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PSYCHOPHYSICS APRACTICALINTRODUCTION SECONDEDITION FREDERICK A.A.KINGDOM McGillUniversity,Montreal,Quebec,Canada
NICOLAAS PRINS UniversityofMississippi,Oxford,MS,USA
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEWYORK • OXFORD • PARIS • SANDIEGO
SANFRANCISCO • SINGAPORE • SYDNEY • TOKYO
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Dedication FKwouldliketodedicatethisbooktohislateparentsTonyandJoan,andpresent familyBeverleyandLeina.NPwouldliketodedicatethisbooktohismotherNelandlate fatherArie.
AbouttheAuthors FrederickA.A.KingdomisaProfessoratMcGillUniversityconductingresearchinto variousaspectsofvisualperception,includingcolorvision,brightnessperception,stereopsis, textureperception,contour-shapecoding,theperceptionoftransparency,andvisualillusions.Healsohasaninterestinmodelsofsummationforthedetectionofmultiplestimuli.
NicolaasPrinsisanAssociateProfessorattheUniversityofMississippispecializingin visualtextureperception,motionperception,contour-shapecoding,andtheuseofstatistical methodsinthecollectionandanalysisofpsychophysicaldata.
PrefacetotheSecondEdition Theimpetusforthisbookwasarecurring question: “Isthereabookthatexplainshow todopsychophysics?” Evidently,abookwas neededthatnotonlyexplainedthetheory behindpsychophysicalproceduresbutalso providedthepracticaltoolsnecessaryfor theirimplementation.Whatseemedtobe missingwasadetailedandaccessibleexpositionofhowrawpsychophysicalresponses areturnedintomeaningfulmeasurementsof sensoryfunction;inotherwords,abookthat dealtwiththenutsandboltsofpsychophysicsdataanalysis.
Theneedforapracticalbookonpsychophysicsinevitablyledtoasecondneed:a comprehensivepackageofsoftwarefor analyzingpsychophysicaldata.Theresult wasPalamedes.Initiallydevelopedin conjunctionwiththe firsteditionofthebook, Palamedeshassincetakenonalifeofits own,andonepurposeofthesecondedition istocatchupwithitslatestdevelopments! Palamedeswillofcoursecontinuetobe developedsoreadersareencouragedtokeep aneyeontheregularupdates.
The firstfewchaptersofthebookare intendedtointroducethebasicconceptsand terminologyofpsychophysicsaswellas familiarizereaderswitharangeofpsychophysicalprocedures.Theremainingchapters focusonspecialisttopics:psychometric functions,adaptiveprocedures,signal detectiontheory,summationmeasures, scalingmethods,andstatisticalmodel
comparisons.Wehavealsoprovidedan updatedquickreferenceguidetotheterms, concepts,andmanyoftheequations describedinthebook.
Inwritingthesecondeditionwehave endeavoredtoimproveeachchapterand haveextendedallthetechnicalchaptersto includenewproceduresandanalyses. Chapter7isthebook ’sonenewchapter.It dealswithanoldbutvexingquestionof howmultiplestimulicombinetoreach threshold.Thechapterattemptstoderive from firstprinciplesandmakeaccessibleto thereaderthemathematicalbasisofthe myriadsofsummationmodels,scenarios, andmetricsthatarescatteredthroughout theliterature.
Writingbotheditionsofthisbookhas beenaconsiderablechallengeforitsauthors. Muchefforthasbeenexpendedintryingto makeaccessiblethetheorybehinddifferent typesofpsychophysicaldataanalysis.For thosepsychophysicaltermsthattousdid notappeartohaveacleardefinitionwehave improvisedourown(e.g.,thedefinitionof “ appearance ” giveninChapter2),andfor othertermswherewefelttherewasalackof claritywehavechallengedexistingconvention(e.g.,byreferringtoaclassofforcedchoicetasksas1AFC).Wherewehave challengedconventionwehaveexplained ourreasoningandhopethatevenifreaders donotagreewithus,theywillstill findour ideasonthematterthought-provoking.
Acknowledgments Weareindebtedtothefollowingpersonsforkindlyreviewingandprovidinginsightful commentsonindividualchapters:NeilMacmillanandDouglasCreelmanforhelpingoneof theauthors(FK)gettogripswiththecalculationof d0 forsame-differenttasks(Chapter6); MarkGeorgesonforprovidingthederivationoftheequationforthecriterionmeasurelnb for a2AFCtask(Chapter6);AlexBaldwinfortheideaofincorporatingastimulusscalingfactor g forconvertingstimulusintensityto d0 whenmodelingpsychometricfunctionswithina SignalDetectionTheoryframework(Chapters6and7);MarkMcCourtforprovidingthe figuresillustratinggrating-induction(Chapter3);LaurenceMaloneyforpermissionto developanddescribetheroutinesforMaximumLikelihoodDifferenceScaling(Chapter8); StanleyKleinforencouragingustoincludeasectionontheChi-squaredtest(Chapter9);and BenJenningsforcarefullycheckingtheequationsinthesummationchapter(Chapter7).
Thanksalsotothemanypersons toomanytomentionindividually whohaveoverthe yearsexpressedtheirappreciationforthebookaswellasthePalamedestoolboxand providedusefulsuggestionsforimprovementstoboth.
IntroductionandAims 1McGillUniversity,Montreal,Quebec,Canada; 2UniversityofMississippi,Oxford,MS,USA
1.1WhatisPsychophysics?1
1.2AimsoftheBook1
1.3OrganizationoftheBook2 1.4What’sNewintheSecond Edition?5 References9
1.1WHATISPSYCHOPHYSICS? Accordingtotheonlineencyclopedia Wikipedia,psychophysics “ quantitativelyinvestigatestherelationshipbetweenphysicalstimuliandthesensationsandperceptionsthey affect.” Thetermwas firstcoinedbyGustavTheodorFechner,whoinhis ElementsofPsychophysics (1860/1966)setouttheprinciplesofpsychophysicalmeasurement,describingthe variousproceduresusedbyexperimentaliststomapouttherelationshipbetweenmatter andmind.Althoughpsychophysicsreferstoamethodology,itisalsoaresearchareainits ownright,andmucheffortcontinuestobedevotedtodevelopingnewpsychophysicaltechniquesandnewmethodsforanalyzingpsychophysicaldata.
Psychophysicscanbeappliedtoanysensorysystem,whethervision,hearing,touch,taste, orsmell.Thisbookprimarilydrawsonthevisualsystemtoillustratetheprinciplesof psychophysics,buttheprinciplesareapplicabletoallsensorydomains.
1.2AIMSOFTHEBOOK Broadlyspeaking,thebookhasthreeaims.The fi rstistoprovidenewcomerstopsychophysicswithanoverviewofdifferentpsychophysicalproceduresinordertohelpthem
Psychophysics http://dx.doi.org/10.1016/B978-0-12-407156-8.00001-3
selecttheappropriatedesignsandanalysesfortheirexperiments.Thesecondaimisto directreaderstothesoftwaretools,intheformofPalamedes,foranalyzingpsychophysical data.Thisisintendedforboth newcomersandexperiencedresearchersalike.Thethirdaim istoexplainthetheorybehindtheanalyses. Againbothnewcomersandexperiencedresearchersshouldbene fi tfromthedetailedexpositionsofthebulkoftheunderlyingtheory. Tothisendwehavemadeeveryefforttomakeaccessiblethetheorybehindawiderangeof psychophysicalprocedures,analyticalprinc iples,andmathematicalcomputations,suchas Bayesiancurve fi tting;thecalculationofd-primes(d ʹ);summationtheory;maximumlikelihooddifferencescaling;goodness-of- fi tmeasurement;bootstrapanalysis;andlikelihoodratiotesting,tonamebutafew.Inshort,thebookisintendedtobebothpracticaland pedagogical.
TheinclusionofthedescriptionofthePalamedestools,placedinthiseditionin separateboxesalongsidethemaintext,will hopefullyofferthereadersomethingmore thanisprovidedbytraditionaltextbooks,suchastheexcellent Psychophysics:TheFundamentals by Gescheider(1997).Ifthereisadownside,however,itisthatwedonotalways delveasdeeplyintotherelationshipbetween psychophysicalmeasurementandsensory functionas TheFundamentals does,exceptwhennecessarytoexplainaparticularpsychophysicalprocedureorsetofprocedures.Inthisregard APracticalIntroduction isnot intendedasareplacementforothertextbooksonpsychophysicsbutasacomplementto them,andreadersareencouragedtoreadotherrelevanttextsalongsideourown.Two noteworthyrecentadditionstotheliteratureonpsychophysicsare Knoblauchand Maloney ’s(2012) ModelingPsychophysicalDatainR and LuandDosher ’s(2013) Visual Psychophysics
Ourapproachofcombiningthepracticalandthepedagogicalintoasinglebookmaynot betoeveryone’staste.Doubtlesssomewouldprefertohavethedescriptionofthesoftware routinesputelsewhere.However,webelievethatbydescribingthesoftwarealongsidethe theory,newcomerswillbeabletogetaquickhandleonthenutsandboltsof psychophysicsmethods,thebettertothendelveintotheunderlyingtheoryifandwhen theychoose.
1.3ORGANIZATIONOFTHEBOOK Thebookcanberoughlydividedintotwoparts.Chapters2and3provideanoverall frameworkanddetailedbreakdownofthevarietyofpsychophysicalproceduresavailable totheresearcher.Chapters4 9arethetechnicalchapters.Theydescribethetheoryand implementationforsixspecialisttopics:psychometricfunctions;adaptivemethods; signaldetectionmeasures;summationmeasures;scalingmethods;andmodelcomparisons (Box1.1).
InChapter2weprovideanoverviewofsomeofthemajorvarietiesofpsychophysical proceduresandofferaframeworkforclassifyingpsychophysicsexperiments.Theapproach takenhereisanunusualone.Psychophysicalproceduresarediscussedinthecontextofacriticalexaminationofthevariousdichotomiescommonlyusedtodifferentiatepsychophysics experiments:ClassAversusClassB;Type1versusType2;performanceversusappearance; forced-choiceversusnonforced-choice;criterion-dependentversuscriterion-free;objective
PALAMEDES AccordingtoWikipedia,theGreekmythological figurePalamedes(“pal-uh-MEE-deez”)is saidtohaveinvented “ . counting,currency,weightsandmeasures,jokes,diceandaforerunnerofchesscalled pessoi,aswellasmilitaryranks.” ThestorygoesthatPalamedesalso uncoveredarusebyOdysseus.OdysseushadpromisedAgamemnonthathewoulddefend themarriageofHelenandMenelausbutpretendedtobeinsanetoavoidhavingtohonorhis commitment.Unfortunately,Palamedes’sunmaskingofOdysseusledtoagruesomeend;he wasstonedtodeathforbeingatraitorafterOdysseusforgedfalseevidenceagainsthim. Palamedeswaschosenasthenameforthetoolboxbecauseofthelegendary figure ’s(presumed)contributionstotheartofmeasurement,interestinstochasticprocesses(hedidinvent dice!),numericalskills,humor,andwisdom.ThePalamedesSwallowtailbutterfly(Papilio palamedes)onthefrontcoveralsoprovidesthetoolboxwithanattractiveicon.
PalamedesisasetofroutinesanddemonstrationprogramswritteninMATLAB for analyzingpsychophysicaldata(PrinsandKingdom,2009).Theroutinescanbedownloaded from www.palamedestoolbox.org.Werecommendthatyoucheckthewebsiteperiodically, becausenewandimprovedversionsofthetoolboxwillbepostedtherefordownload. Chapters4 9explainhowtousetheroutinesanddescribethetheorybehindthem.The descriptionsofPalamedesdonotassumeanyknowledgeofMATLAB,althoughabasic knowledgewillcertainlyhelp.Moreover,PalamedesrequiresonlybasicMATLAB;the specialisttoolboxessuchastheStatisticstoolboxarenotrequired.Wehavealsotriedtomake theroutinescompatiblewithearlierversionsofMATLAB,wherenecessaryincludingalternativefunctionsthatarecalledwhenlaterversionsareundetected.Palamedesisalso compatiblewiththefreesoftwarepackageGNUOctave(http://www.octave.org).
ItisimportanttobearinmindwhatPalamedesisnot.Itisnotapackageforgenerating stimuliorforrunningexperiments.Inotherwordsitisnotapackagefordealingwiththe “front-end” ofapsychophysicsexperiment.ThetwoexceptionstothisrulearethePalamedes routinesforadaptivemethods,whicharedesignedtobeincorporatedintoanactualexperimentalprogram,andtheroutinesforgeneratingstimuluslistsforuseinscalingexperiments. Butbyandlarge,Palamedesisadifferentcategoryoftoolboxfromthestimulus-generating toolboxessuchasVideoToolbox(http://vision.nyu.edu/VideoToolbox/ ),PsychToolbox (http://psychtoolbox.org),PsychoPy(http://www.psychopy.org;seealso Peirce,2007,2009), andPsykinematix(http://psykinematix.kybervision.net/ )(foracomprehensivelistofsuch toolboxessee http://visionscience.com/documents/strasburger/strasburger.html ).Although someofthesetoolboxescontainroutinesthatperformsimilarfunctionstosomeoftheroutines inPalamedes,forexample fittingpsychometricfunctions(PFs),theyareingeneralcomplementaryto,ratherthanincompetitionwith,Palamedes.
Afewsoftwarepackagesdealprimarilywiththeanalysisofpsychophysicaldata.Mostof theseareaimedat fittingandanalyzingpsychometricfunctions.psignifit(http://psigni fit. sourceforge.net/;seealso Fründetal.,2011)isperhapsthebestknownofthese.Another optionisquickpsy,writtenforRbyDanielLinaresandJoanLópez-Moliner(http://dlinares. org/quickpsy.html;seealso Linares&López-Moliner,inpreparation).Eachofthepackages
BOX1.1 (cont'd) willhavetheirownstrengthsandweaknessesandreadersareencouragedto findthesoftware thatbest fitstheirneeds.AmajoradvantageofPalamedesisthatitcan fitPFstomultiple conditionssimultaneously,whileprovidingtheuserconsiderable flexibilityindefininga modelto fit.Justtogiveonesimpleexample,onemightassumethatthelapserateandslopeof thePFareequalbetweenseveralconditionsbutthatthresholdsarenot.Palamedesallowsone tospecifyandimplementsuchassumptionsand fittheconditionsaccordingly.Userscanalso providetheirowncustom-de finedrelationshipsamongtheparametersfromdifferentconditions.Forexample,userscanspecifyamodelinwhichthresholdestimatesindifferent conditionsadheretoanexponentialdecayfunction(oranyotheruser-speci fiedparametric curve).Palamedescanalsodeterminestandarderrorsfortheparametersestimatedinsuch multiplecondition fitsandperformgoodness-of-fittestsforsuch fits.
The flexibilityinmodelspecificationprovidedbyPalamedescanalsobeusedtoperform statisticalmodelcomparisonsthattargetveryspecificresearchquestionsthataresearcher mighthave.Examplesaretotestwhetherthresholdsdiffersignificantlybetweentwoormore conditions,totestwhetheritisreasonabletoassumethatslopesareequalbetweentheconditions,totestwhetherthelapseratedifferssignificantlyfromzero(oranyotherspecificvalue), totestwhethertheexponentialdecayfunctiondescribesthepatternofthresholdswell,etc. Palamedesalsodoesmuchmorethan fitPFs;ithasroutinesforcalculatingsignaldetection measuresandsummationmeasures,implementingadaptiveprocedures,andanalyzingscaling data.
versussubjective;detectionversusdiscrimination;andthresholdversussuprathreshold.We considerwhetheranyofthesedichotomiescouldusefullyformthebasisofafully-fledged classi ficationschemeforpsychophysicsexperimentsandconcludethatone,theperformance versusappearancedistinction,isthebestcandidate.
Chapter3takesasitsstartingpointtheclassi ficationschemeoutlinedinChapter2and expandsonitbyincorporatingafurtherlevelofcategorizationbasedonthenumberofstimulipresentedpertrial.Theexpandedschemeservesastheframeworkfordetailingamuch widerrangeofpsychophysicalproceduresthandescribedinChapter2.
Fourofthetechnicalchapters,Chapters4,6,8,and9,aredividedintotwosections.In thesechaptersSectionAintroducesbasicconceptsandtakesthereaderthroughthePalamedesroutinesthatperformtherelevantdataanalyses.SectionBprovidesmoredetailas wellasthetheorybehindtheanalyses.TheideabehindtheSectionAversusSectionBdistinctionisthatreaderscanlearnaboutthebasicconceptsandtheirimplementationwithout necessarilyhavingtograsptheunderlyingtheory,yethavethetheoryavailabletodelve intoiftheywant.Forexample,SectionAofChapter4describeshowto fitpsychometricfunctionsandderiveestimatesoftheircriticalparameterssuchasthresholdandslope,while SectionBdescribesthetheorybehindthevarious fittingprocedures.Similarly,SectionA
inChapter6outlineswhy dʹ measuresareusefulinpsychophysicsandhowtheycanbe calculatedusingPalamedes,whileSectionBdescribesthetheorybehindthecalculations.
Hereandthere,wepresentspeci fictopicsinsomedetailinseparateboxes.Theideabehind thisisthatthereadercaneasilyskiptheseboxeswithoutlossofcontinuity,whilereadersspecificallyinterestedinthetopicsdiscussedwillbeableto finddetailedinformationthere.Just togiveoneexample,Box4.6inChapter4explainsinmuchdetailtheprocedurethatisused to fitapsychometricfunctiontosomedata,givesinformationastohowsome fitsmightfail, andprovidestipsonhowtoavoidfailed fits.
1.4WHAT’SNEWINTHESECONDEDITION? Amajorchangefromthe firsteditionistheadditionofthechapteronsummationmeasures(Chapter7).Thischapterprovidesadetailedexpositionofthetheoryandpractice behindexperimentsthatmeasuredetectionthresholdsformultiplestimuli.Besidesthe newchapter,alltheotherchaptershavebeenrewrittentoagreaterorlesserdegree,mainly toincludenewproceduresandadditionalexamples.
Anotherimportantchangefromthe firsteditionisthatthedescriptionofthePalamedes routineshasbeenputintoboxesplacedalongsidetherelevanttext.Thisgivesreadersgreater flexibilityintermsofwhether,when,andwheretheychoosetolearnaboutPalamedes.The boxesinthischapter(Box1throughBox3)aredesignedtointroducethereadertoPalamedes anditsimplementationinMATLAB.
BOX1.2 ORGANIZATIONOFPALAMEDES AllthePalamedesroutinesareprefixedbyanidentifier PAL,toavoidconfusionwiththe routinesusedbyMATLAB.After PAL,manyroutinenamescontainanacronymfortheclassof proceduretheyimplement.Box1.3liststheacronymscurrentlyinthetoolbox,whattheystand for,andthebookchapterwheretheyaredescribed.Inadditiontotheroutineswithspecialist acronyms,thereareanumberofgeneral-purposeroutines.
Functions InMATLABthereisadistinctionbetweenafunctionandascript.Afunctionacceptsoneor moreinputarguments,performsasetofoperations,andreturnsoneormoreoutputarguments.Typically,Palamedesfunctionsarecalledasfollows:
>>[xyz] ¼ PAL_FunctionName(a,b,c);
where a, b,and c aretheinputarguments,and x, y,and z theoutputarguments.Ingeneral, theinputargumentsare “ arrays. ” Arraysaresimplylistingsofnumbers.Ascalarisasingle number,e.g.,10,1.5,1.0e 15.Avectorisaone-dimensionalarrayofnumbers.Amatrixisa two-dimensionalarrayofnumbers.Itwillhelpyoutothinkofallasbeingarrays.Asamatter offact,MATLABrepresentsallastwo-dimensionalarrays.Thatis,ascalarisrepresentedasa
1 1(1row 1column)array,vectorseitherasanm 1arrayora1 narray,andamatrix asanm narray.Arrayscanalsohavemorethantwodimensions.
InordertodemonstratethegeneralusageoffunctionsinMATLAB,Palamedesincludesa functionnamed PAL_ExampleFunction, whichtakestwoarraysofanydimensionalityas inputargumentsandreturnsthesum,thedifference,theproduct,andtheratioofthenumbers inthearrayscorrespondingtotheinputarguments.ForanyfunctioninPalamedesyoucanget someinformationastoitsusagebytyping help followedbythenameofthefunction:
>>helpPAL_ExampleFunction
MATLABreturns
PAL_ExampleFunctioncalculatesthesum,difference,product,and ratiooftwoscalars,vectorsormatrices.
syntax:[sumdifferenceproductratio] ¼ PAL_ExampleFunction(array1,array2)
Thisfunctionservesnopurposeotherthantodemonstratethe generalusageofMatlabfunctions.
Forexample,ifwetypeandexecute
[sumdifferenceproductratio] ¼ PAL_ExampleFunction(10,5);
MATLABwillassignthearithmeticsumoftheinputargumentstoavariablelabeled sum, thedifferenceto difference,etc.Incasethevariable sum didnotpreviouslyexist,itwillhave beencreatedwhenthefunctionwascalled.Incaseitdidexist,itspreviousvaluewillbe overwritten(andthuslost).Wecaninquireaboutthevalueofavariablebytypingitsname, followedby <return>:
>>sum
MATLABreturns
sum ¼ 15
Wecanuseanynameforthereturnedarguments.Forexample,typing
>>[sdpr] ¼ PAL_ExampleFunction(10,5) createsavariablestostorethesum,etc. Insteadofpassingvaluesdirectlytothefunction,wecanassignthevaluestovariablesand passthenameofthevariablesinstead.Forexampletheseriesofcommands
>>a ¼ 10;
>>b ¼ 5;
>>[sumdifferenceproductratio] ¼ PAL_ExampleFunction(a,b);
generatesthesameresultasbefore.Youcanalsoassignasinglealphanumericnameto vectorsandmatrices.Forexample,tocreateavectorcalled vect1 withvalues1, 2,4,and105 onecansimplytypeandfollowwitha <return>:
>> vect1 ¼ [1 24105]
Notethesquare,notroundbrackets. vect1 canthenbeenteredasanargumenttoaroutine, providedtheroutineissetuptoaccepta1 4vector.Tocreateamatrixcalled matrix1 containingtwocolumnsandthreerowsofnumbers,typeandfollowwitha <return>,for example
>> matrix1 ¼ [0.010.02;0.040.05;0.060.09]
wherethesemicolonseparatesthevaluesfordifferentrows.Again, matrix1 cannowbe enteredasanargument,providedtheroutineacceptsa3 2(rowsbycolumns)matrix. Wheneverafunctionreturnsmorethanoneargument,wedonotneedtoassignthemallto avariable.Let’ssayweareinterestedinthesumandthedifferenceoftwomatricesonly.We cantype:
>>[sumdifference] ¼ PAL_ExampleFunction([12;34],[56;... 78]);
DemonstrationPrograms AseparatesetofPalamedesroutinesaresuffixedby _Demo.Thesearelocatedinthefolder PalamedesDemos separatefromtheotherPalamedesroutines.The filesinthe PalamedesDemos folderaredemonstrationscriptsthatingeneralcombineanumberofPalamedesfunction routinesintoasequencetodemonstratesomeaspectoftheircombinedoperation.Theyproduceavarietyoftypesofoutputtothescreen,suchasnumberswithheadings,graphs,etc. Whiletheseprogramsdonottakeargumentswhentheyarecalled,theusermightbe promptedtoentersomethingwhentheprogramisrun,e.g.,
>>PAL_Example_Demo Enteravectorofstimuluslevels
Thentheusermightentersomethinglike [.1.2.3].Afterpressingreturntherewillbe someformofoutput,forexampledatawithheadings,agraph,orboth.
ErrorMessages ThePalamedestoolboxisnotparticularlyresistanttousererror.Incorrectusagewillmore oftenresultinaterminationofexecutionaccompaniedbyanabstracterrormessagethanitwill inagentlewarningorasuggestionforproperusage.Asanexample,letuspasssome
BOX1.2 (cont'd) inappropriateargumentstoourexamplefunctionandseewhathappens.Wewillpasstwo arraystoitofunequalsize:
>>a ¼ [123];
>>b ¼ [45];
>>sum ¼ PAL_ExampleFunction(a,b);
MATLABreturns
???Errorusing ¼¼> unknown
Matrixdimensionsmustagree.
Errorin ¼¼> PAL_ExampleFunctionat15
sum ¼ array1 þ array2;
ThisisactuallyanerrormessagegeneratedbyaresidentMATLABfunction,notaPalamedesfunction.PalamedesroutinesrelyonmanyresidentMATLABfunctionsandoperators (suchas “þ”),anderrormessagesyouseewilltypicallybegeneratedbytheseresident MATLABroutines.Inthiscase,theproblemarosewhen PAL_ExampleFunction attemptedto usethe “þ”operatorofMATLABtoaddtwoarraysthatarenotofequalsize.
BOX1.3 ACRONYMSUSEDINPALAMEDES AcronymsusedinnamesforPalamedesroutines,theirmeaning,andthechaptersinwhichtheyare described
AcronymMeaningChapter
AMPM
AMRF
AMUD
MLDS
Adaptivemethods:psimethod5
Adaptivemethods:running fit5
Adaptivemethods:up/down5
Maximumlikelihooddifferencescaling7
PF Psychometricfunction4
PFBA
PFLR
PFML
SDT
Psychometricfunction:Bayesian4
Psychometricfunction:likelihoodratio8
Psychometricfunction:maximumlikelihood4,8
Signaldetectiontheory6
References Fechner,G.,1860/1966.ElementsofPsychophysics.Hilt,Rinehart&Winston,Inc. Fründ,I.,Haenel,N.V.,Wichmann,F.A.,2011.Inferenceforpsychometricfunctionsinthepresenceofnonstationary behavior.J.Vis.11(6),16.
Gescheider,G.A.,1997.Psychophysics:TheFundamentals.LawrenceErlbaumAssociates,Mahwah,NewJersey. Knoblauch,K.,Maloney,L.T.,2012.ModelingPsychophysicalDatainR.Springer. Linares,D.,López-Moliner,J.,inpreparation.Quickpsy:AnRPackagetoAnalysePsychophysicalData. Lu,Z.-L.,Dosher,B.,2013.VisualPsychophysics.MITPress,Cambridge,MA.
Peirce,J.W.,2007.PsychoPy psychophysicssoftwareinPython.J.Neurosci.Methods162(1 2),8 13. Peirce,J.W.,2009.GeneratingstimuliforneuroscienceusingPsychoPy.Front.Neuroinform.2,10. http://dx.doi.org/ 10.3389/neuro.11.010.2008
Prins,N.,Kingdom,F.A.A.,2009.Palamedes:MATLABRoutinesforAnalyzingPsychophysicalData. http://www. palamedestoolbox.org
ClassifyingPsychophysical Experiments * FrederickA.A.Kingdom 1,NicolaasPrins2 1McGillUniversity,Montreal,Quebec,Canada; 2UniversityofMississippi,Oxford,MS,USA
2.3.1
2.1INTRODUCTION Thischapterdescribesvariousclassesofpsychophysicalprocedureandproposesascheme forclassifyingthem.Theaimisnotsomuchtojudgetheprosandconsofdifferent procedures thiswillbedealtwithinthenextchapter buttoexaminehowtheydiffer andhowtheyinterrelate.Theproposedclassificationschemeisarrivedatthroughacritical *ThischapterwasprimarilywrittenbyFrederickKingdom.
2.CLASSIFYINGPSYCHOPHYSICALEXPERIMENTS
examinationofthefamiliar “dichotomies” thatmakeupthevernacularofpsychophysics, e.g., “ClassA” versus “ClassB” observations, “Type1” versus “Type2” tasks, “forcedchoice” versus “nonforced-choice” tasks,etc.Thesedichotomiesdonotalwaysmeanthe samethingtoallpeople,sooneoftheaimsofthechapteristoclarifywhateachdichotomy meansandconsiderhowusefuleachmightbeasacategoryinaclassi ficationscheme. Whyaclassi ficationscheme?Afterall,theseasonedpractitionerdesignshisorherpsychophysicsexperimentbasedonknowledgeaccumulatedoveryearsofresearchexperience, includingknowledgeastowhatisavailable,whatisappropriate,andwhatisvalidgiven thequestionaboutvisualfunctionbeingasked.Andthatishowitshouldbe.However,a frameworkthatcapturesboththecriticaldifferencesaswellasintimaterelationshipsbetweendifferentpsychophysicalprocedurescouldbeusefultonewcomersinthe field,helping themtoselecttheappropriateexperimentaldesignfromwhatmightseemabewildering arrayofpossibilities.Thinkingaboutaclassi ficationschemeisalsoausefulintellectualexercise,notonlyforthoseofuswholiketocategorizethings,putthemintoboxes,andattach labelstothem,butforanyoneinterestedingainingadeeperunderstandingofpsychophysics. Butbeforediscussingthedichotomies,considerthecomponentsthatmakeupapsychophysicsexperiment.
2.2TASKS,METHODS,ANDMEASURES Althoughtheoutcomeofapsychophysicsexperiment typicallyasetofmeasurements reflectsmorethananythingelsetheparticularquestionaboutsensoryfunctionbeing asked,othercomponentsoftheexperiment,inparticularthestimulusandtheobserver’ s task,mustbecarefullytailoredtoachievetheexperimentalgoal.Apsychophysicsexperiment consistsofanumberofcomponents,andwehaveoptedforthefollowingbreakdown:stimulus;task;method;analysis;andmeasure(Figure2.1).Toillustrateouruseoftheseterms, consideroneofthemostbasicexperimentsinthestudyofvision:themeasurementofa “contrastdetectionthreshold. ” Acontrastdetectionthresholdisdefinedastheminimum amountofcontrastnecessaryforastimulustobejustdetectable. Figure2.2 illustratesthe ideaforastimulusconsistingofapatchonauniformbackground.Thepreciseformofthe stimulusmust,ofcourse,betailoredtothespeci ficquestionaboutsensoryfunctionbeing asked,soweassumethatthepatchistheappropriatestimulus.Thecontrastofthepatch canbemeasuredintermsofWebercontrast,definedasthedifferencebetweentheluminance ofthepatchanditsbackground, DL,dividedbytheluminanceofthebackground Lb,i.e., DL/ Lb.ThecontrastdetectionthresholdisthereforethesmallestvalueofWebercontrastneeded todetectthepatch.Manyproceduresexistformeasuringacontrastdetectionthreshold,each involvingadifferenttaskfortheobserver.Beforetheadventofdigitalcomputers,acommon
Psychophysics experiment
Task Stimulus MethodMeasure Analysis
FIGURE2.1 Componentsofapsychophysicsexperiment.
FIGURE2.2 Topleft:circulartestpatchonauniformbackground.Bottomleft:luminanceprofileofthepatchand thedefinitionofWebercontrast.Right:resultsofastandardtwo-interval-forced-choice(2IFC)experiment.The variousstimuluscontrastsareillustratedontheabscissa.Blackcirclesaretheproportionofcorrectresponsesfor eachcontrast.Thegreencurveisthebest fitofapsychometricfunction,andthecalculatedcontrastdetection threshold(CT)isindicatedbythearrow.Seetextforfurtherdetails. L ¼ luminance; Lb ¼ luminanceofbackground; DL ¼ differenceinluminancebetweenpatchandbackground; C ¼ Webercontrast.
methodwastodisplaythestimulusonanoscilloscopeandaskobserverstoadjustthe contrastwithadialuntilthestimuluswasjustvisible.Thejust-visiblecontrastwouldthen berecordedasthecontrastdetectionthreshold.Thismethodistypicallytermedthe “method ofadjustment”,orMOA.
Nowadaysthepreferredapproachistopresentstimulionacomputerdisplayandusea “two-intervalforced-choice,” or2IFC,task.Usingthisprocedure,twostimuliarepresented brieflyoneachtrial,oneofwhichisablankscreen,theotherthetestpatch.Theorderofstimuluspresentation blankscreenfollowedbytestpatchortestpatchfollowedbyblank screen isunknowntotheobserver(althoughofcourse “known” tothecomputer)andis typicallyrandomorquasi-random.Thetwostimuliarepresentedconsecutively,andthe observerchoosestheintervalcontainingthetestpatch,indicatinghisorherchoicebypressingakey.Thecomputerkeepsarecordofthecontrastofthepatchforeachtrial,alongwith theobserver’sresponse,whichisscoredaseither “correct” or “incorrect.” Agivenexperimentalsessionmightconsistof,say,100trials,andanumberofdifferentpatchcontrasts wouldbepresentedinrandomorder.
Withthestandard2IFCtask,differentmethodsareavailableforselectingthecontrastspresentedoneachtrial.Ontheonehand,theycanbepreselectedbeforethe experiment forexample,10contrastsrangingfrom0.01to0.1at0.01intervals.Ifpreselectedinthisway,the10stimuliateachcontrastwouldbepresentedinrandomorder duringthesession,making100trialsintotal.Thisisknownasthe “ methodofconstants. ” Attheendofeachsessionthecomputercalculatesthenumberofcorrectresponsesfor eachcontrast.Typically,therewouldbeanumberofsessionsandtheoverallproportion correctacrosssessionsforeachpatchcontr astcalculated,thenplottedonagraphas shownforthehypotheticaldatain Figure2.2 .Ontheotherhand,onecouldusean “ adaptive” (or “ staircase ”)method,inwhichthecontrastselectedoneachtrialisdeterminedby
theobserver ’sresponsesonprevioustrials.Theideabehindtheadaptivemethodisthat thecomputer “homesin ” onthecontraststhatareclosetotheobserver’scontrastdetectionthreshold,thusnotwastingtoomanytrialsonstimulithatareeithertooeasyortoo hardtosee.AdaptivemethodsarethesubjectofChapter5.
Theterm “analysis” referstohowthedatacollectedduringanexperimentareconverted intomeasures.Forexample,withthemethodofadjustmenttheobserver’ssettingsmightbe averagedtoobtainthethreshold.Ontheotherhand,usingthe2IFCprocedureinconjunction withthemethodofconstants,theproportioncorrectdatamaybe fittedwithafunctionwhose shapeischosentomatchthedata.The fittingprocedurecanbeusedtoestimatethecontrast detectionthresholddefinedastheproportioncorrect,say0.75or75%,asshownin Figure2.2. Proceduresfor fittingpsychometricfunctionsarediscussedinChapter4.
Tosummarize,usingtheexampleofanexperimentaimedatmeasuringacontrastdetection thresholdforapatchonauniformbackground,thecomponentsofapsychophysicalexperimentareasfollows.The “stimulus” isauniformpatchofgivenspatialdimensionsandof variouscontrasts.Example “tasks” includeadjustmentand2IFC.Fortheadjustmenttask,the “method” isthemethodofadjustment,whileforthe2IFCtaskonecouldemploythemethod ofconstantsoranadaptivemethod.Inthecaseofthemethodofadjustment,the “analysis” mightconsistofaveragingthesetofadjustments,whereasforthe2IFCtaskitmightconsist of fittingapsychometricfunctiontotheproportioncorrectresponsesasafunctionofcontrast. Forthe2IFCtaskinconjunctionwithanadaptivemethod,theanalysismightinvolveaveraging contrasts,oritmightinvolve fittingapsychometricfunction.The “ measure ” inallcasesisa contrastdetectionthreshold,althoughothermeasuresmayalsobeextracted,suchasanestimateofthevariabilityor “ error ” onthethresholdandtheslopeofthepsychometricfunction.
Theterm “procedure” isusedubiquitouslyinpsychophysicsandcanrefervariouslytothe task,method,analysis,orsomecombinationthereof.Similarly,theterm “method” hasbroad usage.Theothertermsinourcomponentbreakdownarealsooftenusedinterchangeably. Forexample,thetaskinthecontrastdetectionthresholdexperiment,whetheradjustment or2IFC,issometimestermeda “detection” taskandsometimesa “threshold ” task,while inourtaxonomytheterms “detectionthreshold” refertotheoutputmeasure.Thelesson hereisthatoneneedstobe flexibleintheuseofpsychophysicsterminologyandnotoverly constrainedbyanyprede finedscheme.
Nextweconsidersomeofthecommondichotomiesusedtocharacterizedifferentpsychophysicalproceduresandexperiments.Theaimhereistointroducesomecommonterminology,illustrateothervarietiesofpsychophysicalexperimentbesidescontrastdetection,andto examinewhich,ifany,ofthedichotomiesmightbecandidatesforapsychophysicsclassificationscheme.
2.3DICHOTOMIES 2.3.1
“ClassA” versus “ClassB” Observations Aninfluentialdichotomyintroducedsomeyearsagoby Brindley(1970) isthatbetween “ClassA” and “ClassB” psychophysicalobservations.Althoughonerarelyhearstheseterms today,theyareimportanttoourunderstandingoftherelationshipbetweenpsychophysical measurementandsensoryfunction.Brindleyusedtheterm “observation” todescribethe
FIGURE2.3 TheRayleighmatchillustratesthedifferencebetweenaClassAandClassBpsychophysical observation.ForClassA,theobserveradjustsboththeintensityoftheyellowlightintherighthalfofthebipartite fieldaswellastherelativeintensitiesoftheredandgreenlightsinthemixtureinthelefthalfofthebipartite field untilthetwohalvesappearidentical.ForClassB,theobserveradjustsonlytherelativeintensitiesoftheredand greenlightsinthelefthalftomatchthehueofayellowlightintherighthalfthatinthisexampleisdifferentin brightness.
perceptualstateofanobserverwhileexecutingapsychophysicaltask.ThedistinctionbetweenClassAandClassBattemptedtoidentifyhowdirectlyapsychophysicalobservation relatedtotheunderlyingmentalprocesses.Brindleyframedthedistinctionintermsofacomparisonofsensations:aClassAobservationreferstothesituationinwhichtwophysically differentstimuliareperceptuallyindistinguishable,whereasaClassBobservationrefersto allothersituations.
ThebestwaytounderstandthedifferencebetweenClassAandClassBiswithan example,andforthiswehaveadopted Gescheider’s(1997) exampleoftheRayleighmatch (Rayleigh,1881;ThomasandMollon,2004).Rayleighmatchesareusedtoidentifyandstudy certaintypesofcolorvisiondeficiency(e.g., Shevelletal.,2008),butforthepresentpurposes theaimofaRayleighmatchislessimportantthanthenatureofthemeasurementitself.
Figure2.3 showsabipartitecircularstimulus,onehalfconsistingofamixtureofredand greenmonochromaticlights,theotherhalfayellowmonochromaticlight.1 Duringthe
1Becausethelightsaremonochromatic,i.e.,narrowbandinwavelength,thisexperimentcannotbe conductedonaCRT(cathoderaytube)monitor,becauseCRTphosphorsarerelativelybroadbandin wavelength.Insteadanapparatusisrequiredthatcanproducemonochromaticlights,suchasaNagel AnomaloscopeoraMaxwellianviewsystem.
Class B
measurementproceduretheobserverisgivenfreereigntoadjustboththeintensityoftheyellowlightaswellastherelativeintensitiesoftheredandgreenlights.Thetaskistoadjustthe lightsuntilthetwohalvesofthestimulusappearidentical,asillustratedinthetopofthe figure.Incolorvision,twostimuliwithdifferentspectral(i.e.,wavelength)compositions butthatappearidenticalaretermed “metamers.” AccordingtoBrindley,metamericmatches suchastheRayleighmatchareClassAobservations.Theidentificationofanobservationas ClassAaccordswiththeideathatwhentwostimuliappearidenticaltotheeyetheyelicit identicalneuralresponsesinthebrain.Sincetheneuralresponsesareidentical,Brindley argues,itisrelativelystraightforwardtomapthephysicalcharacteristicsofthestimuli ontotheirinternalneuralrepresentations.
AnexampleofaClassBobservationisshownatthebottomof Figure2.3.Thistimethe observerhasnocontrolovertheintensityoftheyellowlight,onlycontrolovertherelative intensitiesoftheredandgreenlights.Thetaskistomatchthehue(orperceivedchromaticity) ofthetwohalvesofthestimulusbutwiththeconstraintthattheintensity(orbrightness)ofthe twohalvesremainsdifferent.Thus,thetwohalveswillneverappearidenticalandtherefore, accordingtoBrindley,neitherwilltheneuralresponsestheyelicit.Brindleywaskeentopoint outthatonemustnotconcludethatClassBobservationsareinferiortoClassAobservations: ourexampleClassBobservationisnotanecessaryevilduetodefectiveequipment!Onthecontrary,wemaywishtodeterminethespectralcombinationsthatproducehuematchesforstimulithatdifferinbrightness,preciselytounderstandhowhueandbrightnessinteractinthe brain.Inanycase,theaimhereisnottojudgetherelativemeritsofClassAandClassBobservations(foradiscussionofthissee Brindley,1970)butrathertoillustratewhatthetermsmean.
WhatothertypesofpsychophysicalexperimentareClassAandClassB?Accordingto Brindley,experimentsthatmeasurethresholds,suchasthecontrastdetectionthreshold experimentdiscussedintheprevioussection,areClassA.Thismightnotbeintuitively obvious,buttheargumentgoessomethinglikethis.Therearetwostates:stimuluspresent andstimulusabsent.Asthestimuluscontrastisdecreasedtoapointwhereitisbelow threshold,theobservationpassesfromoneinwhichthetwostatesarediscriminableto oneinwhichtheyareindiscriminable.Thefactthatthetwostatesmaynotbediscriminable eventhoughtheyarephysicallydifferent(thestimulusisstillpresenteventhoughbelow threshold)makestheobservationClassA.TwootherexamplesofClassAobservations thataccordtothesamecriterionareshownin Figure2.4.
ClassBobservationscharacterizemanytypesofpsychophysicalprocedure.Following ourexampleClassBobservationin Figure2.3,anyexperimentthatinvolvesmatching twostimulithatareperceptiblydifferentonc ompletionofthematchisClassB.Consider, forexample,thebrightness-matchingexperimentillustratedin Figure2.5 .Theaimofthis experimentistodeterminehowthebrightness,i.e.,perceivedluminance,ofatestdiskis in fl uencedbytheluminanceofitssurround.As arule,increasingtheluminanceofasurroundannuluscausesthediskinsidetodecre aseinbrightness,i.e.,becomedimmer.One waytomeasuretheamountofdimmingistoad justtheluminanceofasecond,matching diskuntilitappearsequalinbrightnesstothetestdisk.Thematchingdiskcanbethought ofasapsychophysical “ ruler. ” Whenthematchingdiskissettobeequalinbrightnessto thetestdisk,thetwodisksaresaidtobeatthe “pointofsubjectiveequality,” orPSE.The luminancesofthetestandmatchdisksattheP SEwillnotnecessarilybethesame;indeedit ispreciselybecausetheyareasarulediffer entthatisofinterest.Thedifferencein
FIGURE2.4 TwootherexamplesofClassAobservations.Top:orientationdiscriminationtask.Theobserveris requiredtodiscriminatebetweentwogratingsthatdifferinorientation,andathresholdorientationdifferenceis measured.Bottom:linebisectiontask.Theobserverisrequiredtopositiontheverticalredlinemidwayalongthe horizontalblackline.Theprecisionorvariabilityintheobserver’ssettingsisameasureofhisorherline-bisection acuity.
luminancebetweenthetestandmatchdisksatthePSEtellsussomethingabouttheeffect ofcontextonbrightness,the “ context” inthisexamplebeingtheannulus.Thistypeof experimentissometimesreferredtoas “ asymmetricbrightnessmatching, ” becausethe testandmatchdisksaresituatedindifferentcontexts(e.g., BlakesleeandMcCourt, 1997;HongandShevell,2004).
ItmightbetemptingtothinkofanasymmetricbrightnessmatchasaClassAobservation,onthegroundsthatitisquitedifferentfromtheClassBversionoftheRayleighmatch describedabove.IntheClassBversionoftheRayleighmatch,thestimulusregionthat
FIGURE2.5 TwoexamplesofClassBobservations.In(a)thegoaloftheexperimentisto findthepointof subjectiveequality(PSE)inbrightnessbetweenthe fixedtestandvariablematchpatchasafunctionoftheluminance(andhencecontrast)ofthesurroundannulus;(b)showstheapproximateluminanceprofi leofthestimulus; (c)istheMuller Lyerillusion.Thetwocenterlinesarephysicallyidenticalbutappeardifferentinlength.The experimentdescribedinthetextmeasurestherelativelengthsofthetwoverticalaxesatwhichtheyappearequalin length.
Test Match
(a)
(b)
(c)
observersmatchinhueisalsotheregionthatdiffersalongtheotherdimension brightness. Inanasymmetricbrightness-matchingexperimentontheotherhand,thestimulusregion thatobserversmatch,brightness,isnotthere gionthatdiffersbetweenthetestandmatch stimuli-inthisinstanceitistheannulus.However,onecannot “ ignore” theannuluswhen decidingwhethertheobservationisClassAorClassBsimplybecauseitisnotthepartof thestimulustowhichtheobservationisdirected.AsymmetricbrightnessmatchesareClass Bbecause,evenwhenthestimuliarematched,theyarerecognizablydifferentbyvirtueof thefactthatonestimulushasanannulusandtheotherdoesnot.
AnotherexampleofaClassBobservationistheMuller Lyerillusionshownin Figure2.5(c),ageometricillusionthathasreceivedconsiderableattention(e.g., Morgan etal.,1990).Thelengthsoftheaxesinthetwo figuresarethesame,yettheyappeardifferent duetothearrangementofthe finsateitherend.Oneofthemethodsformeasuringthesize oftheillusionistorequireobserverstoadjustthelengthoftheaxis,sayofthe fins-inward stimulus,untilitmatchestheperceivedlengthoftheaxisoftheother,say fins-outwardstimulus.ThephysicaldifferenceinlengthatthePSE,whichcouldbeexpressedasaraw,proportional,orpercentagedifference,isameasureofthesizeoftheillusion.Themisperceptionof relativelinelengthintheMuller Lyer figuresisaClassBobservation,becauseevenwhen thelengthsoftheaxesareadjustedtomakethemperceptuallyequal,the figuresremain perceptiblydifferentasaresultoftheirdifferent finarrangements.
AnotherexampleofaClassBobservationismagnitudeestimation.Thisistheprocedure wherebyobserversprovideanumericalestimateoftheperceivedmagnitudeofastimulus, forexamplealongthedimensionofcontrast,speed,depth,size,etc.Magnitudeestimation isClassBbecauseourperceptionofthestimulusandourjudgmentofitsmagnitudeutilize differentmentalmodalities.
Aninterestingcasethatat firstdefiesclassi ficationintoClassAorClassBisillustrated in Figure2.6.Theobserver’staskistodiscriminatethemeanorientationoftworandom arraysoflineelements,whosemeanorientationsareright-andleft-of-vertical(e.g., Dakin, 2001).Belowthreshold,themeanorientationsofthetwoarraysareindiscriminable,yet thetwoarraysarestillperceptiblydifferentbyvirtueoftheirdifferentelementarrangements. InthepreviouslymentionedClassBexamples,the “other” dimension brightnessinthe caseoftheRayleighmatch,annulusluminanceinthecaseofthebrightness-matching experiment wasrelevanttothetask.Howeverinthemean-orientation-discrimination experimentthe “other” dimension elementposition isirrelevant.Doesthefactthat
FIGURE2.6 ClassAorClassB?Theobserver’staskistodecidewhichofthetwostimulicontainselementsthat areonaverageleft-oblique.Whenthedifferenceinmeanelementorientationisbelowthreshold,thestimuliare identicalintermsoftheirperceivedmeanorientation,yetarediscriminableonthebasisofthearrangementoftheir elements.
elementarrangementisirrelevantmakeitClassA,ordoesthefactthatthestimuliare discriminablebelowthresholdonthebasisofelementarrangementmakeitClassB?Readers candecide.
Insummary,theClassAversusClassBdistinctionisimportantforunderstandingthe relationshipbetweenpsychophysicalmeasurementandsensoryfunction.However,we choosenottousethisdichotomyasabasisforclassifyingpsychophysicsexperiments,in partbecausetherearecasesthatseemhardtoclassifyintermsofClassAorClassB,and inpartbecauseotherdichotomiesforusbettercapturethecriticaldifferencesbetweenpsychophysicalexperiments.
2.3.2 “Type1” versus “Type2” Animportantconsiderationinsensorymeasurementconcernswhetherornotanobserver ’sresponsescanbedesignatedas “correct” or “incorrect”.Iftheycanbesodesignated, theprocedureistermedType1andifnotType2(Sperling,2008;seealso Sperlingetal., 1990).ThetermType2hassometimesbeenusedtorefertoanobserver’sjudgmentsabout theirownType1decisions(Galvinetal.,2003);inthiscase,theType2judgmentmightbe aratingof,say,1 5,orabinaryjudgmentsuchas “ confident” or “notcon fident,” inreferencetotheirType1decision2.
Theforced-choiceversionofthecontrastthresholdexperimentdescribedearlierisaprototypicalType1experiment,whereasthebrightness-matchingandMuller Lyerillusionexperiments,irrespectiveofwhetherornottheyemployaforced-choiceprocedure,are prototypicalType2experiments.Thereissometimesconfusion,however,astowhysome forced-choiceexperimentsareType2.ConsideragaintheMuller Lyerillusionexperiment. Aswiththecontrastdetectionthresholdexperiment,thereismorethanonewaytomeasure thesizeoftheillusion.Wehavealreadydescribedtheadjustmentprocedure.Considerhow theMuller Lyermightbemeasuredusingaforced-choiceprocedure.Onemethodwouldbe topresentthetwo finarrangementsasaforced-choicepaironeachtrial,withtheaxisofone fixedinlengthandtheaxisoftheothervariableinlength.Observerswouldberequiredon eachtrialtoindicatethe finarrangementthatappearedtohavethelongeraxis. Figure2.7 showshypotheticalresultsfromsuchanexperiment.Eachdatapointrepresentstheproportionoftimesthevariable-lengthaxisisperceivedaslongerthanthe fixed-lengthaxis,asa functionofthelengthofthelatter.Atarelativelengthof1,meaningthattheaxesarephysicallythesame,theobserverperceivesthevariableaxisaslongeralmost100%ofthetime. However,atarelativeaxislengthofabout0.88,theobserverchoosesthevariableaxisas longeronly50%ofthetime.Thus,thePSEis0.88.However,eventhoughtheMuller Lyer experiment,likethecontrastthresholdexperiment,canbemeasuredusingaforced-choice procedure,thereisanimportantdifferencebetweenthetwoexperiments.Whereasinthe contrastdetectionthresholdexperimentthereisacorrectandanincorrectresponseonevery trial,thereisnocorrectorincorrectresponsefortheMuller Lyertrials.Whateverresponse theobservermakesonaMuller Lyertrial,itismeaninglesstoscoreitascorrectorincorrect, atleastgiventhegoaloftheexperiment,whichistomeasureaPSE.Observersunusedto doingpsychophysicsoftenhavedifficultygraspingthisideaandevenwhentoldrepeatedly
2NotethatthedichotomyisnotthesameasTypeIandTypeIIerrorsinstatisticalinferencetesting.
2.CLASSIFYINGPSYCHOPHYSICALEXPERIMENTS
FIGURE2.7 ResultsofahypotheticalexperimentaimedatmeasuringthesizeoftheMuller Lyerillusionusinga forced-choiceprocedureandthemethodofconstantstimuli.ThecriticalmeasurementisthePSEbetweenthelengths oftheaxesinthe fixedtestandvariablecomparisonstimuli.Thegraphplotstheproportionoftimessubjectsperceive thevariableaxisas “longer.” Thecontinuouslinethroughthedataisthebest-fittinglogisticfunction(seeChapter4). Thevalueof1.0ontheabscissaindicatesthepointwherethe fixedandvariableaxesarephysicallyequalinlength. ThePSEiscalculatedasthevariableaxislengthatwhichthe fixedandvariableaxislengthsappearequal,indicated bytheverticalgreenarrow.Thehorizontalred-arrowedlineisameasureofthesizeoftheillusion.
thattherearenocorrectandincorrectanswers,insistonaskingattheendoftheexperiment howmanytrialstheyscoredcorrect!
TheType1versusType2dichotomyisnotsynonymouswithClassAversusClassB, thoughthereissomeoverlap.Forexample,theRayleighmatchexperimentdescribedabove isClassAbutType2becauseno “correct” matchexists.Ontheotherhand,thetwo-alternative forced-choice(2AFC)contrastthresholdexperimentisbothClassAandTypeI.
TheType1versusType2dichotomyisanimportantoneinpsychophysics.Itdictates,for example,whetherobserverscanbeprovidedwithfeedbackduringanexperiment,suchasa toneforanincorrectresponse.However,oneshouldnotconcludethatType1is “better” than Type2.TheimportanceofRayleighmatches(ClassAbutType2)forunderstandingcolor deficiencyisanobviouscaseinpoint.
2.3.3 “Performance” versus “Appearance” AdichotomyrelatedtoType1versusType2,butdifferingfromitinimportantways,is thatbetween “performance ” and “ appearance. ” Performance-basedtasksmeasureaptitude, i.e., “ howgood ” anobserverisataparticulartask.Forexample,supposeonemeasures contrastdetectionthresholdsfortwosizesofpatch,callthem “small” and “big. ” Ifthresholdsforthebigpatcharefoundtobelowerthanthoseforthesmallpatch,onecanconclude thatobserversarebetteratdetectingbig patchesthansmallones.Bythesametoken, iforientationdiscriminationthresholdsare foundtobelowerincentralthaninperipheral
vision,onecanconcludethatorientationdiscriminationisbetterincentralvisionthaninthe periphery.Bothoftheabovetasksaimtoestablishthelimitsofourperception.Ontheother hand,supposewemeasurethesizeoftheMuller Lyerillusionfortwodifferent fi nangles, say45 and60 (relativetotheaxis),and fi ndthattheillusionisbiggerforthe45 fi ns.It wouldbemeaninglesstoconcludethatweare “ better” attheMuller Lyertaskwhenithas 45 comparedto60 fi ns.PSEsarenotaptitudes.ForthisreasontheMuller Lyerexperimentisbestconsideredasmeasuringstimu lusappearance.Asimpleheuristiccanbe usedtodecidewhetherapsychophysicalproceduremeasuresperformanceorappearance. Iftheendmeasurementcanbemeaningfullyconsideredasshowinggreateraptitudefor oneconditionthananother,thenitismeasuringperformance,andifnot,appearance. Thisstillleavesopenthe questionofaprecisede fi nitionofappearance,otherthan “ notperformance. ” Thetermappearance,however,isnoteasytode fi ne,butformostofthesituationsdescribedinthisbookappearancecanbede fi nedastheapparentmagnitudeofa stimulusdimension.
Sometimesthesamepsychophysicalproced urecanbeusedtomeasurebothperformance andappearance.ConsidertheVernieralignmenttaskillustratedin Figure2.8,appliedto twostimulusarrangements,labelledAandB .Thegoaloftheexperimentusingstimulus AistomeasureVernieracuity,whichisde fi nedasthesmallestmisalignmentthatcanbe detected.Thisisathresholdmeasureandhenceaperformancemeasure.Thegoalofthe experimentusingstimulusBistomeasuretheeffectofthe fl ankingwhitelinesonthe perceivedpositionoftheblacklines.Thewhit elinesinBtendtohaveasmallrepulsiveeffect,causingtheblacklinestoappearslightly shiftedfromtheirnormalperceivedposition, inadirectionawayfromthatofthewhitelines(e.g., BadcockandWestheimer,1985).For bothexperiments,however,thetaskisthe same:decideoneachtrialwhethertheupper blacklineliestotheleft(ortotheright)ofthelowerblackline.
FIGURE2.8 Left:stimulusarrangementsAandBfortwoVernieralignmentexperiments.Right:hypothetical datafromeachexperiment.Theabscissaplotsthehorizontalphysicalseparationbetweentheblacklines,with positivevaluesindicatingthatthetoplineisphysicallytotheleftofthebottomlineandnegativevaluesindicating thatthetoplineisphysicallytoitsright.Theordinategivestheproportionoftimestheobserverrespondsthatthetop lineis “left.” Thecontinuouscurvesarebest-fittinglogisticfunctions.ThegreenarrowindicatesforstimulusAthe VernierthresholdandtheredarrowindicatesforstimulusBthepoint-of-subjectivealignment.
