numerical analysis report and need support to help me learn.
this assignment need someone good at operate a software named MINitab!!! this is important!! for most answer need appropriate minitab output to support. The assignment has a total of 90 marks distributed accross two components. The first component consists of 4 questions each with multiple sub-parts, totalling 62 marks accross all of them. The second component requires you to write a report summarising your results from these four questions, and totals 28 marks without word limit. one document in below named analysis of variance and non parametric procedures is week 9&10 slide which might need for Q2(b).
Requirements: depend on the questions but most question need concise
MATH1065QuantitativeMethodsinHealthReportDue:11pmFriday27October2023Instructions•Thedatayouwillneedtouseisavailablefromthecoursewebsite,andisnamedSleepStudy.xlsx.VariableDescriptionsareincludedintheAppendixattheendofthisdocument.•Thisassignmentisworth20%ofyourfinalgrade.Itisdueby11pmonFriday27October,attheendofweek12.•Youwillneedtosubmityourassignmentvialearnonline,asasinglePDFdocumentwhichincludesbothanswerstothequestions,aswellasyourreport.•YouwillberequiredtouseMinitabinansweringthequestionsforthisassignment.RelevantMinitaboutputshouldbeincludedaspartofyoursolutions,whichcanbeachievedbycopyandpastingtherelevantMinitaboutputasanimageintoaworddocument(whichshouldthenbepublishedtoaPDFwhenyouarereadytosubmit).•Ensurethatappropriateaxislabels(includingunitswhereappropriate),meaningfultitlesandlegendsareincludedwithallgraphicaldisplays.•Conciseanswers—onesthatarebriefandgetstraighttothepoint—willgenerallyearnbettermarksthanwordyanswers.•Theassignmenthasatotalof90marksdistributedaccrosstwocomponents.Thefirstcom-ponentconsistsof4questionseachwithmultiplesub-parts,totalling62marksaccrossallofthem.Thisfirstcomponentissimilartotheassignmentfromearlierinthestudyperiod.Thesecondcomponentrequiresyoutowriteareportsummarisingyourresultsfromthesefourquestions,andtotals28marks.Distributionofmarksaccrosssub-partsisshownbelow.•Poorcommunicationoramessylayoutwillattractapenaltyofupto9marks(10%ofmaximumpossibleavailable).•Latesubmissionintheabsenceofanapprovedextensionwillattractapenaltyof9marks(10%ofmaximumpossibleavailable)perdayorpartthereoftheassignmentislateuptoamaximumoffourdayslate.Assignmentssubmittedmorethan4days(96hours)latecanstillbemarkedatrequestinordertoprovidefeedback,butwillbegivenagradeofzero.•Donotexpectresponsestocorrespondence(emailsandextensionrequests)overweekends.However,weekenddaysdostillcounttowardslatepenalties.Soifyouemailthecoursecoordinatorovertheweekend,youshouldalsosubmitwhatyoucanassoonaspossiblewithoutwaitingforaresponse,andnotexpectaresponseuntilatleasttheMonday(ormorelikelytheTuesday)ofthefollowingweek.1
SuggestedScheduleYoushouldplanoutyourworkstartingassoonaspossibletocompleteitbeforetheduedate.Belowisasuggestedtimeframe,butultimatelyyouareresponsibleforplanningandallocatingyourtimeappropriately.Keepinmindtherewillbeopportunitiesinweeks11and12inparticulartogetadditionalsupportthroughthemathshelpdesksessions,andsoyoushouldaimtohaveattemptedtheentireassessmentbythensothatyoucangethelpwithanypartsyouneed.SuggestedTaskstobeCompletedWeek9•Downloadassignmentinstructionsandsubmissiontemplate;readthroughinstructionsandformattemplate.•DownloaddatafileandmakesureyoucanopenitinMinitabonyourcomputer,andreadthroughtheappendixwithvari-abledescriptionstounderstandthemeaningofthevariables.•AnswerQuestion3andQuestion4Week10•AnswerQuestion1,Question2(a)andQuestion2(c)Week11•AnswerQuestion2(b)•ReviewandfinalizeyouranswerstoQuestions1to4.•WriteyourReport,andcheckyourreportisconsistentwithyouranswerstoQuestions1to4.Week12•Checkyourentiresubmissionforconsistencyandconcise-ness,tidyandsubmit.Notethatdifferentquestionsrelatetodifferentpartsofthecourse,andthatpartofwhatisbeingassessedisyourabilitytoidentifywhatcontentisappropriatetoanswereachquestion.However,Question2(b)requirescontentonlycoveredinweeks9and10ofthecourseandsoyoushouldleaveitforlast,whiletherestofthequestionsrelatetocontentcoveredinweeks1-8andsoyoucanstartworkingonthemimmediately.2
BackgroundInformationSleep,CircadianPreference,andAcademicPerformance.Ifyouarelikemostuniversitystudents,chancesareyouarenotgettingenoughsleep.Sleepisim-portantforanumberofreasons.Itrestoresourenergy,fightsoffillnessandfatiguebystrengtheningtheimmunesystem,helpsusthinkmoreclearlyandcreatively,strengthensmemoryandproducesamorepositivemoodandbetterperformancethroughouttheday.Lackofsleepisassociatedwithbothphysicalandemotionalhealthriskswhichmayinclude:•Moreillness,suchascoldsandflu,duetoaloweredimmunesystem;•Feelingmorestressedout;•Weightgainandobesity;•LowerGPAanddecreasedacademicperformance;•Increasedriskofmentalhealthissues,suchasdepressionandanxiety;•Increasedriskofautomobileaccidentsduetofatigue;•Decreasedperformanceinactivitiesthatrequirecoordination.Arecentstudy1examinedtherelationshipbetweenclassstarttimes,sleep,circadianpreference,academicperformanceandotherfactorsinuniversitystudents.Twohundredandfifty-threepar-ticipantscompletedasurveythataskedmanyquestionsaboutattitudesandhabits.Participantswerealsorequiredtokeepasleepdiarytorecordtimeandqualityofsleepoveratwo-weekperiod.Participantswereundergraduatestudentsagedbetween18and23,ofwhich60%werefemaleand40%weremale.Themajorityofstudentslivedoncampusandheldnooutsidejobs.Theyeardistributionofparticipantswasasfollows:19%firstyear,38%secondyear,21%thirdyearand22%fourthyearstudents.Inthisassesmentyouwillanalysesomeofthedatafromthisstudytoanswerthequestionsthatfollowandprepareareportinwhichyousummariseyourfindings.1Onyper,S,Thacher,P,Gilbert,J&Gradess,S2012,‘ClassStartTimes,Sleep,andAcademicPerformanceinCollege:APathAnalysis’,ChronobiologyInternational,vol.29,no.3,pp.318-335.3
Question1(10marks)HowdoLarksandOwlsdifferintheirsleephabits?Inthisquestionyouaregoingtoanalysesleephabitsofuniversitystudentswithdifferentcircadianpreferences.UseMinitabtoobtaintheconfidenceintervalsforacomparisonbetweenLarksandOwls(ignoretheNeithercategory)oneachofthevariablesWeekdayBed,WeekdayRiseandWeekdaySleep.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.Forfullmarks,identifyanappropriatestatisticalprocedure,includeappropriateMinitaboutputandchecktherequirements(assumptions).DonotusethefullSTATE-FORMULATE-SOLVE-CONCLUDEprocedure.Instead,identifyandinterpretconfidenceintervalsthatcorrespondtostatisticallysignificantdifferencesbetweenLarksandOwls.4
Question2(18marks)Doescircadianpreferencematterwhenitcomestosleepquality?InordertoaddressthisquestionyouaregoingtoworkwithvariablesPoorSleepQualityandLarkOwl.(a)(6marks)UseMinitabtoproduceboxplotsofPoorSleepQualityforeachofthethreegroupsinLarkOwlshownhorizontallyinthesamegraph.Commentbrieflyonhowsleepqualitycomparesbetweenthethreegroupsandifyouexpecttofindanystatisticallysignificantdifferences.(b)(10marks)Isthereastatisticallysignificantdifferenceinsleepqualitybasedonstudents’circadianpreferences?Formulateandperformanappropriatehypothesistestata5%significancelevel.UsetheSTATE-FORMULATE-SOLVE-CONCLUDEprocedure.Forfullmarks,includeappropriateMinitaboutput.Note:Question2(b)relatestocontentfromweeks9and10,andsoshouldbeattemptedinweek10attheearliestorideallyinweek11.(c)(2marks)Isitappropriatetoarguecauseandeffect,ineitherdirection,basedontheseresults?Whyorwhynot?Explainbriefly.Hint:Howwasthisdatacollected?Whattypeofstudyisthis?5
Question3(10marks)Whichsleeprelatedhabitsmightinfluenceacademicperformance?Inordertoanswerthisquestion,youaregoingtoinvestigatetherelationshipbetweenGPAandeachofthefollowingvariables:timetoriseonweekdays,timetogotobedonweekdays,amountofsleeppernightonweekdays,andthenumberofmissedclasses.Answerthequestionsthatfollow.(a)(4marks)UseMinitabtoobtainthePearsoncorrelationcoefficientandthecorrespondingconfidenceintervalsforGPAwitheachofthefollowingvariables:WeekdayRise,WeekdayBed,WeekdaySleep,andClassesMissed.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.Forfullmarks,includerelevantMinitaboutputhere(i.e.fourcorrelationsandtheir95%confidenceintervals).Donotinterpretthatoutput,youwilldothatinpart(b).(b)(6marks)BasedonyourMinitaboutputinpart(a),answerthefollowingquestions:•DosamplecorrelationsprovidesufficientevidenceofanassociationbetweenGPAandtheothervariables?Inotherwords,whichcorrelationestimatesarestatisticallysignificant?Howdoyouknow?•Howstrongaretherelationshipsthatturnedouttobestatisticallysignificant?•Areyourstatisticallysignificantcorrelationspositiveornegative?Whatdoesitmeaninpracticaltermsforeachrelationship?Explainbriefly.6
Question4(24marks)IstherearelationshipbetweenSleepQualityandDASscore?’Inthestudystudentswereratedonsleepquality(PoorSleepQuality)aswellasonDepression,AnxietyandStressscales,withtheDASscore(DASScore)givingacompositeofthethreescores.HowwelldoestheDASscorepredictsleepquality?Answerthequestionsthatfollow.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.(a)(3marks)UseMinitabtoobtainafittedlineplot,includingR-squaredvalueandfittedlineequationwithDASScoreastheindependentvariable(x)andPoorSleepQualityasthedependentvariable(y).(b)(2marks)UseMinitabtoobtainresidualplotscorrespondingtothemodelfitin(a).YouwillusetheMinitaboutputfromheretoanswerquestionsthatfollowinparts(c)to(f).(c)(5marks)Areconditionsforlinearregressionsatisfied?AnswerintermsofLinearity,Indepen-dence,NormalityandPopulationstandarddeviations.(d)(3marks)CommentonthestrengthoftherelationshipbetweensleepqualityandDASscoreusingthecoefficientofdetermination.Whatisitsvalue?Whatpreciselydoesitmeasureinthisscenario?(e)(2marks)Whatisthevalueoftheslope?Whatdoesitmeasureinthisscenario?(f)(3marks)IstherelationshipbetweensleepqualityandDASscorestatisticallysignificant?Inotherwords,istheslopeestimatestatisticallysignificantat5%level?Howdoyouknow?Explainbriefly,andincludeanyMinitaboutputusedinconstructingyouranswer.(g)(6marks)SupposethatoneofthestudentsatthisuniversityhasafairlyhighDASscoreof40.UseMinitabtoobtainapredictionofsleepqualityforthisstudent,includinga90%intervalforthatprediction.Discusstheaccuracyofthatprediction.7
ReportInadditiontoansweringthequestionsabove,youshouldwriteashortreportsummarisingallthatyouhavedone.Yourreportshouldconsistofsectionsdescribedbelow.Pleasenotethisreportshouldbeasummaryofwhatyouhavedone,andsoshouldbeshort,andtothepoint.Itshouldreflectthemostimportantinformationwithoutextensivelyrepeatingallthedetailthathascomebefore.BriefSummary(3marks)Normallyareportlikethiswouldbeginwithan“Introduction”sectionwhichwouldintroducethebroadcontextandrationaleofthestudy.However,asthistypeofdiscussionhasalreadybeenprovidedforyouinthe“BackgroundInformation”sectionabove,insteadyoushouldintroduceyourreportwithabriefsummary.Thereisnowordlimit,butthisshouldbeaverybrief(50-100wordsshouldbesufficient)explanationofwhatwillbefoundinthisreport.Methods(6marks)Discussthemethodsusedtocollectandanalysedatafromthisstudy:•Whattypeofstudywasconducted?Namethestudydesignandbrieflydescribetheprocessbywhichthedatawascollected.•Describethesample(includingthesamplesize)andanykeyinformationyouthinkisrelevantinrestrictingwhatthepopulationwecandrawinferencesaboutis(forexample,iftheallormostofthedatawascollectedonwomen,itmightnotbereasonabletouseittodrawconclusionsaboutmen,etc.).•Brieflydescribevariablesthatyouhaveanalysedandwhattheyrelateto/whytheyareofinterest.•Providealistofstatisticalmethodsthatyouhaveused.Thereisnowordlimit.Asaguideline,oneparagraphforthissectionissufficient.Dot-pointscanbeuseful.Results(10marks)SummarisethekeyfindingsfromyouranalysesfromQuestions1to4.Usingdotpointsisacceptable.Youshouldaimtobeaccurate,complete,butconcise.Aimforalistofapproximately5keyfindings.Thereisnowordlimit,buteachkeyfindingshouldbesummarisedbrieflywhilestillcoveringalltheimportantdetails.50-100wordsperkeyfindingshouldbesufficientifsummarisedappropriately.Stateeachresultandthecorrespondingstatisticalprocedure,andreportP-valuestothreedecimalplaces.However,donotincludenumericalcalculationsorfulldetailsofstatisticalproceduresandconditionchecking(e.g.fullMinitaboutput).IncludecopiesofkeydiagramsfromQuestions1to4asrelevanttoyourpresentationofresults.Usefuldiagramstoincludeinareportarebarcharts,histograms,boxplots,errordiagrams,scatter-plots,etc.NormalProbabilityPlotsorresidualplotsshouldnotbeincludedinareport.Forthisreport,chooseasmallnumberofkeyresultstoincludethatbesthighlightoneortwoofyourkeyfindings.8
Discussion(6marks)Interpretyourstatisticalfindingsbydiscussingtheirpracticalsignificance.Useplainlanguage;thereshouldbenotechnicaldetailsorstatisticalterminology.Discussatleasttworesultsyoufindparticularlysurprising,explainwhytheyaresurprisingandinterestingincontext.Indicateatleasttwokeypotentialshortcomingsofthestudydesignandanalysesthatwereperformed.Arethereanyissueswithinternalandexternalvalidityofthisstudy?Thereisnowordlimit.Butaimtobebrief.Aconciseoneortwoparagraphsthatgetstraighttothekeypointswouldbebetterthanalongdetaileddiscussionofeveryminordetailthatcouldpossiblyberelevant.Remember,marksareawardedforqualitynotquantity!Conclusion(3marks)Whatcanyouconcludefromyouranalysisaboutsleepquality,mood,circadianpreferenceandacademicperformance?Whichfactorsappeartobeimportant?Thereisnowordlimit.Asaguideline,oneparagraphwillbesufficient.Donotintroduceanynewinformationinthissection,anddonotsimplyrepeatstatementsmadeelsewhereinyourreport!Note:Youarenotrequiredtoincludeadditionalsources(e.g.internetarticlesorscientificpapers)butifyoudo,ensureyouincludeareferencelistandcitethemintextappropriately.9
AppendixSomeofthedatafromtheOnyperetal(2012)studyisstoredinthefilecalledSleepStudy.xlsxavailablefromthecoursewebsite.Belowaredescriptionsofthevariablesinthatdatafile:NameDescriptionClassesMissedNumberofclassesmissedinasemesterClassYearYearlevelfromfirsttofourthyear,coded1to4DASScoreCombinedscoreonDepression,AnxietyandStressscale,com-monlyusedtoassessmood.Highervaluesindicatemoremoodcomplaints,e.g.depression,anxietyand/orstressGender0=Femaleand1=MaleGPAGradepointaveragemeasuredon0-4scale,self-reported.LarkOwlResponsestothefollowingsurveyquestion:‘Areyouanearlyriseroranightowl?’Possiblecategories:Lark,Neither,orOwlPoorSleepQualityMeasureofsleepqualityderivedfromresponsestothePittsburghSleepQualityIndex(PSQI)questionnaire.HighervaluesindicatepoorersleepWeekdayBedTypicalweekdaybedtimederivedfromresponsesonPSQIandsleepdiaries,reportedinhourssincepreviousmidnight,e.g.abedtimeof25correspondstogoingtobedat1:00amWeekdayRiseTypicalweekdayrisetimederivedfromresponsesonPSQIandsleepdiaries,reportedinhourssincemidnight,e.g.arisetimeof7.25correspondstogettingupat7:15amWeekdaySleepTypicalweekdaysleepduration,estimatedasaperiodoftimefromshuttingtheeyeswithintenttogotosleepuntilthetimetheparticipantsawokeanddidnotclosetheireyestogobacktosleep.DerivedfromresponsesonPSQIandsleepdiariesandreportedinhours10
MATH1065QuantitativeMethodsinHealthReportDue:11pmFriday27October2023Instructions•Thedatayouwillneedtouseisavailablefromthecoursewebsite,andisnamedSleepStudy.xlsx.VariableDescriptionsareincludedintheAppendixattheendofthisdocument.•Thisassignmentisworth20%ofyourfinalgrade.Itisdueby11pmonFriday27October,attheendofweek12.•Youwillneedtosubmityourassignmentvialearnonline,asasinglePDFdocumentwhichincludesbothanswerstothequestions,aswellasyourreport.•YouwillberequiredtouseMinitabinansweringthequestionsforthisassignment.RelevantMinitaboutputshouldbeincludedaspartofyoursolutions,whichcanbeachievedbycopyandpastingtherelevantMinitaboutputasanimageintoaworddocument(whichshouldthenbepublishedtoaPDFwhenyouarereadytosubmit).•Ensurethatappropriateaxislabels(includingunitswhereappropriate),meaningfultitlesandlegendsareincludedwithallgraphicaldisplays.•Conciseanswers—onesthatarebriefandgetstraighttothepoint—willgenerallyearnbettermarksthanwordyanswers.•Theassignmenthasatotalof90marksdistributedaccrosstwocomponents.Thefirstcom-ponentconsistsof4questionseachwithmultiplesub-parts,totalling62marksaccrossallofthem.Thisfirstcomponentissimilartotheassignmentfromearlierinthestudyperiod.Thesecondcomponentrequiresyoutowriteareportsummarisingyourresultsfromthesefourquestions,andtotals28marks.Distributionofmarksaccrosssub-partsisshownbelow.•Poorcommunicationoramessylayoutwillattractapenaltyofupto9marks(10%ofmaximumpossibleavailable).•Latesubmissionintheabsenceofanapprovedextensionwillattractapenaltyof9marks(10%ofmaximumpossibleavailable)perdayorpartthereoftheassignmentislateuptoamaximumoffourdayslate.Assignmentssubmittedmorethan4days(96hours)latecanstillbemarkedatrequestinordertoprovidefeedback,butwillbegivenagradeofzero.•Donotexpectresponsestocorrespondence(emailsandextensionrequests)overweekends.However,weekenddaysdostillcounttowardslatepenalties.Soifyouemailthecoursecoordinatorovertheweekend,youshouldalsosubmitwhatyoucanassoonaspossiblewithoutwaitingforaresponse,andnotexpectaresponseuntilatleasttheMonday(ormorelikelytheTuesday)ofthefollowingweek.1
SuggestedScheduleYoushouldplanoutyourworkstartingassoonaspossibletocompleteitbeforetheduedate.Belowisasuggestedtimeframe,butultimatelyyouareresponsibleforplanningandallocatingyourtimeappropriately.Keepinmindtherewillbeopportunitiesinweeks11and12inparticulartogetadditionalsupportthroughthemathshelpdesksessions,andsoyoushouldaimtohaveattemptedtheentireassessmentbythensothatyoucangethelpwithanypartsyouneed.SuggestedTaskstobeCompletedWeek9•Downloadassignmentinstructionsandsubmissiontemplate;readthroughinstructionsandformattemplate.•DownloaddatafileandmakesureyoucanopenitinMinitabonyourcomputer,andreadthroughtheappendixwithvari-abledescriptionstounderstandthemeaningofthevariables.•AnswerQuestion3andQuestion4Week10•AnswerQuestion1,Question2(a)andQuestion2(c)Week11•AnswerQuestion2(b)•ReviewandfinalizeyouranswerstoQuestions1to4.•WriteyourReport,andcheckyourreportisconsistentwithyouranswerstoQuestions1to4.Week12•Checkyourentiresubmissionforconsistencyandconcise-ness,tidyandsubmit.Notethatdifferentquestionsrelatetodifferentpartsofthecourse,andthatpartofwhatisbeingassessedisyourabilitytoidentifywhatcontentisappropriatetoanswereachquestion.However,Question2(b)requirescontentonlycoveredinweeks9and10ofthecourseandsoyoushouldleaveitforlast,whiletherestofthequestionsrelatetocontentcoveredinweeks1-8andsoyoucanstartworkingonthemimmediately.2
BackgroundInformationSleep,CircadianPreference,andAcademicPerformance.Ifyouarelikemostuniversitystudents,chancesareyouarenotgettingenoughsleep.Sleepisim-portantforanumberofreasons.Itrestoresourenergy,fightsoffillnessandfatiguebystrengtheningtheimmunesystem,helpsusthinkmoreclearlyandcreatively,strengthensmemoryandproducesamorepositivemoodandbetterperformancethroughouttheday.Lackofsleepisassociatedwithbothphysicalandemotionalhealthriskswhichmayinclude:•Moreillness,suchascoldsandflu,duetoaloweredimmunesystem;•Feelingmorestressedout;•Weightgainandobesity;•LowerGPAanddecreasedacademicperformance;•Increasedriskofmentalhealthissues,suchasdepressionandanxiety;•Increasedriskofautomobileaccidentsduetofatigue;•Decreasedperformanceinactivitiesthatrequirecoordination.Arecentstudy1examinedtherelationshipbetweenclassstarttimes,sleep,circadianpreference,academicperformanceandotherfactorsinuniversitystudents.Twohundredandfifty-threepar-ticipantscompletedasurveythataskedmanyquestionsaboutattitudesandhabits.Participantswerealsorequiredtokeepasleepdiarytorecordtimeandqualityofsleepoveratwo-weekperiod.Participantswereundergraduatestudentsagedbetween18and23,ofwhich60%werefemaleand40%weremale.Themajorityofstudentslivedoncampusandheldnooutsidejobs.Theyeardistributionofparticipantswasasfollows:19%firstyear,38%secondyear,21%thirdyearand22%fourthyearstudents.Inthisassesmentyouwillanalysesomeofthedatafromthisstudytoanswerthequestionsthatfollowandprepareareportinwhichyousummariseyourfindings.1Onyper,S,Thacher,P,Gilbert,J&Gradess,S2012,‘ClassStartTimes,Sleep,andAcademicPerformanceinCollege:APathAnalysis’,ChronobiologyInternational,vol.29,no.3,pp.318-335.3
Question1(10marks)HowdoLarksandOwlsdifferintheirsleephabits?Inthisquestionyouaregoingtoanalysesleephabitsofuniversitystudentswithdifferentcircadianpreferences.UseMinitabtoobtaintheconfidenceintervalsforacomparisonbetweenLarksandOwls(ignoretheNeithercategory)oneachofthevariablesWeekdayBed,WeekdayRiseandWeekdaySleep.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.Forfullmarks,identifyanappropriatestatisticalprocedure,includeappropriateMinitaboutputandchecktherequirements(assumptions).DonotusethefullSTATE-FORMULATE-SOLVE-CONCLUDEprocedure.Instead,identifyandinterpretconfidenceintervalsthatcorrespondtostatisticallysignificantdifferencesbetweenLarksandOwls.4
Question2(18marks)Doescircadianpreferencematterwhenitcomestosleepquality?InordertoaddressthisquestionyouaregoingtoworkwithvariablesPoorSleepQualityandLarkOwl.(a)(6marks)UseMinitabtoproduceboxplotsofPoorSleepQualityforeachofthethreegroupsinLarkOwlshownhorizontallyinthesamegraph.Commentbrieflyonhowsleepqualitycomparesbetweenthethreegroupsandifyouexpecttofindanystatisticallysignificantdifferences.(b)(10marks)Isthereastatisticallysignificantdifferenceinsleepqualitybasedonstudents’circadianpreferences?Formulateandperformanappropriatehypothesistestata5%significancelevel.UsetheSTATE-FORMULATE-SOLVE-CONCLUDEprocedure.Forfullmarks,includeappropriateMinitaboutput.Note:Question2(b)relatestocontentfromweeks9and10,andsoshouldbeattemptedinweek10attheearliestorideallyinweek11.(c)(2marks)Isitappropriatetoarguecauseandeffect,ineitherdirection,basedontheseresults?Whyorwhynot?Explainbriefly.Hint:Howwasthisdatacollected?Whattypeofstudyisthis?5
Question3(10marks)Whichsleeprelatedhabitsmightinfluenceacademicperformance?Inordertoanswerthisquestion,youaregoingtoinvestigatetherelationshipbetweenGPAandeachofthefollowingvariables:timetoriseonweekdays,timetogotobedonweekdays,amountofsleeppernightonweekdays,andthenumberofmissedclasses.Answerthequestionsthatfollow.(a)(4marks)UseMinitabtoobtainthePearsoncorrelationcoefficientandthecorrespondingconfidenceintervalsforGPAwitheachofthefollowingvariables:WeekdayRise,WeekdayBed,WeekdaySleep,andClassesMissed.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.Forfullmarks,includerelevantMinitaboutputhere(i.e.fourcorrelationsandtheir95%confidenceintervals).Donotinterpretthatoutput,youwilldothatinpart(b).(b)(6marks)BasedonyourMinitaboutputinpart(a),answerthefollowingquestions:•DosamplecorrelationsprovidesufficientevidenceofanassociationbetweenGPAandtheothervariables?Inotherwords,whichcorrelationestimatesarestatisticallysignificant?Howdoyouknow?•Howstrongaretherelationshipsthatturnedouttobestatisticallysignificant?•Areyourstatisticallysignificantcorrelationspositiveornegative?Whatdoesitmeaninpracticaltermsforeachrelationship?Explainbriefly.6
Question4(24marks)IstherearelationshipbetweenSleepQualityandDASscore?’Inthestudystudentswereratedonsleepquality(PoorSleepQuality)aswellasonDepression,AnxietyandStressscales,withtheDASscore(DASScore)givingacompositeofthethreescores.HowwelldoestheDASscorepredictsleepquality?Answerthequestionsthatfollow.ThesevariablesarestoredintheSleepStudy.xlsxdatafileandtheirdescriptionscanbefoundintheAppendixattheendofthisdocument.(a)(3marks)UseMinitabtoobtainafittedlineplot,includingR-squaredvalueandfittedlineequationwithDASScoreastheindependentvariable(x)andPoorSleepQualityasthedependentvariable(y).(b)(2marks)UseMinitabtoobtainresidualplotscorrespondingtothemodelfitin(a).YouwillusetheMinitaboutputfromheretoanswerquestionsthatfollowinparts(c)to(f).(c)(5marks)Areconditionsforlinearregressionsatisfied?AnswerintermsofLinearity,Indepen-dence,NormalityandPopulationstandarddeviations.(d)(3marks)CommentonthestrengthoftherelationshipbetweensleepqualityandDASscoreusingthecoefficientofdetermination.Whatisitsvalue?Whatpreciselydoesitmeasureinthisscenario?(e)(2marks)Whatisthevalueoftheslope?Whatdoesitmeasureinthisscenario?(f)(3marks)IstherelationshipbetweensleepqualityandDASscorestatisticallysignificant?Inotherwords,istheslopeestimatestatisticallysignificantat5%level?Howdoyouknow?Explainbriefly,andincludeanyMinitaboutputusedinconstructingyouranswer.(g)(6marks)SupposethatoneofthestudentsatthisuniversityhasafairlyhighDASscoreof40.UseMinitabtoobtainapredictionofsleepqualityforthisstudent,includinga90%intervalforthatprediction.Discusstheaccuracyofthatprediction.7
ReportInadditiontoansweringthequestionsabove,youshouldwriteashortreportsummarisingallthatyouhavedone.Yourreportshouldconsistofsectionsdescribedbelow.Pleasenotethisreportshouldbeasummaryofwhatyouhavedone,andsoshouldbeshort,andtothepoint.Itshouldreflectthemostimportantinformationwithoutextensivelyrepeatingallthedetailthathascomebefore.BriefSummary(3marks)Normallyareportlikethiswouldbeginwithan“Introduction”sectionwhichwouldintroducethebroadcontextandrationaleofthestudy.However,asthistypeofdiscussionhasalreadybeenprovidedforyouinthe“BackgroundInformation”sectionabove,insteadyoushouldintroduceyourreportwithabriefsummary.Thereisnowordlimit,butthisshouldbeaverybrief(50-100wordsshouldbesufficient)explanationofwhatwillbefoundinthisreport.Methods(6marks)Discussthemethodsusedtocollectandanalysedatafromthisstudy:•Whattypeofstudywasconducted?Namethestudydesignandbrieflydescribetheprocessbywhichthedatawascollected.•Describethesample(includingthesamplesize)andanykeyinformationyouthinkisrelevantinrestrictingwhatthepopulationwecandrawinferencesaboutis(forexample,iftheallormostofthedatawascollectedonwomen,itmightnotbereasonabletouseittodrawconclusionsaboutmen,etc.).•Brieflydescribevariablesthatyouhaveanalysedandwhattheyrelateto/whytheyareofinterest.•Providealistofstatisticalmethodsthatyouhaveused.Thereisnowordlimit.Asaguideline,oneparagraphforthissectionissufficient.Dot-pointscanbeuseful.Results(10marks)SummarisethekeyfindingsfromyouranalysesfromQuestions1to4.Usingdotpointsisacceptable.Youshouldaimtobeaccurate,complete,butconcise.Aimforalistofapproximately5keyfindings.Thereisnowordlimit,buteachkeyfindingshouldbesummarisedbrieflywhilestillcoveringalltheimportantdetails.50-100wordsperkeyfindingshouldbesufficientifsummarisedappropriately.Stateeachresultandthecorrespondingstatisticalprocedure,andreportP-valuestothreedecimalplaces.However,donotincludenumericalcalculationsorfulldetailsofstatisticalproceduresandconditionchecking(e.g.fullMinitaboutput).IncludecopiesofkeydiagramsfromQuestions1to4asrelevanttoyourpresentationofresults.Usefuldiagramstoincludeinareportarebarcharts,histograms,boxplots,errordiagrams,scatter-plots,etc.NormalProbabilityPlotsorresidualplotsshouldnotbeincludedinareport.Forthisreport,chooseasmallnumberofkeyresultstoincludethatbesthighlightoneortwoofyourkeyfindings.8
Discussion(6marks)Interpretyourstatisticalfindingsbydiscussingtheirpracticalsignificance.Useplainlanguage;thereshouldbenotechnicaldetailsorstatisticalterminology.Discussatleasttworesultsyoufindparticularlysurprising,explainwhytheyaresurprisingandinterestingincontext.Indicateatleasttwokeypotentialshortcomingsofthestudydesignandanalysesthatwereperformed.Arethereanyissueswithinternalandexternalvalidityofthisstudy?Thereisnowordlimit.Butaimtobebrief.Aconciseoneortwoparagraphsthatgetstraighttothekeypointswouldbebetterthanalongdetaileddiscussionofeveryminordetailthatcouldpossiblyberelevant.Remember,marksareawardedforqualitynotquantity!Conclusion(3marks)Whatcanyouconcludefromyouranalysisaboutsleepquality,mood,circadianpreferenceandacademicperformance?Whichfactorsappeartobeimportant?Thereisnowordlimit.Asaguideline,oneparagraphwillbesufficient.Donotintroduceanynewinformationinthissection,anddonotsimplyrepeatstatementsmadeelsewhereinyourreport!Note:Youarenotrequiredtoincludeadditionalsources(e.g.internetarticlesorscientificpapers)butifyoudo,ensureyouincludeareferencelistandcitethemintextappropriately.9
AppendixSomeofthedatafromtheOnyperetal(2012)studyisstoredinthefilecalledSleepStudy.xlsxavailablefromthecoursewebsite.Belowaredescriptionsofthevariablesinthatdatafile:NameDescriptionClassesMissedNumberofclassesmissedinasemesterClassYearYearlevelfromfirsttofourthyear,coded1to4DASScoreCombinedscoreonDepression,AnxietyandStressscale,com-monlyusedtoassessmood.Highervaluesindicatemoremoodcomplaints,e.g.depression,anxietyand/orstressGender0=Femaleand1=MaleGPAGradepointaveragemeasuredon0-4scale,self-reported.LarkOwlResponsestothefollowingsurveyquestion:‘Areyouanearlyriseroranightowl?’Possiblecategories:Lark,Neither,orOwlPoorSleepQualityMeasureofsleepqualityderivedfromresponsestothePittsburghSleepQualityIndex(PSQI)questionnaire.HighervaluesindicatepoorersleepWeekdayBedTypicalweekdaybedtimederivedfromresponsesonPSQIandsleepdiaries,reportedinhourssincepreviousmidnight,e.g.abedtimeof25correspondstogoingtobedat1:00amWeekdayRiseTypicalweekdayrisetimederivedfromresponsesonPSQIandsleepdiaries,reportedinhourssincemidnight,e.g.arisetimeof7.25correspondstogettingupat7:15amWeekdaySleepTypicalweekdaysleepduration,estimatedasaperiodoftimefromshuttingtheeyeswithintenttogotosleepuntilthetimetheparticipantsawokeanddidnotclosetheireyestogobacktosleep.DerivedfromresponsesonPSQIandsleepdiariesandreportedinhours10
MATH 1065 – Quantitative Methods in Health
Statistical Analysis Report
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Let them eat fruit!
The effect of fruit and vegetable consumption on well-being
Introduction
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Methods
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Results & Discussion
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1Non-parametric proceduresOverviewWhat we have done so far•We have considered:–Statistical procedures concerned with particular population parameters;–Validity derived from the specific set of assumptionsabout underlying populations.University of South Australia -UniSA STEM2•In practice, researchers often have no knowledge of the form of the distribution their data comes from!12
2Non‐parametric or distribution‐free procedures•Used when parametric methods are not applicable:–Key assumptions do not hold;–Outliers are present;–Based onmedians rather than means.University of South Australia -UniSA STEM3Non‐parametric alternatives•One‐sample or matched pairs:–Sign test•Two independent samples:–Mann‐Whitney‐Wilcoxon test (ranks)•More than two independent samples:–Kruskall‐Wallis test (ranks)University of South Australia -UniSA STEM434
3Non-parametric proceduresExamples –Sign testThe Sign test•The sign test procedure:–Convert original observations into + and –signs.–Count the number of observations greater than the hypothetical median.–When dealing with two related samples we count the number of times one treatment has a higher value than the other.–Ties are not counted.•If the null hypothesis is true, we would expect an approximately equal number of + and ‐signs.•If either + or ‐signs predominate, there is evidence that the null hypothesis is false.University of South Australia -UniSA STEM656
4Example: Recovery times•In an anesthetic used for major surgery, the mean number of hours it takes for the anesthesia to wear off is 7 hours. •A new agent has been suggested that supposedly provides relief much sooner. •In a series of 12 surgeries using the new anesthetic, the following recovery times were observed:4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 11University of South Australia -UniSA STEM7Example: Examine the dataBecause the distribution is skewedand has an outlier, the one‐sample t‐test is not appropriate.Use Sign test instead.University of South Australia -UniSA STEM81110987654Time (hours)Recovery times from using a new anesthetic during surgeryResults from a series of 12 surgeriesFormulate:H0: Median = 7H1: Median < 7a= 0.0578
5Example: Hypothesis testSolve:University of South Australia -UniSA STEM9Data4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 11–Sign Test statistic = 2.–From the Minitab output: P‐value = 0.0327 < 0.05, so H0is rejected.Conclude:–At 5% significance level, there is enough statistical evidence to conclude that the new agent reducesrecovery time.Non-parametric proceduresExamples –Mann‐Whitney test910
6The Mann‐Whitney Test•This test is a non‐parametric alternative to the two‐sample t‐test for independent samples.•Assumptions:–No assumptions are made about the shape of the population distribution.•Hypotheses:H0: median1= median2H1: median1median2 (or < , or > )University of South Australia -UniSA STEM11The basis of the Mann‐Whitney Test•A real difference between two treatments should make observations in one sample generally larger than those in the other.•Suppose the null hypothesis is false:–When we combine the two samples together and rank all the combined observations, the data from one sample should be concentrated at one end of the scale, and the data from the other sample should be at the other end.University of South Australia -UniSA STEM121112
7Example: Time to fall asleep•A pharmaceutical company decides to test the effectiveness of a new sleeping pill. •A random sample of 30 patients who regularly suffer from insomnia is chosen. University of South Australia -UniSA STEM13•Half of the subjects are given the newly developed sleeping pill and half the placebo. •Each participant is fitted with a device that measures the time until sleep occurs. Example: Is the new sleeping pill effective?University of South Australia -UniSA STEM141314
8Example: Normal Probability PlotsUniversity of South Australia -UniSA STEM15The sleeping pill sample failed the Normality test with P‐value = 0.008 < 0.05.We can’t apply the two‐sample t‐test.Use the Mann‐Whitney test.P-valueExample: Hypothesis test•Formulate:H0: median1= median2H1: median1
7Example: Setting up for a hypothesis test•State:–Do the mean heart rates for the groups appear to show that the presence of a pet or a friend reduces heart rate during a stressful task?•Formulate:H0: All means are equalH1: Not all meansare equal= 0.05•Solve:–First check the requirements.–We have three independent samples.University of South Australia -UniSA STEM13120100806040999050101120100806040999050101Mean82.52StDev9.242N15AD0.286P-Value0.574ControlMean73.48StDev9.970N15AD0.694P-Value0.055DogMean91.33StDev8.341N15AD0.342P-Value0.443FriendControlHeart rate (bpm)PercentDogFriendNormal – 95% CIPanel variable: groupProbability Plot of study participant heart ratesExample: Requirements checkUniversity of South Australia -UniSA STEM14All P‐values are greater than 0.05, so all three populations are assumed to be Normal.Normality check:Standard deviation check:We can assume equal variances.LargestSmallest
L9.978.34
O2We have all the requirements for ANOVA. 1314
8Example: Minitab output for ANOVAUniversity of South Australia -UniSA STEM15Example: Decision and conclusion•From the Minitab output:–The test statistic is F= 14.08.–It has an Fdistribution with 2 (numerator) and 42 (denominator) degrees of freedom. –Since the P‐value = 0.000 is less than 0.05, H0is rejected.University of South Australia -UniSA STEM16•Conclude:–At 5% significance level, there is enough statistical evidence to conclude that mean heart rates in response to stress among the three groups are different.–Further analysis will be performed to decide which of the three means are different from each other.1516
9Example: Post‐hoc comparisons –Tukey’s methodUniversity of South Australia -UniSA STEM17Friend – DogFriend – ControlDog – Control3020100-10-20If an interval does not contain zero, the corresponding means are significantly different.Tukey Simultaneous 95% CIsDifferences of Means for rateConfidence intervals for differences in means adjustedfor multiple comparisons.Example:Interpreting Tukey’s confidence intervals•Control groupsubtracted from the Dog group: –The 95% confidence interval for the difference in the population means of these two groups does not contain zero. –Conclude that the two population means are not equal.–Confidence limits are negative, implying that the mean heart rate for the Doggroup was lowerthan for the Controlgroup.•Is there any other pair that differs significantly?University of South Australia -UniSA STEM181718
10Analysis of Variance (ANOVA)Two‐way ANOVARecall: The idea behind one‐way ANOVAHow does explained variance compare to the unexplained variance?Total variance in the dataVariance explained by the modelUnexplained varianceUniversity of South Australia -UniSA STEM20What if there are other categorical variables that could be affecting the outcome?1920
11The idea behind two‐way ANOVATotal variance in the dataVariance explained by the modelUnexplained varianceVariance explained by variable AVariance explained by variable BVariance explained by interactionof A and B21University of South Australia -UniSA STEMIn many situations, there are at least two categorical variables that could be considered as explanatory variables.How well do the two variables togetherexplain the outcome?How does eachof the variables A and B affect the outcome?Does the effect of variable A changeas variable B changes?Main and interaction effects•Interaction effect:–The effect of one explanatory variable dependson the specific value or level of the other explanatory variable.•Main effect: –The mean effect of a single explanatory variable, averagedover other explanatory variables.22It is usually the interactions between variables that are the most interesting in a two‐way (or a more general) ANOVA design.University of South Australia -UniSA STEMVersion AMean responseTask 1Task 2Task 3Version B2122
12Checking assumptions in two‐way ANOVA•The samples of observations from different groups are independent.•The response variable in Normally distributed around its mean, which may depend on treatment factors.•The variance of the response variable is a constantand in particular does not depend on treatment factors.•These can be checked by examining residuals.23University of South Australia -UniSA STEMResidualAnalysis of Variance (ANOVA)Two‐way ANOVA example2324
13Example:Perception of time•How accurately can people estimate a given length of time?•In one experiment, subjects were asked to estimate 5‐and 10‐second intervals.•Does age and gender make a difference to whether they over‐or underestimate time intervals?University of South Australia -UniSA STEM25Example:10‐second guessesUniversity of South Australia -UniSA STEM26The P‐value for age group is 0.032. This is good evidence that the expected guess for 10 seconds is not the same for all age groups, averaged over gender.The P‐value for gender is large. This is no evidence of differences in expected guess for 10 seconds between males and females, averaged over age group.The P‐value for interactionis 0.059. This is some evidence that the effect of gender on guessing 10 seconds depends on age group.2526
14Example:Checking residualsUniversity of South Australia -UniSA STEM275.02.50.0-2.5-5.099.99990501010.1ResidualPercent10985.02.50.0-2.5-5.0Fitted ValueResidual3.01.50.0-1.5-3.0-4.520151050ResidualFrequency12011010090807060504030201015.02.50.0-2.5-5.0Observation OrderResidualNormal Probability PlotVersus FitsHistogramVersus OrderResidual plots for ten second guessesThe Normal probability plot is reasonably straight.The plot of residuals vs fits shows similar spread across the different age groups and the residuals look to be randomly scattered around zero.Example:Main effects plotUniversity of South Australia -UniSA STEM28There is very little difference between the average male and female guesses when averaged across the age groups.When averaged over gender, the main difference for age groups is between the oldest group and all the others. malefemale10.610.410.210.09.89.69.49.29.061-7051-6041-5031-4021-3010-20GenderMean guessAgeGroupMain effects plot for ten second guessesData Means2728
15Example:Interaction plotUniversity of South Australia -UniSA STEM2961-7051-6041-5031-4021-3010-2010.510.09.59.08.58.0Age groupMean guessfemalemale GenderInteraction plot for ten second guessesData meansThe gaps between the average male and female guesses are quite different for some of the groups, and they also swap direction.For the 10‐20 year age group, the average male guess was quite a bit larger than the average female guess.For the 51‐60 year age group, this was reversed. 302930
