北大心理學系.心理物理學方法與Matlab實現(xiàn)

心理物理學方法和matlab實現(xiàn)

2015-6-21

ReferencesWatsonandPelli(1983)QUEST:ABayesianadaptivepsychometricmethod.Leek(2001)Adaptiveproceduresinpsychophysicalresearch.Strasburger(2001)Convertingbetweenmeasuresofslopeofthepsychometricfunction.Strasburger(2001)Invarianceofthepsychometricfunctionforcharacterrecognitionacrossthevisualfield.GrassiandSoranzo(2009)MLP:aMATLABtoolboxforrapidandreliableauditorythresholdestimation.-psychoacoustics/內(nèi)省法早期心理學家采用的方法(Wundt)對有意識思考和感知的自我觀察DoIperceivethislightbrighterthanthat?Why?因其主觀性而被科學的方法所拒絕

但提供“先見之明”，有利于設(shè)計實驗和形成假說。

Irealizedthatitishardformetohearveryhighandverylowtones.Thusthefrequencyofatonemaybeafactorinitsperceivedloudness/audibility.Let’stestthisinanexperiment!Psychophysicalfunctions費希納的三個問題第一、覺察給定刺激所必需的最小物理刺激是什么？這個問題同絕對閾限(AL)有關(guān)。第二、覺察兩個不同刺激量所需的最小物理差別是什么？這涉及差別閾限(DL)。第三、判別兩個刺激在心理感覺上相等的條件是什么？這是主觀相等點(PSE)的問題。GustavTheodorFechner1801–1887心理物理實驗法古典心理物理學的基本問題在精心控制的實驗條件下，刺激的變化直接對應(yīng)于感覺的變化心理物理學研究的目的在于決定外部世界的一致性規(guī)律-韋伯定律閾限(Thresholds)Ifalinearrelationshipisassumed,twovaluesdeterminethefunction:X-intercept:minimumstimulusvaluethatevokedanysensation;

absolutethresholdSlope:therateatwhichsensationgrowsasweincreaseintensity;

differencethreshold

(inverselyproportionaltoslope)StimulusintensitySensationmagnitudeLinearpsychophysicalequationX-interceptslopeThresholdsGeneraldefinitions(notassuminglinearity):絕對閾限（Absolutethreshold）:

intensitythattheobservercanjustbarelydetectIntensitiesbelowabsolutethreshold:undetectableIntensitiesaboveabsolutethreshold:detectable差別閾限（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?古典心理物理實驗的基本方法（1）極限法或最小變化法；（2）恒定刺激法；（3）調(diào)整法或平均誤差法。確定絕對閾限的方法：（1）極限法；(2）階梯法（3）恒定刺激法；（4）調(diào)整法。確定差別閾限方法：（1）極限法（最小變化法）；（2）恒定刺激法。極限法:

非常有效，只需少數(shù)刺激就可以確定閾限值。然而被試表現(xiàn)出特定的慣性偏差。恒定刺激法：

刺激以隨機序列的方式呈現(xiàn)，非?？煽坎⑶覠o偏。

調(diào)整法：比如顏色心理物理學。

心理物理學實驗非常精細，通常在人們感覺器官的極限水平上操作，因此，很少讓人感覺到愉悅。請將你的大腦皮層的焦點活力集中在當前當然的任務(wù)。心理物理學的過程為產(chǎn)生并分析錯誤。如果你不犯錯誤，就沒有變異；沒有變異，那么大多數(shù)的心理物理學方法都失效，更別提大量的試次測試。需要達到一種平衡：練習效應(yīng)提高判斷的績效；然而“疲勞”效應(yīng)抵消了判斷的績效。

極限法（Methodoflimits）descendingseriesascendingseriesStimulusintensityStimulusnolongerdetectedStimulusdetectedThreshold:averagestimulusintensity恒定刺激法又叫正誤法，通常由5-7個刺激組成，這幾個刺激在實驗過程中保持不變此法的特點是根據(jù)出現(xiàn)的次數(shù)來確定閾限，即以次數(shù)的整個分布求閾限，所以又叫次數(shù)法

具體作法如下

a、主試從預(yù)備實驗中選出少數(shù)刺激，一般是5到7個，這幾個刺激值在整個測定過程中是固定不變的；

b、選定的每種刺激要向被試呈現(xiàn)多次，一般每種刺激呈現(xiàn)50到200次；

c、呈現(xiàn)刺激的次序事先經(jīng)隨機安排，不讓被試知道。用以測量絕對閾限，即無需標準值，如用以確定差別閾限或等值，則需包括一個標準值；

d、此法在統(tǒng)計結(jié)果時必須求出各個刺激變量引起某種反應(yīng)（有、無或大、?。┑拇螖?shù)。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-確定視覺的相對閾限

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

中央注視點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?心理物理學曲線（Thepsychometriccurve）典型的心理物理學曲線Example:Fitaprobitregressionmodelforyonx.glmfit心理物理學階梯法

如果所有給定的事情對于行為分析很重要，那么利用恒定刺激法否則，考慮使用階梯法(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-聽覺時距判斷/觸覺強度(staircase)StaircaseDoublestaircaseTFLEDurstaircase.mBertelson,1998使用PEST（ParameterEstimationbySequential

Testing)

/QuestPEST:Findthreshold.m,

QUEST:WatsonandPelli,1983利用心理物理法階梯法：對于實驗中反應(yīng)的每一個點，根據(jù)已經(jīng)收集的數(shù)據(jù)和對閾值的先驗知識，計算閾值的最大似然率例3-使用PSET方法-聲音時距比較SndComparison.m使用QuestUsingQuestWatsonandPelli,1983Thequestalgorithmisaveryefficientwaytoconductexperimentsusingpsychophysicalstaircases.Ateachpointintheexperiment,itcalculatesthemaximumlikelihoodestimateofthethreshold,giventhedatacollectedsofarintheexperimentandthepriorwehadonthethresholdgoingintotheexperimentItproposestheintensityofthestaircaseparameter,forwhichatrialwouldresultinthemaximalinformationonthevalueofthethresholdOnemajordisadvantageoftheQuestalgorithmisthatitrequiresinputonalogscale.例子4:目標檢測找紅色圓形的目標。即在一堆的綠色圓和紅色方塊中是否出現(xiàn)紅色圓目標使用Quest方法-目標偵測inputonalogscaleQuestQuantileQuestUpdateQuestcanbesetuptorununtilitreachesanestimateofthethresholdwithaspecificsizeoftheconfidenceintervalaroundgivesasanoutputanestimateofthestaircaseparametergiventhedatastoredinthequeststructupdatesthequeststructwiththeresultofthistrialintializationofthehistorystructbeta=3.5;delta=0.01;gamma=0.5;history.q=QuestCreate(tGuess,tGuessSd,params.pThreshold,beta,delta,gamma);信號檢測理論觀察者對一個信號是否出現(xiàn)，存在一個標準（criterion),這個標準也適用于神經(jīng)經(jīng)濟學家慣常研究的選擇行為(choicebehavior)d-prime(d’):

標準化信號（分布）-標準化噪聲（分布）；

信號檢測理論完美偵測:100%100%0%0%信號檢測理論無法偵測100%0%0%100%信號檢測理論無法偵測0%100%100%0%信號檢測理論無法偵測：擲硬幣

50%50%50%50%信號檢測理論沒有檢測，比如統(tǒng)一匯報看見的比例為30%30%70%70%30%==Rowsequal

nodetection信號檢測理論

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

操作特征曲線(ROC):falsealarmratehitrate100%100%90%30%10%70%信號檢測理論信號檢測理論操作特征曲線

(ROC):falsealarmratehitrate100%100%100%0%0%100%Perfectdetection信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%100%100%0%0%Nodetection:always“yes”信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%0%0%100%100%Nodetection:always“no”信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%50%50%50%50%Nodetection:reporting“yes”in50%ofthetrials(flippingacoin)信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%40%40%60%60%Nodetection:reporting“yes”in40%ofthetrials信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%30%30%70%70%Nodetection:reporting“yes”in30%ofthetrials信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%60%60%40%40%Nodetection:reporting“yes”in60%ofthetrials信號檢測理論操作特征曲線(ROC):falsealarmratehitrate100%100%Diagonal:nodetection信號檢測理論SDT模型:無法消除噪聲但通過ROC，可以分離知覺與決策。

感知覺噪聲決策信號出現(xiàn)/不出現(xiàn)感知覺水平(SL)SL≥

β標準

(β)SL<βYESNO信號檢測理論感覺水平概率如果沒有噪聲，完全偵測是有可能的。標準信號出現(xiàn)信號不出現(xiàn)感知覺噪聲決策信號出現(xiàn)/不出現(xiàn)感知覺水平(SL)SL≥

β標準

(β)SL<βYESNO感覺水平概率標準信號出現(xiàn)信號不出現(xiàn)100%0%0%100%信號檢測理論感知覺噪聲決策信號出現(xiàn)/不出現(xiàn)感知覺水平(SL)SL≥

β標準

(β)SL<βYESNO感覺水平probability噪聲:使得信號分布變得模糊無法完美偵測(特別是信號和噪聲分布重合)信號不出現(xiàn)

(只有噪聲)信號出現(xiàn)

(信號+噪聲)標準信號檢測理論感知覺噪聲決策信號出現(xiàn)/不出現(xiàn)感知覺水平(SL)SL≥

β標準

(β)SL<βYESNO信號檢測理論SensationlevelSensationlevel信號檢測理論SensationlevelSensationlevelfalsealarmratehitrate信號檢測理論falsealarmratehitrateROCcurveβ=8β=6β=10β=6β=8β=10信號檢測理論falsealarmratehitrateβsensationlevelprobability標準(β):定義在ROC曲線上的位置ROC曲線僅由感覺通道的容量（能力）所定義

(即可辨別性)信號檢測理論可辨別性:觀察者從噪聲的疊加分布中區(qū)分出信號的能力測量d’(可辨別性指標，亦稱“敏感度”

)信號檢測理論d’:選擇

ROC曲線β:選擇ROCcurve上的一點對于擊中與虛報，信息采樣是一樣的，但是:擊中與虛報率:

都反映了知覺與決策的特性，但不能分離兩者;

d’:取決于感知覺β:取決于決策β這兩個過程是分離的?。⌒盘枡z測理論Fechner方法:

Isastimulusdetectable?Yesorno?Clear-cutthresholdvalue(withsomevariability)thatcanbemeasuredStimulusintensity>thresholddetectableStimulusintensity<thresholdnotdetectable兩分法、絕對模型信號檢測理論:

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

notdetectableatall線性結(jié)果