REVISING THE PANKO– HALVERSON TAXONOMY OF … · 2019-03-15 · Revising the Panko–Halverson...

REVISINGTHEPANKO–HALVERSONTAXONOMYOFSPREADSHEETERRORSAcceptedforpublicationinDecisionSupportSystems,February2010.

RaymondR.PankoUniversityofHawaiiPanko@hawaii.eduhttp://panko.shidler.hawaii.eduSalvatoreAurigemmaUniversityofHawaiiSA8@hawaii.edu

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ABSTRACT

Errortaxonomiesareusefulbecausedifferenttypesoferrorshavedifferentcommissionanddetectionratesandbecauseerrormitigationtechniquesoftenareonlyusefulforsometypesoferrors.Intheearly1990s,PankoandHalversondevelopedaspreadsheeterrortaxonomy.Thispaperupdatesthattaxonomytoreflecthumanerrorresearchmorefully.Thetaxonomyfocusesonquantitativeerrorsduringdevelopmentandtestingbutnotesthatqualitativeerrorsareveryimportantandthaterrorsoccurinallstagesofthesystemdevelopmentlifecycle.

KEYWORDS

Spreadsheet,spreadsheeterror,enduserdevelopment,endusercomputing,executionerror,taxonomy,error,violation,contexterror,omission,logicerror,planningerror,mistake,slip,lapse.

1. INTRODUCTION

Spreadsheetsarewidelyusedincorporations,andthereisstrongconvergentdatashowingthatmostcorporatespreadsheetshavematerialerrors[15].Consequently,agreatdealofallspreadsheetresearchhasfocusedonthestudyoferrors.Whileone“solution”maybetostopusingspreadsheets,humanerrorresearchsuggeststhaterrorratesprobablyaresimilarforotherdecisionsupportsystemdevelopmenttechnologies[14].

Nearlyallspreadsheeterrorresearchershaveusedtaxonomiestocategorizeerrors.Theyhavedonethisbecausetherearemultipleerrormechanismswithdifferentcommissionrates,differentdetectionrates,anddifferentlysusceptibilitiestoerroravoidanceanddetectionmethods.Errormitigationstrategiesneedtobedevelopedandassessedwithrespecttospecifictypesoferrors.

ThepurposeofthispaperistorevisitandrevisethewidelycitedPankoandHalverson[18]taxonomyofspreadsheeterrors.Thereareseveralreasonsfordoingso.First,thetaxonomywasbasedonaspectsofgeneralhumanerrorresearchknowntoPankoandHalversonin1993.Second,subsequenttaxonomieshaveidentifiedimportanterrortypesthatwerenotincludedinthePankoandHalversontaxonomy.Third,theomissioncategoryinthetaxonomyhasproventobetoonarrow,andthemechanical-logical-omissiontrichotomyingeneralneedstobereplacedbythemorewidelyusedmistake-slip-lapsetrichotomy.

ThispapercoverssomeofthesametopicsaddressedbyPowel,Baker,andLawson[23],whoincludeddiscussionsoferrorclassification,impact,frequency,creationandprevention,anddetection.Mostobviously,ourpaperdiffersbyfocusingprimarilyonthefirsttopic,errorclassification.Wewillnoteotherdifferenceslaterinthispaper.

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2. TAXONOMIES

2.1TAXONOMIES

Taxonomieshavelongbeenusedinscience.SendersandMoray[31],writingabouthumanerror,saidthat:

…ataxonomyisafundamentalrequirementforthefoundationofempiricalscience.Ifwewantadeepunderstandingofthenature,origins,andcausesofhumanerror,itisnecessarytohaveanunambiguousclassificationschemefordescribingthephenomenonwearestudying.[p.82.]

Thereisno“best”errortaxonomyforspreadsheets[9,25]oranyothertypeofhumancognitiveactivity.Researchersandprofessionalswithdifferentfocusesneeddifferentthingsfromerrortaxonomies.Forinstance,spreadsheetdesignersneederrortaxonomiesthatdistinguishbetweentypesoferrorsthatneeddifferentameliorationstrategies.Thelegalsystem,incontrast,needsdistinctionsthathelpassignresponsibilityfordamages[31].Inaddition,eachtaxonomyilluminatessomeaspectsofaphenomenonwhileblindingtheresearcherorpractitionertootheraspectsofthephenomenon[1].

2.2PHENOMENOLOGICALVERSUSDEEP(THEORY-BASED)TAXONOMIES

SendersandMoray[31]distinguishedbetweendifferentlevelsoftaxonomies.Themostsuperficiallevelconsistsofphenomenologicaltaxonomiesthatarebasedonsimpledescriptionsoferrormanifestations.Forinstance,typingerrorsatthislevelwouldbedescribedbysuchthingsaskeystroketranspositions.Atthelevelofphenomenologicalerrors,thereisnoexplanationforwhydifferenterrorsoccur.

Phenomenologicaltaxonomiesareusefulfordestroyingmythsaboutwhattypesoferroroccurfrequently.Ifacertaintypeoferrorprovestobeparticularlyfrequent,itmeritsparticularattention.Conversely,ifatypeoferroroncebelievedtobeimportantactuallyisfairlyrare,thenshiftingresourcesfromthistypeoferrorstoothertypesoferrorsmaybeimportant.Researchusingphenomenologicaltaxonomies,then,canpuncturefalsebeliefbubbles.

Inaddition,inspreadsheetexperimentsonthedetectionoferrors,experimenterstypicallyseedspreadsheetswitherrorsthattheresearchersbelievetobecommonerrors[7,8,11,16].Ideally,theselectionofseedederrorsshouldreflectthetruerelativefrequenciesofdifferentkindsoferrors.Otherwise,theresultsoftheseexperimentsmeasuredasthepercentageoferrorsdetectedwillbemisleading.

Incontrasttophenomenologicaltaxonomies,deepertaxonomiesareinformedbytheory.Thisisespeciallyvaluableiftheorypredictsmanifestationsofresults.Inerrorresearch,forinstance,theorymaysuggestthatdifferenttypesoferrorswillhavedifferenterroroccurrencerates,differentdetectionrates,ordifferentmechanismsformitigation.Unfortunately,thereisnocompletetheoryforhumanerror,socreatingfulldeeptaxonomiesforspreadsheeterrorsisnotpossibletoday.

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2.3ERRORATTRIBUTION

Nearlyallspreadsheeterrorresearchisbasedontheanalysisofspreadsheetsthathavealreadybeendeveloped.Thissuggeststhatweshouldonlyhavephenomenologicaltaxonomies.However,mostpublishedtaxonomiesofspreadsheeterrorstilltrytoexplainobservederrorsintermsofunderlyingtheories.Whilethismaybemethodologicallyundesirable,itisalsoundesirabletousetaxonomiesthatdescribeerrorsbutgivenocluesastowhydifferenttypesoferrorsoccurorhowtheycanberedressed.

Indefenseofattributingerrorcauses,itmaybeplausibletoinferthecauseofmanyerrorsinoperationalspreadsheets.Forinstance,ifasubjectswitchesYear1andYear2salesvaluesafterreadingthemoffasheetofpaper,thisseemslikelytobeduetoalapseinsidethesubject’smemory.

Aswemovefromtightlycontrolledexperimentstotheinspectionofoperationalspreadsheets,wearelikelytoneedmorepurelyphenomenologicaltaxonomies.However,eventhisisonlyaconjecture.Forinstance,ifanoperationalspreadsheetcomputesrevenuesonRow47andinthenextrowmultipliesrevenuesbythecorporatetaxratetocomputecorporatetaxes,itisfairlyclearthatthespreadsheetdevelopermistakenlybelievedthatcorporatetaxesarecomputedonthebasisofrevenuesinsteadofincome.

3. HUMAN ERROR TAXONOMIES

3.1HUMANERRORRESEARCH

Ourconcernisnottaxonomiesingeneralbuthumanerrortaxonomies.Inthis,wearefortunatebecausehumanerrorhasbeenstudiedinmanyhumancognitivedomainsformorethan100years.Thesedomainshaveincludedmathematics,programming,throwingswitches,aircraftaccidents,automobileaccidents,nuclearincidents,proofreading,andlinguistics,tonamejustafew.Inthe1980s,researchersfromdifferenthumancognitiondomainsbegantorealizethattheywereseeingthesametypesoferrorsanderrorfrequenciesindifferentcognitivedomains.Reason[29]summarizedmanyoftheseconvergentfindings.Panko[14]summarizesmeasuredhumanerrorratesinstudiesindifferentfields.

Perhapsthemostimportantfindingfromtheconvergederrorliteratureisthathumancognitiveprocessesproducethecorrectresultnearlyallthetimebuthaveasmallinherenterrorratethatstemsfromthesameprocessesthatproducecorrectresults[29].Inotherwords,thewayweactuallythink(asopposedtothewaywebelievethatwethink)istheheartoftheproblem,notsimplesloppiness.

Unfortunately,thefactthatwemakerelativelyfewmistakesaswedocognitiveworkisnotgoodenoughinsomecontexts.Forinstance,softwareprogrammersusuallyare95%to98%accuratewhentheywritecode[14].However,inprogramsthathavelongflowsoflogic,eventhishighlevelofaccuracyisnotenough.Thesameistrueinspreadsheets.

Athirdimportantfindingisthatwhilewearegoodatavoidingerrorsasweworkandcatchingmanyofourerrorsimmediately,wearenotasgoodatdetectingerrorsafterthefact[14].

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Whenweexamineacognitiveartifactsuchasaprogram,wetypicallyfindonly60%to70%oftheerrors,andthisvarieswidelybyerrortype[14].

Inthispaper,weattempttoexploittheworkonerrortaxonomiesinhumanerrorresearch.ThismakesthispaperdifferentfromthecriticalreviewofPowell,Baker,andLawson[23],whichwasnotbasedonthehumanerrorliterature.

3.2WHATISANERROR?

Themostfundamentalissueinanyerrortaxonomyishowtodefine“error.”SendersandMoray[31]definedanerroras:

“anactionthatisnotintendedbytheactor;notdesiredbyasetofrulesoranexternalobserver;orthatledthetaskorsystemoutsideitsacceptedlimits” SendersandMoray[31],p.25.

Thekeypointisthatthereneedstobeacriterionfordeterminingwhethersomethingiscorrectoranerror.Inmanycases,thecriterionwillbeobvious,suchasamistypednumber.Inothercases,especiallyinmattersofgoodpractices,theremaynotbeauniversallyacceptedcriterion.

3.3MISTAKES,SLIPS,ANDLAPSES

Inhisbook,HumanError,Reason[29]presentedataxonomyofhumanerrorsbasedonpriorworkbyReasonandMycielska[30]andNorman[13].Thistaxonomy,showninFigure1,beginswithabasicdistinctionbetweenplanningandexecutionerrors.Iftheplaniswrong,thisisamistake,regardlessofhowgoodtheimplementationis.However,iftheplaniscorrectbuttheexecutioniswrong,thisisasliporlapse.

Figure1:MistakesversusSlipsandLapses

ThedistinctionbetweenslipsandlapseswasproposedbyNorman[13].Aslipisanerrorduringasensory-motoraction,suchastypingthewrongnumber(say$120,000insteadof$210,000)orpointingtothewrongcellwhenenteringaformula.Incontrast,alapseoccurswithintheperson’shead.Alapseisafailureinmemory.Alapseofteniscausedbyoverloadingthelimitedhumanmemorycapacity.

Thistaxonomyhaspossibleimplicationsforautomatedspreadsheeterrordetectionprograms,whichonlyworkonfinalspreadsheetartifacts.Itislikelythaterrorsinvolvingplanningandmemorythatoccur“offthespreadsheet”willleavefewifanyartifactsinthespreadsheetforautomatedanalysistoolstofind.Evenslipsduringexecutionmaynotleaveartifactsforautomatedspreadsheetanalysisprogramstofind.

Forhumanerrorhunters,too,thethreetypesoferrorssuggestthatconstraininginspectiontothespreadsheetitselfislikelytomissmanyerrors.Itismandatorytoinspectrequirements,designs,anddomainalgorithmstounderstandiftheyhavebeenexecutedproperlyinthespreadsheet.

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3.4RASMUSSEN

Rasmussen[28]furtherdividedmistakesintorule-basedmistakes,whichoccurwhendeveloperortesterappliesaheuristicruleincorrectly,andknowledge-basedmistakes,whichoccurwhennoruleappliesandthepersonmustusehisorhergeneralknowledgeofthedeviceorelectricalengineeringingeneral.AlthoughtheRasmussen[28]taxonomyisimportant,applyingitrunsintotwoseriousissues.First,developersandtestersmustbehighlyexperienced,ortheywillnothavewell-developedheuristicrulesoradequateknowledge.Moreseriously,thistaxonomycannotbeusedwithoutdoingaprotocolanalysis.Wewillnotincludethisdistinctioninourtaxonomybecausemostresearchdoesnotuseprotocolanalysis.

3.5ALLWOOD

AstudybyAllwood[2]examinedthecommissionratesanddetectionratesfordifferenttypesoferrors.Allwood[2]conductedaprotocolanalysisstudyusingstudentssolvingmathematicalproblems.Allwood’sstudentsmade327errorsastheyworked.Sixoutofeverytenerrorswereexecutionerrors,whichinvolvedsomethinglikedoinganadditionincorrectly.However,thesubjectsspontaneouslycaught83%ofexecutionerrorsastheyworked.Consequently,executionerrorsaccountedforonly29%offinalerrors.

Logicerrorsthatinvolvedmathematicalthinking,namelysolutionmethoderrorsandhigher-levelmatherrors,onlyaccountedforaquarterofallerrorsmade,buttheirrelativelylowerrordetectionrates(48%and25%respectively),resultedintheiraccountingfor40%ofallfinalerrors.

Skiperrorsinvolvedsubjectsskippingastepinasolutionprocess.Theseerrorswerecomparativelyrare,accountingforonly9%ofallerrors.However,noneweredetectedspontaneously,sotheyresultedin29%ofallfinalerrors.

PankoandHalverson[18]basedtheirtaxonomyofspreadsheetdevelopmenterrorsheavilyonAllwood’staxonomyandresearchfindings.

3.6FLOWERANDHAYES

AnotherintriguingerrorinsightcomesfromFlowerandHayes[6],whousedprotocolanalysistostudythewritingprocess.Theyfoundthattheirsubjectsneededtoworkatseverallevelsofabstractionsimultaneously.Subjectshadtoselectspecificwordswhilegeneratingsentences;andsentenceproductionhadtofitintotheauthor’splanfortheparagraph,forlargerunitsofthedocument,forthedocumentasawhole,andforthedocument’spurpose(requirements).Planninghadtobedoneatalllevelsofabstractionsimultaneously.Eachlevelofabstraction,furthermore,createdconstraintsthathadtobeobeyedwhenconsideringotherlevels.

Figure2showsthatweportraytheFlowerandHayestaxonomyofconcernsasacontextpyramidthatisinverted,placingalloftheweightofallcontextlevelsonthewritingofeachword.Thiscancreateanenormousloadonthewriter’smemoryandplanningresources.Indeed,interruptionstudieshaveshownthatwritingisoneofthemostcognitively-intensivehumanactivitydomains[6].

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Figure2:ContextPyramidinWriting

Inspreadsheetdevelopment,thesameheavymentalloadislikelytooccur.Wheneveradeveloperentersaformula,heorshehastobecognizantofthealgorithmfortheformula,thealgorithmforalargersectionofthespreadsheet,thespreadsheetdesignasawhole,andthespreadsheet’sexternalrequirements.Anerrormayoccurbecauseofaflawatanyoftheselevels.

3.7VIOLATIONS

Earlier,wenotedthatevenwhenweareattemptingtoworkdiligently,errorsareinevitablebecauseoftheverywaysinwhichhumancognitionworks[29].Insoftware,testing,Beizer[4]hasarguedthatprogrammersmustbeheldblamelessforerrorsfoundintestingbecauseoftheinevitabilityoferrorsevenwhenpeoplearediligent.

However,theargumentthaterrorsareinnocentdoesnotapplyifthepersonisintentionallycircumventingpoliciesandrules.Thisideawasfirstarticulatedinhumanresearchonautomobileaccidents,inwhichspeeding,drinking,andotherviolationsofthelawareviewedasnon-inevitableandblameful[29].Consequently,itmakessensetomakeadistinctionbetweeninnocenterrorsdotohumancognitiveprocessesanderrorsduetoviolations.

Indriving,therearespecificlawsthatprescribemosttypesofdangerousdrivingbehavior.Consequently,identifyingcertaindrivingactionsasviolationsoftenisstraightforward.However,eveniftalkingonahands-freemobilephoneislegal,itsignificantlyreducesaperson’sdrivingability,andaccidentswehavewhentalkingonhands-freemobilephone,whilenotillegal,maystillbenegligence.Theusefulnessofadistinctionbetweeninnocenterrorsandviolationsseemstobemostusefulwherethereisstrongagreementonwhatisacceptableandunacceptable.

4. SPREADSHEET ERROR TAXONOMIES

Sofar,wehavelookedatgeneralhumanerrortaxonomies.Wewillnowlookspecificallyatspreadsheeterrortaxonomies.

4.1HUMANERRORTAXONOMIESANDEXPERIMENTS

Manyspreadsheettaxonomieshavebeenbasedondatafromexperiments.Powell,Baker,andLawson[23],citingReason[20],notethatexperimentsaredangerousbecausetheyoftenarecontrived.Certainly,thisistrueissomeexperiments.However,spreadsheetexperimentsusuallyrequireadevelopertocreateaspreadsheetfromawordproblemortoattempttodetecterrorsinaspreadsheet.Theseactivitiesdonotseemtobeoverlycontrived.

Moreimportantly,experimentsareusefulinisolatingspecificaspectsofhumancognitionanderrormaking.Ingeneral,spreadsheetshavefocusedondeterminingwhetherresearchresultsfromsoftwaredevelopmentwillcarryovertospreadsheetdevelopment.Ingeneral,theydo[16,18].

Inaddition,experimentsareusefulnotonlyinmeasuringrawerrorratesbutinnotinghowcommissionanddetectionratesdifferfordifferenttypesoferrors.Forinstance,Panko[16]foundthatomissionerrorsaredetectedmuchlessfrequentlythanothertypesoferrors—afindingseeninresearchinotherhumancognitivedomains[29].

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Evenforinspectionsforoperationalspreadsheets,resultsfromhumanerrorresearchareofpracticalimportance.Ifdetectionratesreallyaredifferentfordifferenttypesoferrors,thentheprofileofdetectederrorswillnotmatchtheprofileofrealerrorsinspreadsheets.Also,ifresearchshowsthatthedetectionoferrorsinlongerformulasislessthanitisinshorterformulas[16],thismeansthaterrordetectionprotocolsshouldspecifyminimumtimestobespentonmorecomplexformulas.Insoftwarecodeinspection,furthermore,ithasbeenfoundthatdetectionyieldisstronglytiedtothemaximumnumberitemstobecoveredinaninspection,andtheminimumtimetobetakenininspection[5,14].

4.2GALLETTA

Gallettaetal.[8]conductedanexperimentusingMBAstudentsandaccountantsworkingontheirCPAaccreditation.Inthisstudy,subjectsinspectedspreadsheetslookingforerrors.Galletta,etal.[8]dividederrorsintotwotypes.Domainerrorsoccurredwhenaformularequiredknowledgeofaccounting.Deviceerrorsinvolvedusingthecomputerandthespreadsheetprogram—typingerrorsandpointingerrors.Thestudyfoundthatdeviceerrorshadahigherdetectionratethandomainerrors.

4.3PANKOANDHALVERSON

Fortheir1993experimentonerrorsinspreadsheetdevelopmentandinspection,PankoandHalverson[18]createdataxonomyofspreadsheetresearchissuesasathreedimensionalcube.Figure3showsthatthethreesidesofthiscubewereresearchissue,lifecyclestage,andmethodology(experiment,survey,etc.)foraddressingtheresearchissues.

Figure3:PankoandHalversonSpreadsheetRisksResearchCube

Researchissuesincludedstructuralconcerns(poorstructure),actualerrors,userworkpractices,assumptions,andspreadsheetmodel’scharacteristics(size,percentageofcellsthatareformulasordata,complexityofformulas,one-timeuseversusmany-timeuse,thenumberofpeoplewhousethespreadsheet,risks,andcontrolpolicies.Inotherwords,thetaxonomywentwellbeyondquantitativeandqualitativeerrorcategoriesandwellbeyonderrorstudiesingeneral.

Under“actualerrors,”whichmeantquantitativeerrors,thetaxonomynotedseveralwaystocounterrorsandnotedthateachhasadvantagesanddisadvantages.Theerror-countingmetricslistedwerethepercentageofmodelscontainingerrors,thenumberoferrorspermodel,thedistributionoferrorsbymagnitudeorseverity,andthecellerrorrate.

Forerrormagnitudeandseverity,PankoandHalverson[18]notedthat,“Someerrorsareimportant,otherunimportant.Onemeasureisthesizeoftheerrorasapercentageofthecorrectbottom-linevalue.Anotheriswhetheradecisionwouldhavebeendifferenthadtheerrornotbeenmade.Wesuspectthatquiteafewerrorsareeithertoosmalltobeimportantorstillgiveanswersthatleadtothecorrectdecisions.”

Powell,Baker,andLawson[25]discussederrormagnitudeinsomedetailanddidsoevenmoreinanearlier[22]paper.Theyfocusedonthedollarmagnitudesandpercentagemagnitudesof

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errors.Otherstudieshavelookedattheseriousnessoftheerrorsinthecontextinwhichthespreadsheetwasused[15].

Intermsofthecellerrorrate,whichisthepercentageofcellsthatcontainanerror,PankoandHalverson[18]weretakingacuefromsoftwaredevelopmentresearch,whichhaslongmeasuredthefaultsperthousandlinesofnoncommentsourcecode(faults/KLOC).Therateoffaults/KLOCisroughlythesameacrossprograms.Thisallowssoftwaredeveloperstogetaroughestimateofthenumberoferrorstheycanexpecttofindwheninspectingamoduleofcodewithknownlength.Inmanufacturing,reliabilityengineersalsomeasureaverageerrorratesfordifferenttypesofactivities,inordertodesignandmanageprocesses.

Consequently,PankoandHalverson[18]suggestmeasuringerrorfrequencyintermsofthecellerrorrate(CER)—thepercentageofcellscontainingerrors.ForthecomputationofCERs,PankoandHalverson[18]arguedthatspreadsheetresearchshoulddividethetotalnumberoferrorsinvalue(formulaandconstant)cellsbythetotalnumberofvaluecells.WewillseethatthisCERmeasurehasproventobeinadequate.

Likefaults/KLOC,theCERisaroughwaytoanticipatethenumberoferrorsinaspreadsheet,justasfaults/KLOCisinsoftware.Noteveryspreadsheetwillhavethesamecellerrorrate,muchlesseverymoduleinaspreadsheet.Inaddition,forbothfaults/KLOCandCERcalculations,omissionsandsomeothererrorsdonotoccurinaparticularcellandthereforedonotaffectthenumberofcells,except,inthecaseofomissions,toreducethem.Likeothertypesofbaseerrorrates[14],thecellerrorrateisausefulindicatorofanticipatederrorrates,notaprecisiontoolforestimatinghumanerrorrates.However,itisapowerfulwaytoshowthatspreadsheetcellerrorratesarefartoohighforsafety,giventhelongchainsofformulasleadingtoresultsinspreadsheets.

PankoandHalverson[19,20]alsoarguedthaterrorsshouldbecountedonlyonce,inthecellsinwhichtheyoccur.Forexample,ifthiserrorisrepeatedincopiedcells,itshouldonlybecountedasasingleerror.(Theoriginalformulathatiscopiediscalledtherootformula.)Also,onlycellsinwhichtheerrorwasactuallymadeshouldbecounted,notdependentcellsthatareincorrectonlybecauseoferrorsinprecursorcells.Mostsubsequentstudieshaveusedthis“originalsin”approach.Ofcourse,incomputingcellerrorrates,thesamenumeratoranddenominatormustbeused.Forexample,ifonlytherootformulainarowofcopiedcellsisusedasthenumeratorforacopyingerror,thesamemustbetrueinthedenominator.

Figure4showsthePankoandHalverson[18]taxonomyofdevelopmentandtestingerrortypes.Thetaxonomyfirstdivideserrorsintoqualitativeandquantitativeerrors.Thisdemarcationofthetwotypesoferrorswasverysimple.Ifsomethingmakesacomputed(“bottom-line”)valueincorrect,thenitisaquantitativeerror.Ifitdidnot,itisaqualitativeerror.

Figure4:PankoandHalverson1996TaxonomyofDevelopmentandTestingErrorTypes

Themostcommonqualitativeerrorisputtingaconstantinsteadofacellreferenceintoaformula[Panko,1988].Forinstance,ifthetaxequalstheincomebeforetaxtimesthetaxrateof15%,theformulafortaxshouldnotgivethecellreferencetoincomebeforetaxandthenmultiplythisby15%.Ifthetaxratechanges,findingallinstancesofwherechangesshouldbemadeisdifficult.Consequently,someinstancesofthetaxratewouldbechanged,butothersmightnotbe

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changedbecausetheyarenotfound.Thispracticeofinsertinganumberinanequationisoftencalledhardcoding.

Panko[1988]suggestedthathardcoding,whilenotcreatingimmediateerrors,wouldresultinlatererrors.TeoandTan[32]testedthisconjecture.Theyfoundthatstudentswhodidhardcodingdid,infact,makemoreerrorsduringsubsequentwhat-ifanalyses.Reason[29]callserrorsthatdonotproduceanimmediatenumericalerrorbutthatarelikelytoproducesubsequentnumericalerrorslaterlatenterrors.Forexample,supposethedeveloperdoesnotturnoncellprotection(aqualitativeerror).Later,ausermaymistakenlytypeanumberinaformulacell.Now,thespreadsheet’scomputationsareincorrect(aquantitativeerror).

Thedistinctionbetweenquantitativeandqualitativeerrorsisnotthesameasthedistinctionbetweenseriousandnonseriouserrors.Manyquantitativeerrorsaresmall,whilequalitativeerrorscanleadtoextremelyseriouserrorslater.Inaddition,manyqualitativeerrorssuchaspoordesignreduceproductivityandcauseotherproblemseveniftheydonotresultinnumericalerrors.Ignoringqualitativeerrorsisnotanoptionforcorporations.Havingsaidthis,researchershavetendedtofocusonquantitativeerrorsbecausemuchspreadsheeterrorresearchhasbeendoneatleastinparttodocumentthatthereisaspreadsheetaccuracyproblem,andquantitativeerrorsaremoreconvincingthanqualitativeerrors.

FollowingAllwood[2]broadly,PankoandHalverson[18]dividedquantitativeerrorsintothreebasictypes:mechanical,logic,andomissionerrors.

Ø Mechanicalerrorsaretypingerrors,pointingerrors,andothersimpleslipsandlapses.Mechanicalerrorscanbefrequent,buttheyhaveahighchanceofbeingcaughtbythepersonmakingtheerror.

Ø Logicerrorsareincorrectformulasduetochoosingthewrongalgorithmorcreatingthewrongformulatoimplementthealgorithm.

Ø Omissionsarerequirementsleftoutofthemodel.Theyoftenresultfromamisinterpretationofthesituation.Humanfactorsresearchhasshownthatomissionerrorsareespeciallydangerousbecausetheyhavelowdetectionerrorrates[14,29].

PankoandHalverson’sfirststudyusingthetaxonomywasadevelopmentexperimentinwhichsubjectscreatedaspreadsheetworkingalone,ingroupsoftwo,oringroupsoffour[19].Theauthorsconductedaninter-raterreliabilitytestonthetaxonomy’stripartitedistinctionbetweenquantitativemechanical,logical,andomissionerrors.Thesubjectsmadethesame209quantitativeerrorsaccordingtobothresearchers,fora100%reliabilityrateinoverallerrorcounting.Withinthesequantitativeerrors,theresearchersinitiallydisagreedontheclassificationofasingleerrorthatoccurredinthreespreadsheets.Thisrepresented99.6%reliability.Thepointofdisagreementwasasingleerrormadebythreedifferentsubjectswhoaddedexpensestorevenuestogetincome,insteadofsubtractingexpensesfromrevenues.Oneresearcherclassifiedthisasalogicerror(believingthattheyshouldbeadded),theotherasamechanicalerror(typinga+insteadofa-).

Panko[16]laterconductedaninspectionstudy,usingamodificationoftheGallettaetal.[8]inspectiontaskandavariantoftheFagan[5]codeinspectionmethodology.Thistime,Pankotestedthedistinctionbetweenomissionerrorsandothertypesoferrors(mechanicalandlogical).

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Consistentwithotherresearchonhumanerror,omissionerrorsweredetectedmuchlessfrequentlythanothertypesoferrors.Thestudyalsofoundthaterrorsinlongformulasweredetectedlessfrequentlythanerrorsinshorterformulas.

ThethirddimensioninthePanko–Halversonspreadsheetresearchissuescubewaslifecyclestage.Basedonthepriorspreadsheetliterature,PankoandHalverson[18]dividedthespreadsheetlifecycle(notjustthespreadsheetdevelopmentlifecycle)into5stages:requirementsanddesign,cellentry,thedraftstage(aftercarefuldevelopmentbutbeforetesting),debugging(testing),andoperation(useafterdevelopment)PankoandHalverson[18]suggestedthattheerrorratevariesstronglyacrossthislifecycle,asFigure5indicates.Throughthedraftstage,errorstypicallyincreasewithtime.Duringtestingandoperationaluseofthespreadsheetshasbegun,errorstendtodecrease(althougherrorssometimesincreaseduringoperationaluse,especiallyofcellprotectionisnotturnedon).

Figure5:ErrorDensitybyLifeCycleStage

AlthoughthePankoandHalverson[18]taxonomyhasbeenfairlywellvalidatedbyexperiments,somelimitationshavebecomeobviousovertime.First,althoughthetaxonomyhasbothanerrortypedimensionandaspreadsheetlifecycleperspective,PankoandHalversondidnotfleshoutthelifecycledimension.Theydidnotlookatthetypesoferrorsthatoccurduringinitialanalysisandrequirements.Moreconcretely,becausetheydidnotstudyongoingusetheywerenotawareuntillaterofoverwritingerrors,inwhichauseroverwritesaformulainanoperationalspreadsheetwithanumber.

Second,theyfocusedonomissionerrorsbecausethesewerethesubjectofearlierhumanerrorresearch.However,anomissionofarequirementisonlyonetypeofrequirementnoncompliance[12].

Third,thetaxonomydidnotrecognizetheimportantdistinctionbetweensensory-motorslipsandmemorylapses.Thisisimportantbecauseitislikelythatautomatederrordetectiontoolsseemmorelikelytocatchslipsthanlapsesthatoccurinsideaperson’shead.

4.4RAJALINGHAM

Rajalinghamledthecreationofontaxonomyin2000[26]andexpandedonthistaxonomyin2005[27].Theinitialtaxonomy[26],likethePankoandHalverson[18]taxonomy,makesthedistinctionbetweenqualitativeandquantitativeerrors.Itthenmakesadistinctionbetweenaccidentalandreasoningquantitativeerrors.ThisissimilartothePankoandHalverson[18]mechanicalversuslogicaldistinction,butitsterminology(accidentalversusreasoning)isbetterconnotatively.

Anotherimportantadditioninthistaxonomyisthedistinctionbetweendeveloperandend-useraccidentalerrors.PankoandHalverson[18]onlyfocusedondevelopererrors.Theydidnotconsiderthetypesoferrorsthatenduserswouldmakeafterdevelopment.Mostobviously,theyfailedtoconsiderdataentryerrors,whichcanbeveryimportant.Theseerrorscanincludeinputtingincorrectdataorevenoverwritingaformulawithanumber.

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Rajalingham,etal.[26]alsoconsiderserrorsthatusersmakeininterpretingtheresultsofspreadsheets,evenifthespreadsheetisnumericallycorrect.Thiswasamajorinsight.

4.5HOWEANDSIMKIN

Foracodeinspectionexperiment,HoweandSimkin[11]createdanewtaxonomyforspreadsheeterrors.

Ø Dataentryerrors.Outofrangevalues,negativevalues,avalueenteredasalabel.

Ø Clericalandnon-materialerrors.Incorrectdatesinlabels,misleadinglabels,andsoforth.(Previousstudieshaveignoredsucherrors.)

Ø Rulesviolations.Cellentrieswhichviolateastatedcompanypolicy.Theseviolationsdonothavetobedeliberate.

Ø FormulaErrors.Inaccuraterangereferences,embeddedconstants(hardcoding),illogicalformulas.

Violationsarepartsofthemodelthatviolaterequirements.Omissionerrorsdothis,butsodomanyothertypesoferrors,suchascomputingovertimepayforasalariedemployeewhoisnoteligibletoreceiveovertimepay.Thisisdifferentfromtheconceptofviolationsindriving,describedearlier,whichinvolvedeliberatemisconduct.

Oneconcernwiththetaxonomyisthatitmixesquantitativeandqualitativeerrors.Misleadinglabelsmightbeclassifiedaseither,whilehardcodingisnormallyseenasaqualitativeerrorbecauseitdoesnotmakeacomputedvalueincorrectimmediately.

4.6POWELL,LAWSON,ANDBAKER

Fortheirseriesofprojectsinvolvingthecreation,testing,anduseofaninspection(auditing)methodologyforoperationalspreadsheets,Powell,Lawson,andBaker[24,25]developedanothertaxonomyoferrors.

Ø Logicerrors:Formulaisusedincorrectly,leadingtoanincorrectresult.

Ø Referenceerrors:Aformulacontainsoneormoreincorrectreferencestoothercells.

Ø Hard-Coding:Oneormorenumbersappearinformulas,andthepracticeissufficientlydangerous.

Ø Copy/Paste:Aformulaiswrongdotoanincorrectcutandpaste.

Ø DataInput:Anincorrectdatainputisused.

Ø Omission:Aformulaiswrongbecauseoneofitsinputcellsisblank.

Whilelaboratoryexperimentsmayhaveenoughcontexttousetheory-informedtaxonomies,Powell,Lawson,andBaker[24,25]decidedthattheyusedaphenomenologicaltaxonomybasedontheformsoftheerrorstheyencountered.Asnotedearlier,movingtomore

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purelyphenomenologicaltaxonomiesmaybedesirableaswemovefromlaboratoryexperimentstooperationalspreadsheets.

Thistaxonomy’suseofomissionerrorsisverydifferentfromtheuseofomissionerrorsinthePankoandHalverson[18]taxonomy.InthePankoandHalversonusage,somethingintherequirementsisleftoutofthespreadsheet.Thisisnotlikelytobedetectablebylookingatthespreadsheet.Incontrast,inthePowell,Lawson,andBaker[24,25]taxonomy,anomissionerrormeanspointingtoablankcell.ThistypeofomissionerrorprovedtoberareinthePowell,Lawson,andBakerstudy[25].Inthistaxonomy,thereisnothingliketheomissionerrorspositedbyPankoandHalverson[18].

HardcodingisdescribedasaqualitativeerrorinthePankoandHalverson[18]andtheRajalingham[2005]taxonomy.HoweandSimkin[11]alwaysclassifyitasaformulaerror,whichcaneitherbequantitativeorqualitative.InthePowell,Lawson,andBaker[22]taxonomy,hardcodingisusuallynotcountedasanerrorbutis,“unlessitissufficientlydangerous.”Thetaxonomy,then,doesnotfollowtheusualquantitative-versus-qualitativedistinction.Instead,itcountssomequalitativeerrorsiftheyareseriousbutcountsallquantitativeerrors,eveniftheyarenotserious.

5. A REVISED PANKO AND HALVERSON TAXONOMY

Basedonthepreviousdiscussion,wenowpresentourrevisedtaxonomyofspreadsheeterrors.

5.1MEASURINGERRORS

Asdiscussedearlier,itisimportanttohavecommonagreementabouthowtocountthenumberoferrors.Alsoasdiscussedearlier,countingthenumberoferrorsisnottrivial.Moststudiesusethe“originalsin”rule—onlycountinganerrorinthecellinwhichitoccurs.Althoughthisrulegenerallyisrelativelyeasytoapply,somemeasurementgoalsneedtotakedifferentapproaches.Forinstance,ifthegoalistoquantifytheimpactofanerror,thenthefocusfallsexplicitlyonvaluesinsubsequentcells[22].Ifarootcelliscopied,furthermore,thefactthatcopiedformulascreateinaccuraciesinmultiplebottom-linevariablescannotbeignored[22]instudiesofimpacts.

Anotherissueoccurswhencountingerrorsinaworkbookwithmultipleworksheets.Ifthesameerroroccursinmultipleworksheets,thereissomemerittocountingitasasingleerror,butifthegoalistoassesswhatpercentageofallworksheetsthatareincorrect,thenitwouldbebettertocounttheerroronceineachworksheet[25].

Theconceptofcellerrorrates(CERs),asnotedearlier,isderivedfromtheprogrammingconceptoffaultsperthousandlinesof(noncomment)sourcecode(faults/KLOC).Itisimportant,incountingcellerrorrates,tospecificthedenominatorprecisely.Insoftwaredevelopment,commentstatementstypicallyareexcludedfromthedenominator.Inspreadsheets,thiswouldcorrespondtoexcludinglabelcells.

Asnotedearlier,PankoandHalverson[18]usedthenumberofvaluecells—constantsandformulas—asthedenominatorintheirstudies.Somesubsequentstudies,however,usedallnon-emptycells(includingtextcells)intheirdenominator,whileothercellerrorrateshavebeenbased

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onlyonformulacells.DifferencesindenominatorsforcalculatingtheCERcanmakeresearchresultsdifficulttocompareacrossstudies.

Figure6identifiessomepossiblewaysofdefiningcellerrorratesandgivessuggestednamestobeusedinfutureresearch.

Ø CERVisbasedonvaluecells.Thisincludesnumericalandformulacells.

Ø CERFisbasedonformulacells.Ifmosterrorsoccurinformulacells,thenCERFwillbelargerthanCERVforthesamenumberoferrors.

Ø CERNisbasedonnumericalcells.Itisusefulfordiscussingdatainputerrors.

Ø CERAisbasedonallnon-emptycells,includingformulacells,numericalcells,andlabelcells.

Figure6:TypesofCellErrorRates(CERs)

Researchersshouldspecifywhichformofcellerrorratetheyarereporting.Theyshouldalsoreportthenumberofnumerical,formula,andtextcellsseparatelytoallowotherstorebasetheirerrorratesforcomparisonwithresultsfromotherstudies.Forformulas,thenumberofuniqueformulasshouldbereportedaswell,forbothinthenumeratoranddenominator.

5.2VIOLATIONSANDINNOCENTERRORS

Figure7showsourrevisedtaxonomyofspreadsheeterrors.FollowingReason[29],thetaxonomyfirstdividesallerrorsintoviolationsandinnocenterrors.Mosterrorsareinnocenterrors,butsomeproblemsareduetodeliberateviolationsofcorporatestandardsorguidelinesforspreadsheetdevelopment.Worseyet,someincorrectspreadsheetsareincorrectbecauseofmoreseriousviolations,suchasoutrightfraudorpuffery(usingexaggeratedor“cooked”numberstoencouragepeopletomakepoordecisions).Whileemployeesshouldnotbepunishedforinnocenterrors,violationsdeservesanctions.

Figure7:RevisedTaxonomyofSpreadsheetErrors

Whataboutunknowingdeparturesfrompoliciesandspecifiedgoodpractices?Aretheyalsoviolations?Webelievethattheyarenot.Unlessadepartureisintentionalorischaracterizedbyconsiderablenegligence,itisnotaviolation.Thisfollowsthemensrearequirementforcriminalprosecutionsunderthelaw.

5.3QUALITATIVEVERSUSQUANTITATIVEERRORS

Forinnocenterrors,thistaxonomycontinuestousethedistinctionbetweenqualitativeandquantitativeerrors.Quantitativeerrors,quitesimply,areincorrectformulasordatacellsthatmakethemodelincorrect.Qualitativeerrors,inturn,mayleadtoquantitativeproblemslaterbutdonotmakethemodelincorrectimmediately.

IntheoriginalPankoandHalverson[18]taxonomy,quantitativeerrorsproducedimmediateincorrectresults.However,amodelcanbecomeincorrectwithoutimmediatelygivingthewrongnumber.Forinstance,ifauseroverwritesaformulawithanumber,bottom-linecalculationsmaybecorrectforthisusagealthoughthemodelisnolongergenerallycorrect.Togiveanotherexample,if

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anincorrectcellreferencepointstoacellthathappenstohavethesamevalueasacorrectcell,thenthispointingerror,whileclearlyanerror,willnotresultinanincorrectvalue[22].

Evenwithspecialcases,itappearsthatquantitativeerrorscanbecountedfairlyunambiguously.Qualitativeerrors,incontrast,typicallyareviolationsofgoodspreadsheetdevelopmentpractice.However,thereisnotstrongconsensusforwhatconstitutesgoodspreadsheetpractices.

5.4PLANNINGERRORS(MISTAKES)VERSUSEXECUTIONERRORS(SLIPSANDLAPSES)

Thetaxonomydividesquantitativeerrorsintoplanningerrorsversusexecutionerrors.Thisdistinctionfocusesontheinstantwhentheuserbeginstoentertheformula.Anerrorbeforethatinstantisaplanningerror.Anerrormadeafterthatinstantisanexecutionerror.IntermsoftheNormanandReasondistinctionsdescribedearlier,aplanningerrorisamistake,whileanexecutionerrorisasliporalapse.

5.5DOMAINANDSPREADSHEETEXPRESSIONPLANNINGERRORS

Thetaxonomydividesplanningerrorsintodomainplanningerrorsandspreadsheetexpressionplanningerrors.Thisdistinctionarguesthatplanninghastwoaspects.First,planningforaformulaorsectionneedstohaveadomaincomponent.Ifthespreadsheetdealswithaircraftwingdesign,aerodynamicsislikelytobeimportantincreatinganalgorithm.

Inaddition,thedevelopermusthaveaplanforexpressingthedomainplanonaspreadsheet.Spreadsheetexpressionmayincludetheuseoffunctions.Italsomaymeanexpressingdomainconceptsthatdonotnaturallyfittherow/columndesignofspreadsheetsintoaspreadsheetsectionwithmultipleformulas.

Thisdistinctionisimportantbecauseautomatedspreadsheeterrordetectionprogramsseemmorelikelytofindspreadsheetexpressionplanningproblemsthandomainplanningproblems.Domainplanningproblemsmaynotbedetectiblewithoutdomainknowledge.

5.6SLIPANDLAPSEEXECUTIONERRORS

Executionerrorsfitthedistinctionbetweenslipsandlapsesdiscussedearlier.Thisdistinctionmayalsohaveimplicationsforautomatederrordetection.Slipsmayleadtoerrorsinpointingtothewrongcellandothererrorsthatleavedetectablepatternsonaspreadsheet.Lapses,whichoccurwithinthebrain,maybelesslikelytoleavesuchdetectiblepatterns.

5.7LIFECYCLESTAGESANDROLES

Figure7showsdevelopmentandtestingerrors.However,asthePankoandHalversontaxonomy[18]noted,wealsonotethatspreadsheetsgenerallygothroughasystemlifecyclethatbeginswiththeanalysisofthecurrentsituationandneedsandendswhenthespreadsheetisterminatedorreplaced.

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Thefirstpartofthislifecycleisthesystemdevelopmentlifecycle.However,mostofaspreadsheet’slifeisspentinoperationaluse,soweneedtofocusontheentiresystemlifecycle—notonlyonthesystemsdevelopmentlifecycle.

Differenttypesoferrorswilloccuratdifferentstagesofthesystemslifecycle.Forrequirementsanddesign,thesoftwareengineeringliteraturemayprovidegoodguidanceonwhattolookfor—includingthefactthatalargefractionofallerrorsoccurduringrequirementsanddesigninsteadofduringprogrammingandtesting[12].Inaddition,spreadsheetdevelopmentoftenusesaprocessmoreakintoagiledevelopmentthantraditionaldevelopment,sospreadsheetprofessionalsshouldlookforerrorresearchinthecontextofnontraditionaldevelopment.

Arguablythemostimportantstageisoperationaluse.Manyspecificerrors,suchasenteringthewrongnumberforavariableorincorrectlyimportingdata,occurprimarilyduringoperationaluse.Violationsalsomustbeanticipated,suchasviolationsofprivacyortheuseofspreadsheetstocommitfraud.Otheroperationaluseproblemsincludelackofmaintenanceofdocumentation,ofversioncontrol,andtransitionswhenthedeveloperormaintainerchangesjobs.

Anotheraspectoflifecyclethinkingisthatthereareseveralpossibleorganizationrolesinvolved.Duringdevelopment,forinstance,theremaybeseparatedevelopers,testers,managers,andorganizationalclients.Duringoperationaluse,theremaybeseparateowners,operatorswhoenterdataanddootherhands-ontasks,customersoftheinformation,andotherroles.Weneedtothinkaboutviolationsandinnocenterrorsthatmaybemadebyeachpotentialroleduringeachstageofthelifecycletounderstanderrormitigationneeds.

Ofcoursesomeoftheserolesmaybecombined—mostobviouslyifthedeveloperisalsothetester,clientanduserofthespreadsheet.However,evenwhenrolesarecombined,itmaystillmakesensetothinkintermsoflogicalrolestoconsiderpossibleerrors.Inaddition,whilecombiningrolesmaydecreasesomeerrors,suchascommunicationerrors,itmaymakeothersmorelikely,suchasthetendencytobecomefixatedinwaysthatmakeapersonlessabletoseetheerrorsthattheymade.

6. INTER-RATER RELIABILITY ANALYSIS

Taxonomies,likeanyotherresearchmethodology,shouldbejudgedonanumberofcriteria.Everytaxonomyshouldfacetheentirebatteryoftestsrequiredtoassessitsinternalandexternalvalidity,butaparticularconcernisreliability.Reliabilitymeansthatifdifferentpeopleusethetaxonomytoclassifythesameeventsoritems,theywillclassifyindividualitemsinthesameway.Ataxonomythatcannotbeappliedreliablybydifferentpeopleisafailedtaxonomy.Toassessthereliabilityofourtaxonomy,thetwoauthorsconductedaninter-raterreliabilitystudyinwhichtheyindependentlyclassifiederrorsinacorpusofspreadsheets.

Reliabilityneveris100%.Ingeneral,aninter-raterreliabilityof90%orhigheristhegoal,althoughaninter-raterreliabilityof60%to70%maymakeastudypublishableasanexploratorystudy.Infieldstudies,whichdealwithmessiersituations,somewhatlowerinter-raterreliabilityvalueswillbeacceptable.Eventhen,however,methodologydesignersmustusecoarsertaxonomieswhosebroadercategoriescanbeassignedrobustly,sothatinter-raterreliabilitywillstayhigh.

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Thecorpusofspreadsheetswascreatedforapreviousstudy[17].Inthatstudy,studentsdevelopedspreadsheetmodelsfromtheKookerwordproblem.Thistaskhadstudentsdevelopatwo-yearproforma(projected)incomestatement.Thefullcorpushas74spreadsheets.Forthisstudy,weusedthefirst50spreadsheetsinthiscorpusbutthrewoutsixthatcouldnotbeanalyzedwithatrialversionofSpreadsheetProfessional™.Thislimitationwasirrelevanttothisstudy,butwewishedtomaintaincommonalityforotherstudiesusingthecorpus.Ofthese44remainingspreadsheets,40containederrors.Thetotalnumberoferrorswas98.

Asapre-test,thetwoauthorsindependentlyclassifiederrorsinthefirst5spreadsheetsofthecorpus.Whentheycomparedtheresults,theyrealizedthattheywerenotfocusingpreciselyonwhethertheerrorhappenedduringformulaplanningorexecution.Afterclarifyingthattarget,thetwoauthorscategorizederrorsintheremaining39spreadsheets,whichcontainedatotalof86errors.

Errorsinthecorpushadbeenidentifiedpreviously.TheKookertaskhasanunambiguoussolution.Arater(differentfromtheonesinthisstudy)foundspreadsheetswithincorrectanswers,identifiedtheerror,andfixedtheerror.Ifthespreadsheetwasstillincorrect,herepeatedthisprocessuntilthespreadsheetwascorrect.Herecordedtheerrors.

Inthereliabilityprotocol,thefirstthingtodowastoclassifytheerrorasaplanningerror(mistakebeforeenteringtheformula)oranexecutionerrorinenteringtheformula.Thetwoauthorsdidthisbeforetheysub-classifiedplanningandexecutionerrorsintosubtypes.Theythenwentbacktoeacherror.Theyclassifiedeachplanningerrorasadomainplanningerrororasaspreadsheetexpressionplanningerror.Theyclassifiedeachexecutionerrorasalapseorasaslip.

Forthe39spreadsheetsusedinthisphase,theauthorsagreedonthetwo-phaseclassificationof85outofthe88errors,foraninter-raterreliabilityvalueof96.6%.Thisisacceptablereliability.Althoughclassificationmayseemtobedifficultintheabstract,thetwoauthorsnotedthatitfairlyeasytoclassifymosterrorswhentheywereseenincontext.Overall,thetaxonomyappearstobereliablewhenratersusedtheprotocoltoclassifyerrors.However,likeanytaxonomyitisnotperfect.Applyingthistaxonomyandprotocoltoothercorpusesmaydiscloseotherweaknesses.Inparticular,wesuspectthaterrorsinlongcomplexformulaswouldbeverydifficulttoclassify.

7. ERROR FREQUENCY

7.1ERRORFREQUENCY

Amajorbenefitoftaxonomiesistheabilityoftaxonomyuserstoexaminetherelativefrequenciesofdifferenttypesoferrors.Asnotedearlier,differenttypesoferrorsmaycallfordifferentavoidanceanddetectionstrategies.Ifarareerrortypeisextremelyexpensivetoaddress,addressingitmaynotbeworththeeffort.Incontrast,ifanerrortypethoughttoberareprovestobefrequent,moreattentionmaybeneededtoitsstrategiesforitsamelioration.

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7.2SPREADSHEETERRORDETECTIONPROGRAMS

Apotentiallyimportanttoolfordetectingerrorsistheautomatedspreadsheeterrordetectionprogram,whichistypifiedbySpreadsheetProfessionalandExcelErrorCheck.Thesetoolsworkbyhighlightinganomalouspatternsinthespreadsheet,suchasacellwithnoprecedentsorachangeinthecopyingpatternofaformulaasitiscopiedacrosscolumnsorrows.Itisreasonabletoassumethatthesetoolswillworkbestforidentifyingsliperrors.Planningerrorsandlapseswithinthedeveloper’sheadmayleavenopatternforthesoftwaretoidentify.

7.3ERRORSINOURCORPUS

Althoughthepurposeofthereliabilityanalysiswastoassessthereliabilityofthetaxonomyandprotocol,itisinterestingtonotethedistributionoferrorsfoundinthestudy.Figure8summarizesthe85jointlyclassifiederrors.Thefigureshowsthat82%oftheerrorsweremistakes(planningerrors),andallbutoneofthesemistakeswasadomainplanningerror.Only18%oftheerrorswereexecutionerrors,andmoreofthesewerelapsesthanslips.

Figure8:ReliabilityStudy

ThispatternoferrorssuggeststhatSpreadsheetProfessionalandMicrosoftErrorCheckarenotlikelytobeeffectiveonthiscorpusofspreadsheets.Actually,onlysomespreadsheetsinthecorpuswereincludedinthereliabilitystudybecausethesespreadsheetshadpreviouslybeenusedinastudyoftheabilityofSpreadsheetProfessionalandExcelErrorChecktoflagknownerrorsinthespreadsheets[3].Inthatstudy,fivestudentsappliedSpreadsheetProfessionalandExcelErrorChecktothespreadsheetsinthecorpus.Therewere88errorsinthecorpus.Foreachtool,then,therewere440errorstoassessasbeingflaggedornotflagged.OnestudentjudgedthatExcelErrorCheckcorrectlyflaggedasingleerror,forasuccessrateof0.22%.Onestudentjudgedthatspreadsheetprofessionalcorrectlytagged4errors,forasuccessrateofalmostonepercent.

Itmaybethatthiscorpuswasmisleadingbecausethestudentsubjectsmadeaverylargenumberofdomainerrorsduetoignorance.However,anotherdevelopmentstudyonalmostthesametaskfoundthatundergraduatestudentswithoutspreadsheetworkexperienceandMBAstudentswithsubstantialspreadsheetdevelopmentandtestingexperiencemadeverysimilartypesoferrors.Inaddition,inhisthree-personcodeinspectionofanoperationalspreadsheet,Hicks[10]foundthatmosterrorswerelogicerrors.

Anotherconcernisthatthestudentsdidnotdoamapanalysisinwhichtheyvisuallycouldseepatternsinthespreadsheet.However,thefirstauthorofthispaperdidaSpreadsheetProfessionalmapanalysis.Itdidnothelpinfindinganyoftheknownerrorsinthespreadsheet.

7.4ERRORSINTHEPOWELL,BAKER,ANDLAWSONAUDITOF50SPREADSHEETS

Intheirauditingstudyof50operationalspreadsheets,Powell,Baker,andLawson[24]foundaverydifferentpatternoferrors.Inthatstudy,testerscollectedandrecordedinformationaboutthespreadsheet.TheythendidmapanalysiswithSpreadsheetProfessional,ranSpreadsheetProfessionalteststoflagerrors,ranXLanalystagainstthespreadsheet,anddidacodeinspectiononremainingformulas.Ignoringhardcodingerrors,whichweclassifyasaqualitativeerror,63%ofthe

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errorswerereferenceerrors,copy/pasteerrors,andomissionerrors(referencinganemptycell).Thesecorrespondtoslipsinourclassification.Only35%oftheerrorsdiscoveredwerelogicerrors,mostofwhichwouldseemtobewhatwecallplanningerrors(mistakes).Finally,dataerrorsaccountedfor2%oftheerrors.

Inaddition,Powell,Baker,andLawson[24]foundmostoftheirerrorsusingerror-detectionprograms.Mapanalysis,SpreadsheetProfessionaltests,andXLAnalystfound81%oftheerrors.Codeinspectiononlyfound18.2%oftheerrorsdiscoveredinthestudy.

OnepossibleexplanationisthattheoperationalspreadsheetsthatPowell,Baker,andLawson[24]studiedreallydidhaveverydifferenterrorpatternsthanourstudent-generatedspreadsheets.AnotherexplanationisthatPowell,Baker,andLawson[24]’scodeinspectionwasineffectivesothatfewerrorswerefoundbeyondthosefoundbyusingtheautomatedtools.

Onespecificconcernisspeedofinspection.Fagan[5]foundthatrapidcodeinspectionfindsfewererrorsthanslowercodeinspection.Insomestudies,thefall-offindetectioneffectivenessisverylarge[14].ThemedianamountoftimespentinthePowell,Baker,andLawson[24]studyontheentireauditwas195minutes.Themediannumberofformulaswas1,294.Evenifalltheauditingtimewereusedforcodeinspection,thiswouldallowonly9secondperformula.Ofcourse,mostcodeinspection(butcertainlynotall)wouldfocusonrootformulas.Therewasamedianofonly105or193unique(root)formulas,givingmoretimeperformula.Evenso,giventhecomplexityoftheprotocol,codeinspectionprobablytookarelativelysmallpercentageofthetotaltime.

AnotherspecificconcernisthateachofthePowell,Baker,andLawson[24]inspectionsusedonlyasingleinspector.Insoftwaredevelopment,codeinspectionisdoneinteams[5,14].Inspreadsheetcodeinspectionexperiments,subjectsworkingaloneonlycaughtabouthalfofallerrors[15].Whenone-personinspectionisaddedtotheinspectionrateproblem,itseemsplausiblethatthecodeinspectionpartofthestudywasinefficient.Whilesoftwareauditingtoolsmightdowellinfindingsliperrors,inadequatecodeinspectionwouldtendtoundercountlogic(planningerrors).

AthirdspecificconcernisthatinthePowell,Baker,andLawson[24]audit,theinspectorsdidnotknowtherequirementsforthespreadsheettheywereinspecting.Thiswouldmakeitmoredifficulttoidentifymistakes.Intheirlaterstudyof25spreadsheets,Powell,Baker,andLawson[22]didhavetherequirements,butthedetaileddatafromthestudyexaminedinthissectionisnotavailableforthenewerstudy.

Forthesethreereasons,webelievethatthePowell,Baker,andLawson[24]studyprobablyundercountedplanningerrors.

8. PERSPECTIVE

8.1CHANGESINTHETAXONOMY

ThispaperhasrevisedandexpandedthePankoandHalverson[18]taxonomyofspreadsheeterrors.Thepurposeoftheearlytaxonomywastosupportquantitativeresearchstudiestodemonstratethatquantitativespreadsheeterrorsarefrequent,thatquantitativespreadsheeterrorsaredifficult

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todetect,andthatmanyspreadsheeterrorsaresignificant.Figure7showstherevisedtaxonomy.Thistaxonomymakesanumberofnewdistinctions.

Ø First,thereisadistinctionbetweenblameless(innocent)errorsandculpableviolationsoflawsorrequiredcorporatepractices.

Ø Second,thedistinctionbetweenlogic,mechanical,andomissionerrorshasbeenreplacedbythemorecommondistinctionbetweendomainandspreadsheetexpressionplanningerrors(mistakes)ontheonehandandimplementationerrors(slipsandlapses)ontheotherhand[13,29].Planningerrorsareincorrectintentions.Implementationerrorsaretheincorrectimplementationofplans.

Ø Amongplanningerrors,domainplanningerrorsoccurwhenthedevelopermakesamistakeintheknowledgedomainofthemodel(finance,ecology,physics,etc.).Spreadsheetexpressionplanningerrorsoccurwhenthedeveloperplansanincorrectspreadsheetexpressionofthedomainalgorithm.

Ø Logicerrorsbecomemistakes,whilemechanicalerrorsaredividedintoslipsandlapses.Slipsaresensory-motorerrors,suchastypingandpointingerrors.Incontrast,lapsesarememoryerrors[13].

8.2RELATIVEERRORFREQUENCY

Weneedresearchtoassesstherelativefrequencyofvarioustypesoferrors.Inourcorpus,forwhichwehadunambiguousquantitativeerrordata,thatmosterrorswereplanningerrors,andmostoftheseweredomainplanningerrors.Amongtheexecutionerrors,morethanhalfwerelapsesoccurringinthedeveloper’shead.Powell,Baker,andLawson[24]foundverydifferentthingsintheirexaminationof50operationalspreadsheets,althoughwehaveconcernsabouttheabilityoftheirmethodologytodetectplanningerrorsandperhapslapses.

8.3TIMETOCHANGEOURRESEARCHFOCUS

Today,theideathatsignificantquantitativeerrorsarefrequenthasbeenbroadlyaccepted.Inanycase,peoplewhostillrejectthatexperimentalandfieldevidenceregardingthemarenotlikelytohavetheiropinionschangedbyfurtherquantitativeresearch.Itisnowtimetoshiftourfocustowardqualitativeerrors,whichmaybefarmorecommonthanquantitativeerrors,andidentifyingthelargenumberofdifferenttypesoferrorsthatarepossibleindifferentlifecyclestagesandbypeoplewithdifferentrolestoplay.

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FIGURES

Figure1:MistakesversusSlipsandLapses

Stage of Error Type of Error

Error in Planning Mistake Logic or mathematical error, etc.

Error in Execution Slip Sensory-motor error

Lapse Error cause by memory overload

Sources: Norman [13]; Reason [29].

Figure2:ContextPyramidinWriting

Figure3:PankoandHalversonSpreadsheetRisksResearchCube

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Figure4:PankoandHalverson1996TaxonomyofDevelopmentandTestingErrorTypes

Figure5:ErrorDensitybyLifeCycleStage

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Figure6:TypesofCellErrorRates(CERs)

Acronym Denominator Use

CERV Value cells (numbers and formulas)

Cell error rates have traditionally been measured this way

CERF Formula cells Focuses on formula error rates, which usually are much higher than value error rates

CERN Number cells Good for looking at input errors

CERT Text cells Good for looking at documentation

CERA All nonempty cells (label and value cells)

Not very useful, but some studies use it

Figure7:RevisedTaxonomyofSpreadsheetErrors

Figure8:ReliabilityStudy

Number Percent

Total Errors 88

Total Errors Jointly Classified* 85 100%

Planning Errors (Mistakes) 70 82%

Domain 69 81%

Spreadsheet Expression 1 1%

Execution Errors 15 18%

Slip 6 7%

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Lapse 9 11%