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Chapter3FundamentalsofStatisticalStudiesDefinitionofStatisticsStatisticsisthestudyofvariation,interactionsand,operationaldefinitions.Statisticsisthestudyofdatatoprovideabasisforactiononapopulationorprocess.TypesofStatisticalStudiesEnumerative studies arestatisticalinvestigationsthatleadtoactiononastaticpopulation(thatis,agroupofitems,people,etc.thatexistinagiventimeperiodand/oratagivenlocation).Analytic studies arestatisticalinvestigationsthatleadtoactiononadynamicprocess.Sincethisisatextonqualityimprovement,theprimaryfocuswillbeonanalyticstudies.EnumerativeStudiesBasicConceptsApopulation(oruniverse)isthetotalityofunits,items,orpeopleofinterestthatexistinagiventimeperiodand/orgivenlocationAdministration.Aframeisalistoftheitemsinapopulation.Thegapisthedifferencebetweentheframeandthepopulation.Asample isaportionoftheframeunderinvestigation,andisselectedsothatinformationcanbedrawnfromitabouttheframe.BasicConceptsNonrandom samples areselectedonthebasisofconvenience(convenience sample),theopinionofanexpert(judgment sample),oraquotatoensureproportionalrepresentationofcertainclassesofitems,units,orpeopleinthesample(quota sample).Allnonrandomsampleshavethesameshortcomingtheyresubjecttoanunknowndegreeofbiasintheirresults.Thisbiasiscausedbytheabsenceofaframe.Nonrandomsamplesshouldbeusedonlywhenbetterinformationistoocostlytoobtain.Random samples areselectedsothateveryelementintheframehasaknownprobabilityofselection.Typesofrandomsamplesincludesimple,stratified,andcluster.Allrandomsamplesallowgeneralizedstatementstobemadeabouttheframefromthesample.Arandomsampleisselectedbyoperationallydefiningaprocedurethatutilizesrandomnumbersintheselectionofthesampleditemsfromtheframetoeliminatebiasandholduncertaintywithinknownlimits.Sevenstepsareinvolvedinselectingasimplerandomsample:Step 1.Countthenumberofelementsintheframe,N.Step 2.Numbertheelementsintheframefrom1throughN.IfNis25,thentheelementsintheframeshouldbenumberedfrom01through25.Allelementsmustreceiveanidentificationnumberwiththesamenumberofdigits.Step 3.Selectapageinatableofrandomnumbers.Forexample,selectingapageandstartingpointyields.193040092878311398676069611339043462052856735990548709422934276212493869294093Step 4.Ontheselectedpageofrandomnumbers,selectacolumnofnumbers,selectastartingpointinthatcolumn,anduseasmanydigitsastherearedigitsinN(twodigitsinthecaseofN=25).Forexample,beginningwiththetopofourcolumn,selecting,andusingthefirsttwodigitsofeachnumberinthatcolumn,thefirstrandomnumberis19.Sample NumberIdentification NumberItems119S209I304D405E513M612LStep 5.Determinethenecessarysamplesize.Step 6.Fromthechosencolumnontheselectedpage,selectthefirstsixtwo-digitnumbersbetween01and25,inclusive.Ifanumberisencounteredthatissmallerthan01(e.g.,00)orlargerthan25(e.g.,31),ignorethenumberandcontinuedownthecolumn.Ifanacceptablenumberappearsmorethanonce,ignoreeveryrepetitionandcontinuemovingdownthecolumnuntilsixuniquenumbersbetween01and25havebeenselected.Ifthebottomofthepageisreachedbeforesixuniquerandomnumbersareobtained,gotothetopofthepageandmovedownthenexttwo-digitcolumn.Step 7.Finally,analyzetheinformationasabasisforaction.Twoimportantpointstorememberare:1.differentmethodsofmeasurementwillalsoyielddifferentresults.2.differentsamplesofsizesixwillyielddifferentresults,andRandomsamples,however,donthavebias,andthesamplingerrorcanbeheldtoknownlimitsbyincreasingthesamplesize.ConductinganEnumerativeStudyThefollowing13stepspresentaguideforconductinganenumerativestudy.Thestepsarethesamewhetherthestudyisbasedonacompletecountofthepopulationorasample.Step 1.Specifythereason(s)youwanttoconductthestudy(forexample,toestimatetheaveragenumberofsickdaysperemployeeintheXYZCompanyin2002).Ifthisaverageisgreaterthan8.0days,thenanewhealthcareplanwillbeinstituted.Ifitislessthanorequalto8.0days,thecurrentplanwillbemaintained.Step 2.Specifythepopulationtobestudied.Inourexample,thepopulationwouldbeallfull-timeemployeesintheXYZCompanyin2002.Anemployeeisconsideredfull-timein2001ifhehadfull-timestatusdesignationatanytimeduringtheyear.Step 3.Constructtheframe(alistofallfull-timeemployees).Everyonewhowillusethestudysresultsasabasisforactionmustagreethattheframerepresentsthepopulationuponwhichtheywanttotakeaction.Step 4.Performsecondaryresearch(suchastheexaminationofpre-publisheddata)todeterminehowmuchinformationisalreadyavailableabouttheproblemunderinvestigation.Forexample,checktheHumanResourcesDepartmentsrecords.Step 5.Determinethetypeofstudytobeconducted(forexample,mailsurvey,personalinterviews,analysisofunits).Inthisexample,wewouldanalyzeemployeeabsenteecardsfor2002.Step 6.Makeitpossibleforrespondentstogiveclear,understandableinformation,and/orfortheresearchertoelicitclear,understandableinformation.Forexample,themethodforanalyzingabsenteecardsshouldbeclearandstraightforward.Considertheproblemofnon-response.Inthisexample,besurenoabsenteecardsaremissing,andmakesurethedatagatherersknowhowtointerprettheabsenteecards.Step 7.Establishthesamplingplantobeused,determinetheamountofallowableerrorintheresults,andcalculatethecostofthesamplingplan.Atthisstage,Steps1and2mayneedrevisionsduetocostconsiderations.Forexample,wemaydecidetodrawasimplerandomsampleofemployeeabsenteecardsusingrandomnumbers,atacostof$1percard,assuminganallowableerrorofonequarterofadayintheestimate.Step7requiresarandomsample.Theresultofanonrandomsampleinanenumerativestudyisworthnomorethanthereputationofthepersonwhosignsthereport.Step 8.Establishprocedurestodealwiththenon-responsesanddifferencesbetweeninterviews,testers,inspectors,andsoon.Forexample,beabletoassessdifferencesincollecteddataduetodifferencesinthedatagatherersabilities.Step 9.Prepareunambiguousinstructionsforthedatagatherersthatcoverallphasesofdatacollection.Step 10.Establishplansfordatahandling,includingformatoftables,headings,andnumberofclasses.Step 11.Pretestthedata-gatheringinstrumentanddata-gatheringinstructions.Step 12.Conductthestudyandthetabulations.Itiscriticalthatthestudybecarriedoutaccordingtoplans.Fromthegathereddata,calculatethesamplingerrorsofinterest.Thisisimportantsothatthestudysuserscanunderstandthedegreeofuncertaintypresentinthestudyresults.Inourexample,wewouldcalculatethestandarderrorfortheaveragenumberofdaysabsentperemployee.Step 13.Interpretandpublishtheresultssothatdecisionmakerscantakeappropriateaction.Forexample,iftheaveragenumberofdaysabsentperemployeeisgreaterthaneight,thenestablishthenewhealthcareprogram.AnalyticStudiesBasicConceptsAnalyticstudiesarestatisticalinvestigationsthatleadtoactionsthatwillimproveorinnovateaprocessovertime.Theconceptofapopulationdoesnotexistforananalyticstudybecausefutureprocessoutput,whichdoesnotyetexist,cannotbepartofthepopulation.Aframecannotexistwithoutapopulation.Lackofapopulationandframemakesitimpossibletodrawarandomsampletostudyaprocesssbehavior.Modelscanbeusedtostudythesecause-and-effectsystems.Thesemodelsincludeflowchartsofaprocess,simulationsoftheprocess,andcause-and-effectdiagrams.Inananalyticstudy(unlikeanenumerativestudy),thereisnounderlyingstatisticaltheorythatenablesquantificationofuncertainty.Expertopinionisinvaluableinunderstandingthemagnitudeoftheuncertaintycausedbychangestoaprocess.Generally,thisuncertaintyisbestexplainedbyanexpertwhoisinvolvedwiththeprocessunderstudy.ImprovementorinnovationofaprocessisaccomplishedusingthePlan-Do-Study-Act(PDSA)cycle.ThePDSAcycleisusedtonarrowthedifferencebetweenprocessperformanceandcustomer(eitherinternalorexternal)needsandwants.TheaimofthePLANstageistodetermineanimprovementorinnovationtoaprocessthatwillnarrowthedifferencebetweenprocessperformanceandcustomerneedsandwants.(i.e.oldflowcharttonewflowchart)TheDOstageofthePDSAcyclerequiresthatplannedexperimentsbeconductedtodeterminehowbesttoimplementthePLANestablishedinthepreviousstage.Experimentsshouldbeconductedonasmallscale,usingalaboratory,anofficeorplantsite,or,withhisconsent,evenacustomerslocation.TheaimoftheSTUDYstageistodetermineifthePLANhasbeeneffectiveindecreasingthedifferencebetweenprocessperformanceandcustomerneedsandwants.IntheACTstage,thePLANshouldbeintegratedintotheprocess.ErrorsinAnalyticStudiesAtype one error occurswhenactionistakenonaprocesswhenitshouldhavebeenleftalone.Atype two erroroccurswhenwefailtotakeactiononaprocesswhenactionisappropriate.DesignofAnalyticStudiesWecanincreaseourdegreeofbeliefinapredictionfromananalyticstudybyconsidering:BuildingofknowledgeinasequentialfashionTestingoverawiderangeofconditionsSelectionofunitsforthestudyBuilding of Knowledge in a Sequential FashionExperimentsperformedintheiterationsofthePDSAcycle,incombinationwiththeoryabouttheprocessfromsubjectmatterexperts,mayincreasethedegreeofbeliefinpredictionsaboutthefuturebehavioroftheprocessunderstudy.Thisdegreeofbeliefisincreasedassequentialpredictionsabouttheprocesssfuturebehaviorcomeclosertotheactualperformanceoftheprocess.Testing over a Wide Range of ConditionsThedegreeofbeliefinthepredictivevalueoftheknowledgegainedfromananalyticstudyisincreasediftheanalyticstudyyieldsthesameresultsoverawiderangeofconditions.Onlyanexpertinthesubjectmatterunderstudycananswerquestionssuchashowwidearangeofconditionsisadequatetohaveadegreeofbeliefsufficienttomakeaprediction,orhowclosetoactualconditionsmusttheexperimentalconditionsbetohaveadegreeofbeliefhighenoughtomakepredictions.Selection of the Units for the StudySincethereisnoframeinananalyticstudy,therecanbenorandomsampleandquantifiabledegreeofuncertaintyinapredictionaboutthefuture.Judgmentsamplesareusedtoconductanalyticstudies.AnalysisofDatafromAnalyticStudiesA Stable ProcessAstableprocessprovidesaforumforasubjectmatterexperttoconductexperimentstogainknowledgetopredictthefuturebehavioroftheprocess.Graphical AnalysisThegeneralapproachforconductinganalyticstudiesreliesongraphicaltechniques,suchascontrolcharts,whichutilizebothstatisticalknowledgeandsubjectmatterknowledgetolearnabouttheprocesstopredictitsfuturebehavior.DistinguishingBetweenEnumerativeandAnalyticStudiesIfa100percentsampleoftheframeanswersthequestionunderinvestigation,thestudyisenumerative;ifnot,thestudyisanalytic.
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