methodsanalysisofdataarisingfromprocessestoolsmethodypothesesexperimenypothesesspeakingmethodsAppliedStatisticstheapplicationofstatisticalmethodstosolverealmethodologyReadChuponmethodsapplicationsthan ID: 887929
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1 troductiontroduction methodsanalysisofda
troductiontroduction methodsanalysisofdataarisingfromprocessestoolsmethodypothesesexperimenypothesesspeakingmethodsAppliedStatisticstheapplicationofstatisticalmethods
2 tosolverealmethodology ReadCh uponme
tosolverealmethodology ReadCh uponmethodsapplicationsthanelsewherealanalysislongitudinaldatasubjectappealingmethodologymethods methodsMathematicalnotationandtechnique
3 sarenecessaryNoapologieswillstudyals
sarenecessaryNoapologieswillstudyalsovimportanmethodsmethodswillgetyformerthe Data ypespopulationbersqualitiesattributesAppendixbornbloodreproduced ReadCh ts
4 subjectstheinfantsofarandomsampleofsi
subjectstheinfantsofarandomsampleofsize subjectsubject ypesypesmethods ScaleCharacteristic emperature Operations Operations AdditionMultiplicationScaleCountingDi
5 vision NominalpOrdinalppIntervalpppRatio
vision NominalpOrdinalppIntervalpppRatiopppp betbetypesimportan betypesmoderatebloodberbodysubdividedpossibleEgnberofpregnanciesshoesizenberofmissingteethbetpossibl
6 ebersariablehasofpossibleincludingallvb
ebersariablehasofpossibleincludingallvbodybetpossible betthemeasurementismeasuredtothenearestcenperhapsmillimetersoAnotherexamplealtimeismeasuredtothenearestdafootballu
7 ponexperimenimportanexperimendeliberatel
ponexperimenimportanexperimendeliberatelyimposessubjectsexperimenexperimensubjectsresponseelopedexperimengoodhighbecausethereisnotowhichcomparisoncanbemadeplacebo Suppos
8 eybeHerewedontknowwhethersaccharineis
eybeHerewedontknowwhethersaccharineiscarcinogenicorifgeneticstrainanextremelyimportantaspectofexperimentalde Inthesaccharineexampleweshouldstartoutwithhomoge butofc
9 oursetheywilldiersomeensuresthatthetoe
oursetheywilldiersomeensuresthatthetoexperimentalgroupswillberespectpotenbodyabout Anotherimportantconceptespeciallyinhumanexperimentationisexperimensubjectssupposepl
10 aceboExperimenlooksubjectsplaceboexperim
aceboExperimenlooksubjectsplaceboexperimenthetreatmentsandmeasurestheresponsedoesnotknowwhichtreat experimenExperimenbehasubjectsresponseExperimenexpensivpossibleExperim
11 enpossibleerexperimentsarerarelyfeasib
enpossibleerexperimentsarerarelyfeasibleinpublichealthepidemiologyInhealthsciencesmedicineexperimentsinolvinghumansare ypesAdescriptivofinharacteristicsegsubject
12 pothesesoorypothesesretrospectivlooking
pothesesoorypothesesretrospectivlookingypessubjectssubjectssubjectsoftsubjectsexposedpossessedAssociationbetexposureperiodspotenexposuresmethodologicalDependenmethods
13 proper subjectspoinfocuspoinpopulationp
proper subjectspoinfocuspoinpopulationpeopleperiodbecauseexposurepoinpossibleArebiasedtoarddetectingcaseswithdiseaseoflongdurationandcaninemisclassicationsofcasesinremis
14 sionorunder prospectivpeoplepoinAcohorto
sionorunder prospectivpeoplepoinAcohortofdisease freesubjectsareselectedandtheirexposureAssociationbetexposuresexposureexpo Canelucidatetemporalrelationshipbetexposureandd
15 is exposurebersubjectsExpensivSubjects
is exposurebersubjectsExpensivSubjectsretrospectivexposuredeterminingsubsequendiseaseoccurrencebettimeofexposure importanpossiblepossiblepossiblegrouped proportionper
16 cen emaleMale Total proportionproportio
cen emaleMale Total proportionproportionpercenpercenproportionbetproportionpercenpossible ber ber ormore Total Herenecessarythedata Thefollowingtablecontainsthe
17 ageatdeathindaysfor casesofsuddenoccuri
ageatdeathindaysfor casesofsuddenoccuring CumAgeInterveCumulativeRelativeFrequencyFrequency FrequencyFrequency cutpoinbetbetterespecially thisexamplewe
18 haealsotabulatedthecumefrequencyandberef
haealsotabulatedthecumefrequencyandberefrequencypercen Piechartsareusefulfordisplayingtherelativefrequencydistributionhool importanypesespecially hool goriescanbere order
19 edarbitrarilywithoutaectingtheinformati
edarbitrarilywithoutaectingtheinformation Histogramsareofeac aboWidthabo Notethatthechoiceofnberofbinsandbinwidthcanaecthistograms betpolygonsareformedbyplottingline
20 sbetmidpoinpolygonpolygons Aonewayscatt
sbetmidpoinpolygonpolygons AonewayscattertherealkmarksorsometimesdotshobservaluevariableHereone wayscatterplotSIDSdata locatingpercenpercenberpercenpercenpercenlocate
21 s HereisaSIDSdataalsoone wayscatterplot
s HereisaSIDSdataalsoone wayscatterplotof per InMinitabsimplementationofaboxplothoerthewhiskextendtotheadjactenalueswhicharedenedtobethemostextremevaluesinthearenotm
22 orethan timesbeyThewidthoftheboxisthed
orethan timesbeyThewidthoftheboxisthedistancebettherstandthirdpoinsomewhatconersialbutonewytodeneanoutlierisasapoinbeyBasedonthisdenitiontherearefourlargeoutliersint
23 heSIDS methods Noticethatthemarginstable
heSIDS methods NoticethatthemarginstablegivethefrequencydistributionstwovariablesCross tabulationsorvariablestitativeInyvariablesEgherecross tabgestastionalgrmhem
24 GestationalAgeGerminalHemorrhage
GestationalAgeGerminalHemorrhage yingtherelationshipbetaquanariableandsuperimposedpolygons graphicaltoolyingthebetariablesisaH
25 ereisonethatdisplablood poinoceanasitu
ereisonethatdisplablood poinoceanasituationitisusefultoconstructpointsgivesasenseofthetimetrendandanyothertemporalpatternAboExpectanciesexpectancies NumericalSummaryMeas
26 ures aboutbetpopulationsubjectspopulat
ures aboutbetpopulationsubjectspopulation Planetmiles MercuryVenMars JupiterSaturn NeptunePluto importanperformpopulationpopulation
27 ReadCh populationpopulationpopulation
ReadCh populationpopulationpopulationcorrespondingpopulationypothesesaboutproportionperformancepopulationberproportionplememberswhoeasamplestatisticisusedtoestimatet
28 hecorrespondingproportionpopulationmajor
hecorrespondingproportionpopulationmajorbe Notation xymean Supposebersxber Locationlocationx nx x xn poin ixi populationpo
29 pulationpopulationisnotclearlydenedto
pulationpopulationisnotclearlydenedtonasrepreseneoftheentireUSorofsimilarmetropolitanpoinpoin doespercenThatisthemedianisavaluesuchthatatleasthalfofthedataaregreaterod
30 dmedianisev middleveithermiddlevalueor
dmedianisev middleveithermiddlevalueorberbet Modemodeoccurringmodesmodesbelomode modeespeciallyariablesthateonasmallnberofpossiblevmodalmodaloccurbimodalul
31 timodalbimodaldescribepeaks enotedthem
timodalbimodaldescribepeaks enotedthemedianisthethpercenpercenprocedurepercen isanpercenofthe postionpercenpercenpercenRounduptosothatthethpercentileisthesevthsor
32 tedlocatelocations DispersionThetomosti
tedlocatelocations DispersionThetomostimportantaspectsofaunimodaldistributionarethelocationdispersionSupposemodestransportation Location DierentTBikeDierentSameBikeD
33 ierentDierent DispersionCoecien depe
ierentDierent DispersionCoecien dependsuponbetpercen# importandispersionrootpoin ber
34
E Sum
35 E Mean Onewa
E Mean Onewaytomeasurespreadisthethendeterminefareachobservationfrom x n Xixi betxxxx pos positivbefore
36 Xixi x isthepopulat
Xixi x isthepopulationpopulationpopulationbecomes populationxexponenBecausethisisthedeviationfromthemeanintheoriginaldatapopulationrootpopulat
37 ionpopulation vuut Supposepopulatio
ionpopulation vuut Supposepopulation better Thesamplestandarddeviationissimplythesquarerootofthisquan svuut n nXixi x variance insuranceclaims n nXi
38 xi x fx x x xg
xi x fx x x xg squaredstandarddeviationp goodbecausebetter n Whenusinganotheraseriesofcalcu lationskeepstepsmemoryourcalc
39 ulatortoavoidround oerrors Coeciensup
ulatortoavoidround oerrors Coeciensupposealidquestion ycoecienpopulation samples xFtCDCdataavailablewebIobtainedstandarddeviationswkgandearhildrenasfollows A
40 ges xCV yearoldswtsaremor
ges xCV yearoldswtsaremorevariablerelativetotheira Groupedoccur beroccurs
41 $ % $Pkii% Anothe
$ % $Pkii% AnotherExampleApgarScoresofLowBirth ApgarScoreF otal grouped reported Pkimi xfi $Pkifi% r
42 body SupposeSupp
body SupposeSupposeaboutdoesntSupposeaboutdoes Thez scoregiveskindzixi x subject abo abo abodependsupon ChebychevsTheorem Atleast kvalu
43 esofvari ablemustkSDsofmeanfork Thisr
esofvari ablemustkSDsofmeanfork ThisresultsimpliesforexampleAtleastationsmustfork expectbet expectbet boundper perhapsbound
44 about bell shapedshaped A bell-shaped d
about bell shapedshaped A bell-shaped distribution for X, sayx=value of XFrequency density of x -202 0.00.10.20.30.4 Another bell-shaped distribution for Y, sayy=value of
45 YFrequency density of y -202 0.10.20.3
YFrequency density of y -202 0.10.20.3 aboOneparticularbell shapeddistributionisthenormaldistributionimportanpossiblebell shapeddistributionaboeleftisnormaltheaboerighis
46 similar percenwhatsoevbell shapedabobe
similar percenwhatsoevbell shapedabobell shaped supposebell shapedexpectredsBMIwassohisBMIismoreextremethantexpectal Comparetheseresultswithboundsbell shapedobes
47 e troduction todaoddsofSmartbeingpokasth
e troduction todaoddsofSmartbeingpokastheexperimenexperimenypeexperimenabotodapok ReadCh experimenprocess Experimen Doesdoes experimenexperimenbetterelihood describey
48 ofanoddsdescribestoooddsodds doesoccur
ofanoddsdescribestoooddsodds doesoccur beroperationsdoesoccuroccursoccursbothtersectionoftheevoccursandoccursdescribeoperations bermethodmethodsubjectivmethodmethod
49 experimenbe possibleProbabilitiesarebetp
experimenbe possibleProbabilitiesarebetpercenexperimenMethodexperimenEgwhentossingafaircointhereareequallylikelyoutcomespossible methodspecialrequencyMethodTheproba
50 bilityofanevtistherelativefrequencyoccur
bilityofanevtistherelativefrequencyoccursrepeatexperimenberoccursexperimen Supposesupposemethod expectber ber associatedoperations experimendoesntdepend experimenexp
51 erimenpossibleMMMFFMFFcorrespondsFF
erimenpossibleMMMFFMFFcorrespondsFF A B correspondingMFFMFF occur independence occurredoccur supposeyofoccurredIndependenceindep
52 endenoccurredoccurbolsindependen PBas
endenoccurredoccurbolsindependen PBasBPBjAPB A PAPA B PAasA ExampleAgaintheprobabilityofonewobirthsis supposeistheconditionalprobabilityofatgirlgi
53 v PAcWeknothatprobabilityhildPA
v PAcWeknothatprobabilityhildPA Ac PA happenexperimenMFMF ThereforetheconditionalprobabilityatonerstchildisaisPA BjAcPfA B Acg PAc
54 SupposeobesebloodbloodSupposepe
SupposeobesebloodbloodSupposepercenobeseobesitobesebloodobeseabo PBjA PBjAc obeseblood Notethatingeneralgiventhatanevhasoccurredeitheroccur
55 soroccurappliestoconditionalprobabilit
soroccurappliestoconditionalprobabilitiestooobesitbloodythatobesedoesblood obesedoesblood obesedoesblood HighBPObese YtB evBc
56 Independenceindependenoccu
Independenceindependenoccurredaboutoccurbolsindependenindependencebecomesbecomesindependenpenoccurredaboutoc depenindependenObesitBloodobesitindependen
57 PBjAPB ecanckindependencekingwhe
PBjAPB ecanckindependencekingwhether PA BPAPB ehaeseenthatwhentoevaredependentthenoccurredoccuroc curredtogofromourprobabilitybeforethen
58 ewinformationwasaposterioraboutObesitobe
ewinformationwasaposterioraboutObesitobese PBjA PBjAc Supposedoctorpop obese ByultiplicationruleweAjBPA B bloodsubjectsubjectobeseobese Thisrelationship
59 issometimescalledthewoftotalprobabilitoc
issometimescalledthewoftotalprobabilitoccursoccurbecomes PB AB Ac becausebecomes obese PBjAPABjAcPAc aboAbecomes PBjAPABjAPAB
60 jAkPAk Obesitobesesupposeobese PBj
jAkPAk Obesitobesesupposeobese PBjAPABjAPABjAPA happen PB importanapplicationofBadiagnosticorrespectMammogramsfo
61 rbreastcancerPapsmearsforcer vicalcance
rbreastcancerPapsmearsforcer vicalcancerProstate SpecictigenPSAestforprostateSupposemethodexpensivmethodSupposeinexpensivpositivsubject positivpositivdoespositivposi
62 tivdoesdoespositivspeci citdoespositivpo
tivdoesdoespositivspeci citdoespositivpos doespositivpositivspecicit PropertiesSupposeestResult evA a b n eventAc c d n propertiessubjectssubjectssubjectsposi
63 tivsubjects Supposearandomsampleofsubjec
tivsubjects SupposearandomsampleofsubjectsisobtainedandeachsubjectbothspecicitpositivSupposesubjectssubjectspecicitpositivaboutSupposesubjectspositivsubjectssubjectposi
64 tivspecicitadditionalinformationaboutyo
tivspecicitadditionalinformationaboutyofapositivetest possibleproportionsparticularlyquictbe ararediseaseitwillrequirealargeasuciensubjectsSupposebeforepositivSuppose
65 supposespecicitbeenpositiv PAjBPBAj
supposespecicitbeenpositiv PAjBPBAjBcPBcSimilarlyPBcjAcevanegativeenbyPBcjAcPAcjBcPBc PAcjBcPBcAcjBPB Supposediabetesbeenelopedpropertiesdiabet
66 icsnon diabeticswingdataestResultDiabeti
icsnon diabeticswingdataestResultDiabeticNondiabetic eventA eventAc Supposediabetesspecicitpositiv positiv positivdiabetes Res betspecicitsubjectspossible
67 neurologic
neurologicalabnormalitieswhereshouldthecut obesetforthediagnosis Supposeewillcatchalltrueabnormalsthiswy'thesensitivitspeci Supposespecici
68 tbetspecicitspecicit possiblespecicit
tbetspecicitspecicit possiblespecicit Specicit specicit AnROCcurveisoftenusedtohelpdetermineanappropriatethresh poinupper leftspecicitThedashedlineinthisplot
69 showswherethereareequalprobabilitiesposi
showswherethereareequalprobabilitiespositivAtestfallingonthislinemisclassiesnormalsubjectssubjectsbetter EstimationofPrevaScreeningT Supposespecicitpopulationdiabetespo
70 sitivspecicitdiabetesernowsupposethatt
sitivspecicitdiabetesernowsupposethatthisprevalencevaluewasfortheUSpopulationSupposepositivestResult A n Ac n diabetes diabetes PAjBPAjBc
71 PAPAcjBc% positiv n specicitdiabe
PAPAcjBc% positiv n specicitdiabetes PAjB$ dPAcjBc $ % RiskRelativeRiskandOddsRatio describebetbetpopulationsoddswillcallthepopulationsexposedu
72 nexposedpopula populations exposure bein
nexposedpopula populations exposure beingOnesimplewytoquantifythedierencebetexposedunexposedIndependencebeteenexposurestatusanddiseasestatuscorrespondssupposeexposedune
73 xposedof andbutamongfemalestheexp
xposedof andbutamongfemalestheexposedandunexposedgroupsdoesbeingexposed exposed unexposedIndependencebeteenexposurestatusanddiseasestatuscorrespondseriskespeciall
74 yexposureforrareEgtheprobabilitythata
yexposureforrareEgtheprobabilitythatamanoertheageofdiesofcancer ypesbothoddsexposedunexposedoddsoddsdiseaseexposed oddsdiseaseunexposedoddsodds PAcPA
75 exposedexposed% unexposedunexposed%
exposedexposed% unexposedunexposed% IndependencebeteenexposurestatusanddiseasestatuscorrespondsoddsbetterstatisticalpropertiesellexplainthisThelatteradvtagecomesfro
76 mthefactthatusingBaesTheoremexposured
mthefactthatusingBaesTheoremexposurediseasedexposurediseased% exposurenondiseasedexposurenondiseased%isusefulbecauseyofexposurecanbeestimatedamongdiseasedandnond
77 is exposureoccurs kvictimswandeacofthese
is exposureoccurs kvictimswandeacofthese cases wasmatcsubject beenexposedunexposedprobabilitiesofconenpresenceodds oddstook Th
78 eoreticalProbabilityDistributions Proba
eoreticalProbabilityDistributions ProbabilityDistributions berpossibleberpossiblepossible ReadCh berepisodesSuppose PXx abopossiblepossiblebetyfunctio
79 nscanbeenintablesasaboorgraphseg
nscanbeenintablesasaboorgraphseg Expected expectedpopulationorarandomvitsexpectedvalueisusuallydenotedETheexpectedvalueforadiscretervcanbecomputedfromitspro
80 babilitpossibleexpectedber xPXxxPXx
babilitpossibleexpectedber xPXxxPXx EX ber populationpopulationexpectationspossibleber PXxXxXPXx arX
81 population X inourexample
population X inourexample TheBinomialProbabilityDistribution describedberoccurexperimenexperimenpropertiesexperimenpossibleindependenhappensdoesnthappens
82 experimenberoccurlabelsbeingpossibleexp
experimenberoccurlabelsbeingpossibleexperimenabopropertiesberoccurpossibleindependen berobesesubjectsobesitpossibleobeseobesesubjectobeseobesesubjectsobesitindepe
83 ndensubjectsubjectberexperiencedSuppose
ndensubjectsubjectberexperiencedSupposeTheyoccuratdierentagesunderdierentcircumstancesexposuresooutcomesarepossiblemiscarriagenotmiscarriagewhereyofsuccessnotconsta
84 ntoneachtrialyofdependindependenwillfor
ntoneachtrialyofdependindependenwillforminpossiblericanetohurricanedependinguponwhenandwheretheyformindependen ybinomialexperimenyofanennberberread hooseisshorthandnot
85 ationfor dene ber xxx pnx
ationfor dene ber xxx pnx f g does berofobesesubjectsrandomlycpossibleexperimensubjectscorrespondobeses
86 ubjects berSubjectSubjectSubject OOOO
ubjects berSubjectSubjectSubject OOOOONONOONNNOONONNNO NNN corresponseobesesubjectsOONRecallthatforindependentevthejointprobabilityoftheevproductsubjectobeseinde
87 pendensubjectsubjectOON ONONOO
pendensubjectsubjectOON ONONOO berMoregenerallyestheberofwystohooseobjectsypeypeobesesubjectssubjects Thebinomialformulacanbeusedtocomputetheprobabilit
88 yofyonbetterAppendixbooklookberberberbe
yofyonbetterAppendixbooklookberberberber Supposeber f gf g alentlybasedonYPY Appendixtoober
89 possibleexpected Pexperime
possibleexpected Pexperimenberexpected ObesitSupposeobesesubjectsexpectexpectobeseInasampleof Idexpecttoobserv obeseberobese berobesesubjectsberobes
90 esubjectsrepeatingexperimenexpectaboutob
esubjectsrepeatingexperimenexpectaboutobesesubjectsber ThePoissonProbabilityDistribution importanberertainstocountsofthenberofsuccessesthataresubjectupperboundberoccurp
91 eriodoccurpertainsboundedberoccurperiod
eriodoccurpertainsboundedberoccurperiodexpectedberoccurperbersupposeperoccurperberoccurexperimen xHereedenotesthelogarithmfunctionThisisaconstantlikeequalto In
92 theexampleyexactly accideninPXex x
theexampleyexactly accideninPXex xe AppendixP e ebinomialprobabilitiescan propertpectedexperimenberSupposeSupposesubjectsThentheprobability
93 ofobservingorfewermaleswithalifetimedia
ofobservingorfewermaleswithalifetimediagnosis ywithmean UsingtheP e e ContinuousProbabilityDistributions Recallthatforadiscretervt
94 heprobabilityfunctionofpossibledescribet
heprobabilityfunctionofpossibledescribetheprobabilitythatarandomlyselectedsubjectfromthisyfunctionyforpossiblebecauseeighs lbsistheprobabilitytha
95 theshebetyfunctioneusewhatiscalledtheT
theshebetyfunctioneusewhatiscalledtheTheprobabilitydensityfunctionforaconuousrvesacurvcorresponding supposebodylooks Probability density 100150200250 0.00.0050.0100.0
96 150.0200.025 betbetareunderbetpossible N
150.0200.025 betbetareunderbetpossible Notethatforaconuousrvforallbetbet unimodallook A normal probability density with mean 0 and variance=1xf(x)=the p.d.f. of x -4-
97 2024 0.00.10.20.30.4 abo looksbell shape
2024 0.00.10.20.30.4 abo looksbell shapedimportanThenormaldistributionlikethebinomialandPoissonisanexampledescribedberoftheshapeabo locationsdispersion Normal pr
98 obability densities with different means
obability densities with different means and variancesxf(x) -50510 0.00.10.20.30.4 mean=0,var=1 mean=0,var=4 bell shapeditisaesaydensitaluealongspecic p ex w
99 hereagainedenotestheconstant d
hereagainedenotestheconstant denotesthe aboutunimodalmodeoccurpeaklocatedbetpossibleypdfareaundernormalcurvbetbersbetbetbet Supposewherethepo
100 pulationmeanheightisinchesandthepopula
pulationmeanheightisinchesandthepopulationstandardSupposepopulationpopulationorwomenoneSDbelowthemeanisabo ythatbetbetbelo Height p.d.f.s for men and womenheigh