北大心理学系.心理物理学方法与Matlab实现

心理物理学方法和matlab实现

2015-6-21

ReferencesWatsonandPelli(1983)QUEST:ABayesianadaptivepsychometricmethod.Leek(2001)Adaptiveproceduresinpsychophysicalresearch.Strasburger(2001)Convertingbetweenmeasuresofslopeofthepsychometricfunction.Strasburger(2001)Invarianceofthepsychometricfunctionforcharacterrecognitionacrossthevisualfield.GrassiandSoranzo(2009)MLP:aMATLABtoolboxforrapidandreliableauditorythresholdestimation.-psychoacoustics/内省法早期心理学家采用的方法(Wundt)对有意识思考和感知的自我观察DoIperceivethislightbrighterthanthat?Why?因其主观性而被科学的方法所拒绝

但提供“先见之明”，有利于设计实验和形成假说。

Irealizedthatitishardformetohearveryhighandverylowtones.Thusthefrequencyofatonemaybeafactorinitsperceivedloudness/audibility.Let’stestthisinanexperiment!Psychophysicalfunctions费希纳的三个问题第一、觉察给定刺激所必需的最小物理刺激是什么？这个问题同绝对阈限(AL)有关。第二、觉察两个不同刺激量所需的最小物理差别是什么？这涉及差别阈限(DL)。第三、判别两个刺激在心理感觉上相等的条件是什么？这是主观相等点(PSE)的问题。GustavTheodorFechner1801–1887心理物理实验法古典心理物理学的基本问题在精心控制的实验条件下，刺激的变化直接对应于感觉的变化心理物理学研究的目的在于决定外部世界的一致性规律-韦伯定律阈限(Thresholds)Ifalinearrelationshipisassumed,twovaluesdeterminethefunction:X-intercept:minimumstimulusvaluethatevokedanysensation;

absolutethresholdSlope:therateatwhichsensationgrowsasweincreaseintensity;

differencethreshold

(inverselyproportionaltoslope)StimulusintensitySensationmagnitudeLinearpsychophysicalequationX-interceptslopeThresholdsGeneraldefinitions(notassuminglinearity):绝对阈限（Absolutethreshold）:

intensitythattheobservercanjustbarelydetectIntensitiesbelowabsolutethreshold:undetectableIntensitiesaboveabsolutethreshold:detectable差别阈限（Differencethreshold）(justnoticeabledifference/JND/

anddifferencelimen):

minimumintensitydifferencethatisnoticeabletotheobserverAchangeinintensitythatissmallerthanthedifferencethreshold:undetectableAchangeinintensitythatislargerthanthedifferencethreshold:detectableDifferencethresholdsLinearfunction

differencethreshold(slope)isconstantAnobserverabletodetectthedifferencebetweenintensities100and110shouldalsobeabletodetectthedifferencebetween1000and1010.Thisisnotthecase:theobserverisabletodetectthedifferenceonlybetween1000and1100500&550Hztones5000&5050Hztones5000&5500HztonesDifferencethresholdisnotconstant!StimulusintensitySensationmagnitudeLinearpsychophysicalequationconstantslopeDifferencethresholdsDifferencethresholdisnotconstant(changeswithintensity)

functionisnonlinearWeber’slaw:differencethresholdisaconstantproportionoftheinitialstimulusvalueΔI/I=cPrevious

examples:

c=10%Weber’slaw

holdsonly

approximately!StimulusintensitySensationmagnitudeNonlinearpsychophysicalequationslopechangeswithintensityAbsolutethresholdsEvenintheabsenceofstimulation,thereissomerandomfiringonsensorynervesThisinnernoisecanevenvaryfrommomenttomomentObserverscannotdistinguishinnernoisefromtheeffectofaweakstimulusEvenwhenthereisnolight(perfectdarkness),observersmayexperienceadimlight(darklight,intrinsiclight)ObserversinananechoicchamberoftenreporthearingawhistlingsoundMeasuringtruly„absolute”thresholdsisproblematic:observersmayconfuseinnernoisewiththerealthingPsychophysicalmethodsThresholdmeasurements:absolutethr/differencethr.–Isitintenseenoughtosee?Howsmalladifferencecanyousee?-Fechner’s3methodsMethodofconstantstimuliMethodoflimitsMethodofadjustment-ModificationofFechner’smethodsStaircasemethodModificationofthemethodofconstantstimuli(adaptive,nostandard)Forcedchoice,objectivemethodsSensorydecisiontheory(SDT)PsychologicalfunctionsfrompsychometricdataDirectscaling:growthofsensationwithintensity,Howbrightdoyouseealight?-MagnitudeestimationandthepowerlawMultidimensionalscaling:degreetowhichstimuliarecomparablealongsomedimensions

Alongwhichdimensionsdoyoujudgethesimilarityoftwostimuli?古典心理物理实验的基本方法（1）极限法或最小变化法；（2）恒定刺激法；（3）调整法或平均误差法。确定绝对阈限的方法：（1）极限法；(2）阶梯法（3）恒定刺激法；（4）调整法。确定差别阈限方法：（1）极限法（最小变化法）；（2）恒定刺激法。极限法:

非常有效，只需少数刺激就可以确定阈限值。然而被试表现出特定的惯性偏差。恒定刺激法：

刺激以随机序列的方式呈现，非常可靠并且无偏。

调整法：比如颜色心理物理学。

心理物理学实验非常精细，通常在人们感觉器官的极限水平上操作，因此，很少让人感觉到愉悦。请将你的大脑皮层的焦点活力集中在当前当然的任务。心理物理学的过程为产生并分析错误。如果你不犯错误，就没有变异；没有变异，那么大多数的心理物理学方法都失效，更别提大量的试次测试。需要达到一种平衡：练习效应提高判断的绩效；然而“疲劳”效应抵消了判断的绩效。

极限法（Methodoflimits）descendingseriesascendingseriesStimulusintensityStimulusnolongerdetectedStimulusdetectedThreshold:averagestimulusintensity恒定刺激法又叫正误法，通常由5-7个刺激组成，这几个刺激在实验过程中保持不变此法的特点是根据出现的次数来确定阈限，即以次数的整个分布求阈限，所以又叫次数法

具体作法如下

a、主试从预备实验中选出少数刺激，一般是5到7个，这几个刺激值在整个测定过程中是固定不变的；

b、选定的每种刺激要向被试呈现多次，一般每种刺激呈现50到200次；

c、呈现刺激的次序事先经随机安排，不让被试知道。用以测量绝对阈限，即无需标准值，如用以确定差别阈限或等值，则需包括一个标准值；

d、此法在统计结果时必须求出各个刺激变量引起某种反应（有、无或大、小）的次数。恒定刺激法

(Methodofconstantstimuli)StimulusintensityStimulusdetectedStimulusnotdetectedFechner’sthreemethodsPresentingonestimulusatatimeThestimulusisveryweakPossibleresponses:

“Yes,Iseeit.”/

“No,Idon’tseeit.”AbsolutethresholdDifferencethresholdMethodofconstantstimuliMethodoflimitsMethodofadjustmentnotusedPresentingtwostimuliatatime:Standard:fixed,easilydetectableComparison:eithermoreorlessintensethanthestandardPossibleresponses:

“Comparisonisstronger.”/

“Comparisonisweaker.”MethodofconstantstimuliformeasuringabsolutethresholdsSelectarangeoflightintensitiesfromcertainlyinvisibletocertainlyvisiblePickafew(4-7)pointsuniformlyinthisintensityrange;thiswillbetheconstantstimulussetWeakStrongLightintensityMethodofconstantstimuliformeasuringabsolutethresholdsTesteachstimulusmanytimes(20-25)inrandomorder…MethodofconstantstimuliformeasuringabsolutethresholdsPresentthestimulioneatatimeandasktheobserverifitwasvisibleornotVisible?

YES NOClicktostartCouldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?Couldyouseethespotoflight?MethodofconstantstimuliformeasuringabsolutethresholdsCalculatetheproportionof“yes”and“no”responsesateachlightlevel + - + + + - - - + + + - - - - + 0% 5% 20% 50% 80% 95% 100%MethodofconstantstimuliformeasuringabsolutethresholdsPlotthepercentagesagainststimulusintensity

psychometricfunctionStimulusintensityPercentage“seen”0%100%50%75%25%Psychometricfunction

forabsolutethresholdsIdealFIG(Sekuler)FixedabsolutethresholdStepfunctionActualFIG(Sekuler)Absolutethresholdvariessomewhatfromtrialtotrial(duetoconstantfluctuationsinsensitivity)Conventionally,theintensitycorrespondingto50%isconsideredtobethethresholdsigmoidfunctionMethodofconstantstimuliformeasuringdifferencethresholdsStandardstimulushasafixedintensityTheintensitiesofcomparisonstimulibracketthestandardLightintensityStandardstimulus:Comparisonstimuli:MethodofconstantstimuliformeasuringdifferencethresholdsAllpairsofstandardandcomparisonstimuliaretestedmanytimesMethodofconstantstimuliformeasuringdifferencethresholdsForeachpair,theobserverjudgesifthecomparisonstimuluswasstrongerorweakerthanthestandard

STRONGER

WEAKERMethodofconstantstimuliformeasuringdifferencethresholdsForeachcomparisonlevel,thepercentageof“stronger”responsesiscalculatedandresultsareplottedasapsychometricfunctionLightintensityofcomparisonstimuliPercentage“stronger”0%100%50%75%25%PsychometricfunctionfordifferencethresholdsWhentheobservercannotseeadifference,he/shechoosesrandomlybetween“stronger”and“weaker”;thiscorrespondsto50%onthepsychometricfunction

pointofsubjectiveequivalence(PSE)LightintensityofcomparisonstimuliPercentage“stronger”0%100%50%75%25%PSEPsychometricfunctionfordifferencethresholdsByconvention,theintensityat75%isconsideredtobejustnoticeablystrongerthanthestandard

DSAcomparisonintensityat25%isjustnoticeablyweakerthanthestandard

DWDifferencethreshold=theaverageofDSandDWLightintensityofcomparisonstimuliPercentage“stronger”0%100%50%75%25%DWDSPsychometricfunctionfordifferencethresholdsMethodoflimitsformeasuringabsolutethresholdsOneachtrial,theobserverreportsifshe/hecouldseethelightornot.Startwithpresentingalightintensitywellabovetheexpectedthreshold(theobservercancertainlyseeit)DecreasetheintensityuntiltheobservercannotseeitThresholdestimate:theintensityatwhichtheresponsechanges+-+++++----LightintensityTrialsDescendingseries:startfromabovetheexpectedthresholdanddecreaseintensityAscendingseries:startfrombelowtheexpectedthresholdandincreaseintensitythresholdestimateClicktostartMethodoflimitsformeasuringabsolutethresholdsAscendinganddescendingseriesmayyielddifferentresults

usebothEveninthesamedirection,thereisvariabilityinthethreshold(innernoise,etc)

averagemanymeasurementsMeasuredthresholdcorrespondsto50%pointinapsychometricfunction(methodofconstantstimuli)+-+++++-----+++++----LightintensityTrialsthresholdestimateMethodoflimitsformeasuringdifferencethresholdsIntensityofthecomparisonstimulusisdecreased(descending)orincreased(ascending)untiltheresponsechangesThresholdestimate:intensitydifferencebetweenthestandardandcomparisonstimuliwheretheresponsechangesAverageresultsfrommultipleseriesinbothdirections+-++++LightintensityofcomparisonstimulusTrials+ comparisonbrighter- comparisonweaker+----+-++++-----+

例子1-确定视觉的相对阈限

(Hecht,Shlaer,andPirenne,1942-energy,quantaandvision)

中央注视点clearall;%Emptyingworkspacecloseall;%closingallfigurestemp=uint8(zeros(400,400,3));%Createadarkstimulusmatrixtemp1=cell(10,1);%Createacellthatcanhold10matricesfori=1:10%Fillingtemp1temp(200,200,:)=255;%Insertingafixationpointtemp(200,240,:)=(i-1)*10;%Insertingatestpoint40pixelsrightofit.%Brightnessrange0to90temp1{i}=temp;%Puttingtherespectivemodifiedmatrixincellend%Donedoingthat

h=figure%Creatingafigurewithahandlehstimulusorder=randperm(200);%Creatingarandomorderfrom1to200.%Forthe200trials.Allowstohavea%preciselyequalnumberperconditionstimulusorder=mod(stimulusorder,10);%Usingthemodulusfunctionto%createarangefrom0to9.20eachstimulusorder=stimulusorder+1;%Now,therangeisfrom1to10,asdesired.score=zeros(10,1);%Keepingscore.Howmanystimuliwerereportedseen.fori=1:200%200trials,20perconditionimage(temp1{stimulusorder(1,i)})%Imagetherespectivematrix.As%designatedbystimulusorderi%Givesubjectfeedbackaboutwhichtrialwearein.Nootherfeedbackpause;%Getthekeypresstemp2=get(h,'CurrentCharacter');%Getthekeypress,"."forpresent,%","forabsenttemp3=strcmp('.',temp2);%Comparestrings.If.(present),temp3=1,%otherwise0score(stimulusorder(1,i))=score(stimulusorder(1,i))+temp3;%Addup%Intherespectivescoresheetend%Endthepresentationoftrials,after200havelapsed.Whichisbrighter?心理物理学曲线（Thepsychometriccurve）典型的心理物理学曲线Example:Fitaprobitregressionmodelforyonx.glmfit心理物理学阶梯法

如果所有给定的事情对于行为分析很重要，那么利用恒定刺激法否则，考虑使用阶梯法(staircasemethod)Leek(2001)Transformedup-downmethodImprovementofthesimpleup-down(staircase)methodXn+1dependson2ormoreprecedingresponsesE.g.1-up/2-downor2-steprule:IncreasestimuluslevelaftereachincorrectresponseDecreaseonlyafter2correctresponsesφ=70.7%Threshold:

mid-runestimate8rulesfor8differentφvalues

(15.9%,29.3%,50%,70.7%,79.4%,84.1%)reversalpointstwo-down,one-upprocedure,whichtargetsthe70.7%levelonthepsychometricfunctionSimpleup–downprocedure,boththepositiveandthenegativesequencesconsistofonetrial,andthetracklevelmovesaftereachresponse,targetingthe50%performancelevel.例子2-听觉时距判断/触觉强度(staircase)StaircaseDoublestaircaseTFLEDurstaircase.mBertelson,1998使用PEST（ParameterEstimationbySequential

Testing)

/QuestPEST:Findthreshold.m,

QUEST:WatsonandPelli,1983利用心理物理法阶梯法：对于实验中反应的每一个点，根据已经收集的数据和对阈值的先验知识，计算阈值的最大似然率例3-使用PSET方法-声音时距比较SndComparison.m使用QuestUsingQuestWatsonandPelli,1983Thequestalgorithmisaveryefficientwaytoconductexperimentsusingpsychophysicalstaircases.Ateachpointintheexperiment,itcalculatesthemaximumlikelihoodestimateofthethreshold,giventhedatacollectedsofarintheexperimentandthepriorwehadonthethresholdgoingintotheexperimentItproposestheintensityofthestaircaseparameter,forwhichatrialwouldresultinthemaximalinformationonthevalueofthethresholdOnemajordisadvantageoftheQuestalgorithmisthatitrequiresinputonalogscale.例子4:目标检测找红色圆形的目标。即在一堆的绿色圆和红色方块中是否出现红色圆目标使用Quest方法-目标侦测inputonalogscaleQuestQuantileQuestUpdateQuestcanbesetuptorununtilitreachesanestimateofthethresholdwithaspecificsizeoftheconfidenceintervalaroundgivesasanoutputanestimateofthestaircaseparametergiventhedatastoredinthequeststructupdatesthequeststructwiththeresultofthistrialintializationofthehistorystructbeta=3.5;delta=0.01;gamma=0.5;history.q=QuestCreate(tGuess,tGuessSd,params.pThreshold,beta,delta,gamma);信号检测理论观察者对一个信号是否出现，存在一个标准（criterion),这个标准也适用于神经经济学家惯常研究的选择行为(choicebehavior)d-prime(d’):

标准化信号（分布）-标准化噪声（分布）；

信号检测理论完美侦测:100%100%0%0%信号检测理论无法侦测100%0%0%100%信号检测理论无法侦测0%100%100%0%信号检测理论无法侦测：掷硬币

50%50%50%50%信号检测理论没有检测，比如统一汇报看见的比例为30%30%70%70%30%==Rowsequal

nodetection信号检测理论

操作特征曲线(ROC):falsealarmratehitrate100%100%

操作特征曲线(ROC):falsealarmratehitrate100%100%90%30%10%70%信号检测理论信号检测理论操作特征曲线

(ROC):falsealarmratehitrate100%100%100%0%0%100%Perfectdetection信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%100%100%0%0%Nodetection:always“yes”信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%0%0%100%100%Nodetection:always“no”信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%50%50%50%50%Nodetection:reporting“yes”in50%ofthetrials(flippingacoin)信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%40%40%60%60%Nodetection:reporting“yes”in40%ofthetrials信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%30%30%70%70%Nodetection:reporting“yes”in30%ofthetrials信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%60%60%40%40%Nodetection:reporting“yes”in60%ofthetrials信号检测理论操作特征曲线(ROC):falsealarmratehitrate100%100%Diagonal:nodetection信号检测理论SDT模型:无法消除噪声但通过ROC，可以分离知觉与决策。

感知觉噪声决策信号出现/不出现感知觉水平(SL)SL≥

β标准

(β)SL<βYESNO信号检测理论感觉水平概率如果没有噪声，完全侦测是有可能的。标准信号出现信号不出现感知觉噪声决策信号出现/不出现感知觉水平(SL)SL≥

β标准

(β)SL<βYESNO感觉水平概率标准信号出现信号不出现100%0%0%100%信号检测理论感知觉噪声决策信号出现/不出现感知觉水平(SL)SL≥

β标准

(β)SL<βYESNO感觉水平probability噪声:使得信号分布变得模糊无法完美侦测(特别是信号和噪声分布重合)信号不出现

(只有噪声)信号出现

(信号+噪声)标准信号检测理论感知觉噪声决策信号出现/不出现感知觉水平(SL)SL≥

β标准

(β)SL<βYESNO信号检测理论SensationlevelSensationlevel信号检测理论SensationlevelSensationlevelfalsealarmratehitrate信号检测理论falsealarmratehitrateROCcurveβ=8β=6β=10β=6β=8β=10信号检测理论falsealarmratehitrateβsensationlevelprobability标准(β):定义在ROC曲线上的位置ROC曲线仅由感觉通道的容量（能力）所定义

(即可辨别性)信号检测理论可辨别性:观察者从噪声的叠加分布中区分出信号的能力测量d’(可辨别性指标，亦称“敏感度”

)信号检测理论d’:选择

ROC曲线β:选择ROCcurve上的一点对于击中与虚报，信息采样是一样的，但是:击中与虚报率:

都反映了知觉与决策的特性，但不能分离两者;

d’:取决于感知觉β:取决于决策β这两个过程是分离的！！信号检测理论Fechner方法:

Isastimulusdetectable?Yesorno?Clear-cutthresholdvalue(withsomevariability)thatcanbemeasuredStimulusintensity>thresholddetectableStimulusintensity<thresholdnotdetectable两分法、绝对模型信号检测理论:

Howwellisitdetectable?Howsensitivetheobserveristothestimulus?Measuredbyd’Thehigherd’is,themorethestimulusisdetectabled’=0

notdetectableatall线性结果