanationsforthesignificantdifferenceinaverageGCIvalues.
• Whatmightsomeconfoundingfactorsbe?
![Page 17: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/17.jpg)
BreastfeedingandIntelligence
• CanyouconcludethatbreastfeedingimprovesaverageGCIatage4?• No.Thestudywasnotarandomizedexperiment.• Wecannotconcludeacause-and-effectrelationship.
• TheremightbealternativeexplanationsforthesignificantdifferenceinaverageGCIvalues.• Maybebettereducatedmothersaremorelikelytobreastfeedtheirchildren
• Maybemothersthatbreastfeedspendmoretimewiththeirchildrenandinteractwiththemmore.
• Somemotherswhodonotbreastfeedarelesshealthyortheirbabieshaveweakerappetitesandthismightslowdowndevelopmentingeneral.
![Page 18: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/18.jpg)
BreastfeedingandIntelligence
• Couldyoudesignastudythatallowsdrawingacause-and-effectconclusion?• Wewouldhavetorunanexperimentusingrandomassignmenttodeterminewhichmothersbreastfeedandwhichwouldnot.(Itwouldbeimpossibletodouble-blind.)
• Randomassignmentroughlybalancesoutallothervariables.
• Isitfeasible/ethicaltoconductsuchastudy?
![Page 19: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/19.jpg)
StrengthofEvidence• Wealreadyknow:
• Assamplesizeincreases,thestrengthofevidenceincreases.
• Justaswithproportions,asthesamplemeansmovefartherapart,thestrengthofevidenceincreases.
![Page 20: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/20.jpg)
MoreStrengthofEvidence• Ifthemeansarethesamedistanceapart,butthestandarddeviationschange,thenthestrengthofevidencechangestoo.
• Whichgivesstrongerevidenceagainstthenull?
![Page 21: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/21.jpg)
MoreStrengthofEvidence• Ifthemeansarethesamedistanceapart,butthestandarddeviationschange,thenthestrengthofevidencechangestoo.
• Whichgivesstrongerevidenceagainstthenull?
• Smaller SDs lead to stronger evidence against the null.
![Page 22: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/22.jpg)
EffectsonWidthofConfidenceIntervals
• Justasbefore:• Assamplesizeincreases,confidenceintervalwidthstendtodecrease.
• Asconfidencelevelincreases,confidenceintervalwidthsincrease.
• Thedifferenceinmeanswillnotaffectthewidth(marginoferror)butwillaffectthecenteroftheCI.
• Aswesawwithasinglemean,astheSDsofthesamplesincrease,thewidthoftheconfidenceintervalwillincrease.
![Page 23: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/23.jpg)
PairedData.Chapter7
![Page 24: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/24.jpg)
Introduction• Thepaireddatasetsinthischapterhaveonepairofquantitativeresponsevaluesforeachobs.unit.
• Thisallowsforacomparisonwheretheotherpossibleconfoundersareassimilaraspossiblebetweenthetwogroups.
• Paireddatastudiesremoveindividualvariabilitybylookingatthedifferencescoreforeachsubject.
• Reducingvariabilityindataimprovesinferences:• Narrowerconfidenceintervals.• Smallerp-valueswhenthenullhypothesisisfalse.• Lessinfluencefromconfoundingfactors.
![Page 25: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/25.jpg)
3.Paireddataandstudyingwithmusicexample.Example7.1
![Page 26: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/26.jpg)
StudyingwithMusic• Manystudentsstudywhilelisteningtomusic.• Doesithurttheirabilitytofocus?• In“CheckingItOut:Doesmusicinterferewithstudying?”StanfordProfCliffordNass claimsthehumanbrainlistenstosonglyricswiththesamepartthatdoeswordprocessing.
• Instrumentalmusicis,forthemostpart,processedontheothersideofthebrain,andNassclaimsthatlisteningtoinstrumentalmusichasvirtuallynointerferenceonreadingtext.
![Page 27: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/27.jpg)
StudyingwithMusicConsidertheexperimentaldesigns:ExperimentA — Randomassignmentto2groups• 27studentswererandomlyassignedto1of2groups:
• Onegrouplistenstomusicwithlyrics.• Onegrouplistenstomusicwithoutlyrics.
• Studentsplayamemorizationgamewhilelisteningtotheparticularmusicthattheywereassigned.
![Page 28: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/28.jpg)
StudyingwithMusicExperimentB— Paireddesignusingrepeatedmeasures• Allstudentsplaythememorizationgametwice:
• Oncewhilelisteningtomusicwithlyrics• Oncewhilelisteningtomusicwithoutlyrics.
ExperimentC— Paireddesignusingmatching• Sometimesrepeatingsomethingisimpossible(liketestingasurgicalprocedure)butwecanstillpair.• Testeachstudentonmemorization.• Matchstudentsupwithsimilarscoresandrandomly:
• Haveoneplaythegamewhilelisteningtomusicwithlyricsandtheotherwhilelisteningtomusicwithoutlyrics.
![Page 29: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/29.jpg)
StudyingwithMusicWewillfocusontherepeatedmeasurestypeofpairing.• Whatifeveryonecouldrememberexactly2morewordswhentheylistenedtoasongwithoutlyrics?
• UsingExperimentA,therecouldbealotofoverlapbetweenthetwosetsofscoresanditwouldbedifficulttodetectadifference,asshownhere.
Without Lyrics
With Lyrics
![Page 30: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/30.jpg)
StudyingwithMusic• Variabilityinpeople’smemorizationabilitiesmaymakeitdifficulttoseedifferencesbetweenthesongsinExperimentA.
• Thepaireddesignfocusesonthedifference inthenumberofwordsmemorized,insteadofthenumberofwordsmemorized.
• Bylookingatthisdifference,thevariabilityingeneralmemorizationabilityistakenaway.
![Page 31: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/31.jpg)
StudyingwithMusic• InExperimentB,therewouldbenovariabilityatallinourhypotheticalexample.
• Whilethereissubstantialvariabilityinthenumberofwordsmemorizedbetweenstudents,therewouldbenovariabilityinthedifferenceinthenumberofwordsmemorized.Allvalueswouldbeexactly2.
• Hencewewouldhaveextremelystrongevidenceofadifferenceinabilitytomemorizewordsbetweenthetwotypesofmusic.
![Page 32: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/32.jpg)
PairingandRandomAssignment
• Pairingoftenincreasespower,andmakesiteasiertodetectstatisticalsignificance.
• Canwemakecause-and-effectconclusionsinpaireddesign?
• Shouldwestillhaverandomassignment?
![Page 33: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/33.jpg)
PairingandRandomAssignment
Inourmemorizingwithorwithoutlyricsexample:• Ifweseesignificantimprovementinperformance,isitattributabletothetypeofsong?
• Whataboutexperience?Couldthathavemadethedifference?
• Whatisabetterdesign?• Randomlyassigneachpersontowhichsongtheyhearfirst:withlyricsfirst,orwithout.
• Thiscancelsoutan“experience”effect
![Page 34: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/34.jpg)
ParingandObservationalStudies
Youcanoftendomatchedpairsinobservationalstudies,whenyouknowthepotentialconfounderaheadoftime.Ifyouarestudyingwhethertheportacaval shuntdecreasestheriskofheartattack,youcouldmatcheachpatientgettingtheshuntwithapatientofsimilarhealthnotgettingtheshunt.Ifyouarestudyingwhetherlefthandedness causesdeath,andyouwanttoaccountforageinthepopulation,youcouldmatcheachleftiewitharightie ofthesameage,andcomparetheiragesatdeath.
![Page 35: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/35.jpg)
4.Simulation-BasedApproachforAnalyzingPairedData,androundingfirstbaseexample.Section7.2
![Page 36: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/36.jpg)
RoundingFirstBaseExample7.2
![Page 37: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/37.jpg)
RoundingFirstBase• Imagineyou’vehitalinedriveandaretryingtoreachsecondbase.
• Doesthepaththatyoutaketoroundfirstbasemakemuchofadifference?• Narrowangle• Wideangle
Narrow
Wide
![Page 38: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/38.jpg)
RoundingFirstBase
• Woodward(1970)investigatedthesebaserunningstrategies.
• Hetimed22differentrunnersfromaspot35feetpasthometoaspot15feetbeforesecond.
• Eachrunnerusedeachstrategy(paireddesign),witharestinbetween.
• Heusedrandomassignmenttodecidewhichpatheachrunnershoulddofirst.
• Thispaireddesigncontrolsfortherunner-to-runnervariability.
![Page 39: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/39.jpg)
FirstBase• Whataretheobservationalunitsinthisstudy?
• Therunners(22total)• Whatvariablesarerecorded?Whataretheirtypesandroles?• Explanatoryvariable:baserunningmethod:wideornarrowangle(categorical)
• Responsevariable:timefromhomeplatetosecondbase(quantitative)
• Isthisanobservationalstudyoranexperiment?• Randomizedexperiment.
![Page 40: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/40.jpg)
Theresults
![Page 41: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/41.jpg)
TheStatistics
• Thereisalotofoverlapinthedistributionsandsubstantialvariability.
• Itisdifficulttodetectadifferencebetweenthemethodswhentheseissomuchvariation.
•
Mean SDNarrow 5.534 0.260Wide 5.459 0.273
![Page 42: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/42.jpg)
RoundingFirstBase
• However,thesedataareclearlypaired.• Thepairedresponsevariableistimedifferenceinrunningbetweenthetwomethodsandwecanusethisinanalyzingthedata.
![Page 43: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/43.jpg)
TheDifferencesinTimes
![Page 44: 1. Finishing up the bicycles and commute times and SIDS ...frederic/13/F16/day10.pdf1. Finishing up the bicycles and commute times and SIDS and Back to Sleep examples. 2. Comparing](https://reader034.vdocuments.mx/reader034/viewer/2022050305/5f6dc7d8b9c5ee45414ddce2/html5/thumbnails/44.jpg)
TheDifferencesinTimes
• Meandifferenceis�̅�d=0.075seconds• StandarddeviationofthedifferencesisSDd =0.0883sec.
• Thisstandarddeviationof0.0883issmallerthantheoriginalstandarddeviationsoftherunningtimes,whichwere0.260and0.273.