Principles of Perceptual Measurementsonify.psych.gatech.edu/~walkerb/classes/... · A SCIENTIFIC...

Principles ofPerceptualMeasurement

In this chapter . . .• You will discover the main controversies that arose instudies todetermine the

relationship between physical stimuli and the sensations they evoke within us.You will also learn how todescribe and give examples of the human ability toestimate sensations.

• You will examine famous classical psychophysicists, such as Gustav Fechnerand Ernst Weber, and the experimental methods they designed to studysensory perception. You will become familiar with psychometric functionand how it can be affected by both sensory and nonsensory parameters.

• You will become familiar with the difference threshold, which determines howmuch extra stimulus is needed in order to justnotice a change. You will alsobecome familiar with Webers law, which states that the difference thresholddoes not remain constant as the stimulus increases in intensity; and Fechner'slaw, which was found tobe flawed but transformed the field ofsensory scienceand remains influential to this day.

• You will learn about Stanley S. Stevens,who began the era ofmodern psychophysics.You will also learn about the method of magnitude estimation, whichled tothe development ofthe power law.

• You will study the difference between prothetic and metathetic stimuli and howthey are assessed. Finally, you will become famil iar with differences inhumansensitivity to stimuli and how researchers use techniques to compare thosedifferences in terms ofz-scores,

Most ofus would be abletocorrectly identify the colour red orgreenorblue. But does that mean we are all experiencing an identicalpsychological event, orcould it be that each ofus experiencessomething slightly different? Photo:Trout55/iStockphoto.com

A SCIENTIFIC BASIS OF PERCEPTUALMEASUREMENT

B CLASSICAL PSYCHOPHYSICS1. Psychophysical Methods2. Absolute Threshold3. Difference Threshold4. Weber's Law5. Fechner's Law

C MODERN PSYCHOPHYSICS1. Magnitude Estimation and the

Power Law2. Psychophysical Scaling3. Scaling of Nonsensory Variables4. Signal Detection Theory

True SciCIlCC investigates and bri1 t,<s to 1/l1I/1a1l

perception sutli truths and such kllowlcdgc asthe pe ople I!fagivcll time and society considermost important.

- Leo Tolstoy

Fundamentals ofSensory Perception

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Although the terms sensationand perceptionare often usedinterchangeably, it is import-ant toestablish the distinctionbetween them atthe outset.Sensoryprocesses captureinformation from the physicalworld and transform theminto biologicalsignals thatare interpreted by the brain.Inso doing, the brain createsa perceptual representationinourmind that allows us toappreciate the physical world .Thus, perception representsasingleunified awareness ofastimulus that in turn arisesfrom the sensation producedby our sensory systems.

We are co nstantly bei ng bombarded by ene rgyfrom the physical wo rld, whether it is in theform of visual, audito ry, tactile, or che mose nsory stimulation. T hese stimuli are very realand can be measured . The inte nsity of lightreflected by an object, for example, can beexac tly determined wi th a device called a radiometer.T his device will spec ify the intensity in aset of units for wh ich it has been calibrated. Ingeneral, all physical stimuli that we are capableofperceiving can be spec ified in real terms thatgive us a value acco rding to some dim ension ofits physical reality.

But what abo ut the psychological eventsthat evoke within us an appreciation of thatphysical stim ulus ? Can the resulting perceptualexperience also be measured?That depends onwh o is doin g the measurin g. If it happens to beanyone other than the perceiver, the answer ofcourse is /l 0 . Percepti on is a very private experience, and since it canno t be exposed to anyoneelse, it canno t be directly measured by anyone else either. Consider the followin g. Mostof us wo uld be able to correctly identify thecolour of a stoplight. But does that mean weare all expe rien cing an identi cal psychologicalevent, or could it be that each of us experiencessome thing slightly different but that we have allbeen taught to call it red since childhood? Wemay never know the answer to this.

If an outsider is not capable of measuring our own percepti on s, then are we? Arewe capable of determining, say, the psychological int ensity of a sound that is experiencedin our mind, giving it a value, and comparing its perceived inte nsity with a differentsound or a different type of sensation altogethe r? R em arkably, the answer is yes. And itturns out that we are actually quite goo d at iteven though perceptions do not reside in thevery real world of physics (Stevens, 1986). Andtherein lies a rath er thorny probl em . Manypsychologists have asserted that even makin gthe attempt at measuring a perceptual event isfruitl ess because it is not a measurable thing andtherefore can never be verified (He idelbe rger& Klohr, 200 4).

To say that this issue has gene rated somelively debate in the past wou ld be an understateme nt . This is largely because of theopposite view held by some experime ntalpsychologists that the perceived intensity ofsensations can indeed be reliably estimatedby the perceiver. Furthermore, the information so obtained is generally consistent across

indi vidua ls, and therefore the data can be scienti fically validated (Gescheider, 1997). Wewill return to th is deb ate and explore theissues on both sides later in this chapter. Butfirst, it is necessary to learn some thing abo utthe experimental approaches to studying sensory processes, the kinds of problems to whichthey can be applied, and the infor mation theyreveal about the op eration of the brain . Whatwill follow is a set of core concepts that willsurface throughout this book as we examineeach of the sensory systems in detail.

.A. Scientific Basis ofPerceptual Measurement

The most obvious question to begin with is"Why take a scientific approach to this problem ?" That is, what do we hop e to gain bydeveloping and applying a set of rigorousexperi me ntal procedures to the study of perception? The reason most psychologists wouldfirst offer is that it satisfies an intellectual cur iosity. Perception is such a myster ious and almost .magical phenomenon that a first step towardlearning anything about it is to establish a quantifiable relationship between the two variablesin this process-the physical stimulus and theresulting perceptual impression (SideNote 1.1).Since it is impossible to open up the mind andobserve the process of percepti on , one advantage of knowing th is relationship is that it mayoffer clues about the nature of the brain, theway it processes information, and, ultim ately,how the biological operations within it lead tosensation and perception.

Quantitative relationships and their benefitsThere are several additional advantages tounderstanding the math ematical relation shipbetween the physical and perceptual wo rlds.One is that it provid es an estimate of the perceptual quality of a stimulus in numer ical termsand thu s allows comparisons with other stimuli. Say for example that a new perfume hasj ust been developed and the co mpany wishesto test its aromatic acceptance by the publi cbefore spending millions of dollars on its promoti on . By applying a set of experime ntal procedures, which we will soon learn, it is possibleto obtain a numerical index of its impact onthe sense of sme ll and then use th is to providea meanin gful comparison wi th the perceptualimpression made by other perfumes. Such data

Threepossiblefunctions thatmay relate the physical intensityofastimulus (I) totheperceived intensity ofsensation (S).

Chapter 1 Principles of Perceptual Measurement

shown in Figure 1.1.The simplest is a linear functi on. For any

given increase in physical intensity, th ere is acertain inc reme nt in th e perceived intensity.T he prop ortion between th e two remai nsco nstant across the who le range . In othe rwo rds, th e slope remai ns co nstant .This is notthe case for th e othe r two possibiliti es shownin Figure 1.1. In an expo ne nt ial relation ship,the perceived sensation intensity changesvery slow ly at low values of physical intensity.But after a ce rtain point, th e function takesoff suc h that even small changes in stimulusintensity produce a dramatic increase in perception. In an exponential fun ction, th erefore,th e slope itself progressively increases wi thphysical int ensity. The opp osite is true of alogarithmic functi on where the slope is verylarge at th e beginning suc h that perceivedintensities can change dramatically wi th smallchanges in stimulus int ensity. However, thiseffect diminishes and th e func tio n tails offat higher stimulus intensi ties. A logar ithmicfunction th erefore displays a decreasing slopeover its entire range. According to th is mathema tical description, a sensory system wo uldno lon ger be additionally responsive to furth er increments in stimulus int ensity beyonda certa in point.

There are two gene ral approac hes toobtaining the precise relationship betweenphysical events and perceptual experience.Thefirst is to simply ask human subjects to ratethe perceived intensity of a certain stimulus,say the loudness of a sound, at various physicalintensities (Gesche ider, 1984). It would then bepossible to plot the two sets of values and determin e whi ch of the gene ral functi ons shown inFigure 1.1 best describes the transformationof a physical input-in this case, sound-intoa perceptual event. We will look at the information revealed by this kind of approac h later

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can predict the likely social acceptability of thenew produ ct and therefore can be used by thecompa ny's execut ives to make imp ortant commercia l decisions (Lodge, 198 1).

Quant itative relation ships also have theadvantage that they allow co mparisons amo ngindividuals and even species.The later chaptersof this book will cover many details about ourlimits and capacities in processing informatio nfrom the physical world, how they vary withage, and, where appropriate, how they co mparewith other animals. The facto rs that are usedin such comparisons are always math ematical descriptors of the system in question . Anextension of this idea is the comparison amo ngthe different sensory modalities-a so- calledcross-modal comparison-r-io see if any similaritiesexist among them (Luce, 1990). For example, ifwe perceive warmth on the skin in some definable way to the temperature of the object, thenhow does this relation ship co mpare to the wayin which we perceive the loudness of sound asa function of its physical intensity? Before weexplore such sophisticated Issues, we need toaddress a basic question .

Is there ageneral relationship betweenphysical stimulus and perception?This is one of the fundame ntal questions ofperceptual psycho logy and one to which mucheffort has been directed over the last 150 years.Th e early expe rime ntalists wh o approachedthis probl em were motivated in findin g ageneral formula that could describe all sensory systems.What might such a formula looklike-or, rath er, wh at kind ofa function couldrelate the physical intensity of a stimulus to itsperceived magnitude? We kn ow from everyday experience that this will be an increasingfunction. That is, as the physical intensity of thestimulus increases, so will our percepti on of it.But that could happen in a number of ways, as

Fundamentals of Sensory Perception

GustavTheodor Fechner(1801-1887)© INTERFoTO/Alamy

in this chapter. The second approach is a bitmore convoluted because it requires a measureof the smallest change in stimulus input thatcauses a j ust discriminable change in sensation.To understand how this can reveal anyt hingimp ortant , we have to examine the ideas firstproposed by the experime ntal psychologists ofthe 19th century. T hey had understood thata math ematical relation ship between physicaland perceptual qualities could be established byobtaining two basic charac ter istics or descriptors of that function-the start ing point andthe slope.

B. Classical PsychophysicsLooki ng again at Figure 1.1, we see that allthree func tions do not begin at the origin bu tare displaced somewhat to the right . This isbecause we are unable to detect very low levels of stimulus intensity. Although a stimulusis physically present, the biological elementsthat are involved in capturi ng th e stimulus andtransforming it into a sensory experience donot normally fun ction well if the physicalint ensity is too low (Engen, 1971). R ath er, theintensity has to reach a cer tain minimum level,the so-ca lled absolute threshold, befo re itis registered by the brain as a sensory event.Stimulus intensities below this poin t are calledsubthreshold and will not produ ce detectablesensation. So the first item that has to be determin ed is th e absolute threshold , which wo uld\hen \ e\\ U 'S. \.h e \,Q\n\. (~Q\n 'Nn \ <:n \.0 bc~\\~

plotting our function.We would next want to know what

happens beyond th is point in the so-calledsuprathreshold region wh ere sensatio n takesplace. For this, we will have to determine howthe slope changes as a function of physicalintensity. Furthermore, th e slope wo uld haveto be determined not just for one suprathreshold point but also for several othe rs in orderto see how it is changin g. O ne possible wayto obtain th is inform ation is by knowing justhow small a change in stimulus inte nsity isrequired to produce a discrimin able change insensation.This so-ca lled difference thresholdcan be used to estimate how the slope changesat suprathresho ld levels. And once we knowthis, we can determine which function bestdescrib es the transform ation ofphysical stimuliin the real wo rld into psychological events thatwe experience as percept ion .

We have j ust describ ed th e genera l outline of a scientific approach that had beenformulated by th e Ge rman physicist GustavFechner in 1860. Fechner wan ted to determine th e relationship between mind andbod y and set out to establish not only a guiding principle but also a set of experimentalmeth ods that were to be used in thi s newfield called psychophysics. H e believed thatthere existed a general relation ship betweenphysical and perceptual qualities, that it wassimilar for all types of sensations, and that itco uld be obtained by knowin g the stimulus ene rgy at which the output can just bedetected or discr iminated-that is, th e absolute threshold and the difference threshold(Heidelbe rge r & Klohr, 2004). Fechner wasno t just int erested in knowin g these thresholdsbecause th ey wo uld reveal some thing abo utth e opera tio nal sensitivity of senso ry systemsbut because he believed that they representedfun dame nta l param eters in the grand formulaof percepti on.

1. PSYCHOPHYSICAL METHODS

It is possible to apply anyone of three gen eral meth ods that were develop ed by Fechnerto obtain absolute and differen ce th resholds(Gesche ider, 1997). T he simplest of these isth e Method of Adjustment whe re a humansubject is to ld to sim ply adj ust the physicalinte nsity of a stimulus until it is barely de tec table. T he initial' inte nsity wo uld be set eithera.bovt.: 0 1' b c\o 'N t.hTC~ho\d . a nd t.he ...\.\hic c't

wo uld acco rdingly change the value until thestimulus is just perceptible or whe n the sensation j ust disappears. Alth ou gh th is procedureis very fast and actively engages the subject inthe psychophysical experime nt, the Me thodof Limits is preferable if speed is not an issuebeca use this technique prov ides more reliable estimates. H ere, the subject is present edwi th a stim ulus whose inte nsity is chosenfrom an ascending or descending series . Ifan ascending series is used , the intensity ofthe stimulus is initially set at a subthresholdvalue and inc reased by a fixed amo unt in successive tr ials until th e subject reports that it isperceived. Alternatively, if a descending seriesis used,a suprath reshold intens ity value is gradually reduce d until the percept disappears.T hetransition points from several suc h ascendingand descending ser ies prov ide a reasonableestima te of the threshold.


SideNote11.3

SideNote 1..:.1.:.:.2=-- _

Asimplepsychophysics setupinwhich ahuman subjectobserves computer-generatedstimuli onamonitor fromafixeddistance.The responseisindicatedwith thepress ofabuttonand sent tothe computer, which stores this information for lateranalysis.

Oneprobleminundertaking athresholdexperiment with theMethodof Constant Stimuliischoosing an appropriaterange ofstimulus intensities.Optimally, the threshold shouldbe somewhere in the middleof this range.Sincethisistheparameterbeing determinedexperimentally, it becomesdifficult toconstruct a rangearound an unknown value. Oneway toget around this istodoa"quick anddirty" Method ofAdjustment experiment,whichwill give an approximate valuefor the threshold.

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to produce detectable sensation, and so oursubject sho uld consistently respond NO whe nasked if some thing is visible. However, once wereach an intensity that is sufficient to tr iggersensatio n, the subject should then co nsisten tlyrespond YES. The transition between thesetwo response levels can then be defined as theabsolute threshold .The subjec t is presumed tobehave like an ideal detector in such a scenario- that is, all subthresho ld intensities fail toproduce a detectable sensory event, wh ereasall suprathresho ld ones consistently produce apositive sensatio n. Furthermore, the subject isabsolutely perfect in being able to distinguishbetwe en these two conditions.

Humans are not ideal detectorsIn reality, however, our respon ses are quitedifferent. As Figure 1.3 (page 8) shows, theresponse curve that wou ld eme rge from anactual experime nt wo uld look more like anS-shaped function or ogive.Alth ou gh we reliably detect very high intensities and always failto detect very low ones, it appears that the intervening inte nsity levels cause some uncertaintyas to whet her or not a sensory event occ ur red.According to Figure 1.3, it is clear that as theintensity increases, there is a progressive increasein the likelihood that it will be detected .This so-called psychometric function provides a typical profile of how our sensory systems respond as a function of physical intensity(Falmagne, 2002). And as such, it is clear that

~--------The expected response profile in an absolute thresholdexperiment looks likeastep function.All stimulus intensitiesup toacertain point will fail toproducesensation, whereas allintensities beyond that pointwill always do so.Theabsolutethreshold is the intensity at whichthis transitionoccurs.

Both the M eth od of Limits and theMeth od of Adju stment allow th e subject tohave an idea of wh at the next stimulus will belike compared to the last one.T his predictability in stimulus presentation makes both ofthesemethods less accura te. A more suitable procedure is the Method of Constant Stimuliwhere the intensity values are rand oml ychosen from a preset range and presented tothe subject. N either th e expe rime nter nor thesubject usually knows the value of the nextstimulus to be present ed . T he subject merelyreplies whether or not a sensation occ ur redand a freque ncy chart is established based onthe respo nses collected from many presentations at each intensity.

As an example, let us consider an experiment on the visual system where we willattempt to obtain the absolute threshold fordetecting light using the M eth od of ConstantStimuli. Such expe rime nts are typically conducted with a sophisticated optical setup.However, we will simplify the experime nt sothat the stimulus will be under computer control and presented on a mon itor. The subjec twill view the stimulus from a fixed distanceand after each trial will indi cate a response tothe compute r. This is a typical setup for mostmodern psychophysical experime nts on vision(SideNote 1.2). After each stimulus presentation , the subject hits eithe r a YES or a NO button to indi cate wh ether a sensation occ ur red,that is, whether ligh t was detected or not. Forany given tri al, the stimulus intensity will berandoml y chosen by the computer from a predefined set of values.T he lowest intensity valuemust be one that is never de tected , whereasthe highest value should always be detected . Inthis way, the threshold intensity will be locatedsomewhere within this range (SideNote 1.3).At the end of the experime nt, each intensitywill have been present ed an equal number oftimes, and a summary of the freque ncy of YES

responses to each stimulus intensity wi ll beprovided by the computer.

Before looking at the data that such an experiment might gene rate, let us co nsider what theresponse profile would look like based simplyon intuition. One likely possibility is shownin Figure 1.2 wh ere the respon se curve lookslike what is called a step fu nction.All intensities below a certain point wo uld be too weak

2. ABSOLUTE THRESHOLD


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Cognitive factors can arise fromnoise in the decision-makingprocess. For example, asub-jectmay actually perceive thestimulus butopttorespondNO due toreduced confidence.Alternatively, asuolect maynot actually have perceived thestimulus but chose torespondYES due toeagerness. Cognitivefactorsareextremely importantinpsychophysical experimentsand will be discussed later inSection C.4.

SideNote 11-'1....:..5=--- _

Let us assume that the sensation produced by astimulus hasanormal probability distributiondue tothe effects ofnoise.Thedetection probability ofasignalis given by the cumulativeprobabilities-thatis, the areaunder the distribution-up tothatpoint.The ogive psychometric function resultsfromthe cumulative probabilitiesdetermined inthismanner atprogressively greater valuesofsensation magnitude.The0.5(or 50%) level inthe ogivecorresponds tothemean ofthedistribution, which iswhy it isused toestimate thethreshold.

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we do not behave as ideal detectors, leadin g tothe natural qu estion of why this is so.

Under mo st circumstances, our sensorysystems have to deal with several sourcesof un certainty (Ma rks, 1974). These facto rsbecome espec ially critica l at very low physicalint ensities where detect ion threshold s typically arise. O ne such source is th e stimulusitself. There is usually some variabi lity in theintensity of a stimulus simply because nophysical device can provide perfect del iveryat a spec ified int ensity, espec ially whe n it isvery low. This stimulus is th en captu red by asensory system th at adds further noise to th esignal. It is a biological fact that our nervou ssystem is inh erentl y noisy, which becomesespec ially probl em atic at th e lim its of sensory func tion whe re the noise interferes wi thsignal detect ion to produce instances of mispercept ion . And finally, once this somewhatvariable stimulus has been delivered and th encaptu red by our noi sy senso ry system, we stillhave to make a judgm ent as to wheth er itwas perceived . That judgment can be influ ence d by a number of physical, emo tional,and cognitive facto rs (Side Note 1.4). Whilethe magn itude of th ese would certainly varyamong different peopl e, th ese factors can alsovary wi th time wi thin an indi vidu al subject.Togeth er, th ese different sources of variability-from stimulus to subject- ma ke oursensory systems beh ave quite differentl y froman ideal det ector.

Conventional approaches tothreshold estimation

Given that we are not ideal detectors, thenwhic h intensity value do we take fromFigure 1.3 to represent the absolute threshold? Because there is a gradual increm ent instimulus detectabiliry with increasing physicalint ensity, there actu ally is no well- defined pointth at can serve as the thresho ld. We thereforehave to adopt an arbitrary response level thatcan be used to obtain the threshold (Engen,1971). By convention, psycho physicists haveused the 50% response level for that purpose(SideNote 1.5).Therefore, the physical intensity that produces th is respon se is taken to bethe absolute threshold . An expe rime nter cancerta inly use a different criterion so lon g asit is made clear which respon se level that is.For examp le, it is possible to use the 60% YES

value as the de finitio n of th reshold sensation. In that case, the stim ulus intensity tha tproduces this would be taken as the absolutethreshold of detec tio n. W hat this means is thatin reality there is no ali-or-none condition forstimulus detect ion . R ath er, our thresholds canfluctu ate a little, and therefore the noti on ofa threshold now becomes defined in a morestatistical mann er.

Since Fechner's time, th ere has beenmuc h effort at determining absolute thresholdvalues for different sensory systems under different conditions (Gescheider, 1997; Stevens,1986). T hese results have shown that we areind eed extremely sensitive creatures, andunder some conditions, the laws of physicsoften impose th e limits to detection . Here aresome examples of how well we do.

701/c1z-a dimpling of the skin by as lit tle as10-5 ern is sufficient to be detected.

Smell-under op timal co nditions, the absorption of on ly 40 molecules by detectors in thenose is sufficie nt to produce a detectable smell.

Hearillg-detect ion threshold is so small that itrepresents moveme nt of the eardru m by only10-10 cm.This is smaller than th e diameter ofa hydrogen molecul e.

Visioll-the eye can be exposed to as little as54-1 48 ph ot on s to produce a detectable sensation ofligh t. Ifl osses in transmiss ion throughthe eye are co nsidered, it turns out tha t thisrepresents the absorp tion of a single pho tonin abo ut 5 to 14 detector cells of the retina.

These figures attes t to th e remarkable biological co nstruc tion of our senso ry systems.


3. DIFFERENCE THRESHOLDAs noted before, one of Fechner's central goalswas to understand the relationship between thephysical and mental worlds-in other wo~ds,

the way in whi ch stimuli of different physicalintensities produce different amounts of sensation, or sensory magnitude. The absolutethreshold gives only on e point in that profile,that is, the starting point for any of the possiblerelationships that are shown in Figure 1.1. Butthis is obviously not enough to determine whatthe rest of the function would look like. Forthis Fechner needed to have an idea of whatthe 'slope of the func tion was at suprathresholdlevels and how that slope changed withincreasing intensity (Engen , 1971; Manning &R.osenstock, 1967) . If the slope remains constant, then the relationship between sensorymagnitude and stimulus intensity is describe~

by a linear function. However, if the slope IS

either increasing or decreasing, then the function becomes either an exponent ial or a logarithmi c one, respectively.

A clue as to which of these possible functions correctly describes the transformation ofphysical to mental events came to Fechn er froma series of experiments on difference thresholds that were carried out by a co nte mporary German physiologist named Ern st Weber.Weber had been interested in determinin gthe gradations of sensory experience at suprathreshold levels (Weber, 1996). The questionnow was no longer whether or not a stimuluswas perceived but rather how mu ch it neededto change in order to produce a detectablechange in sensation.T he differen ce in physicalintensity that was required to accomplish thisbecame known as the dt[fcrc//cc threshold.Weberworked mainly with the discrimination ofobject weights, carrying out a series of carefulexperime nts on the smallest detectable changefor a series of different starting weights.

Adifference threshold experimenton the visual system

Let us illustrate the principles that Weberdeveloped using discrimination of light intensities as an example. We can set up a psychophysical experiment as before but now ask thesubje ct to examine two stimuli-a referen celight, whose intensity is always kept constant,and a target light , whose int ensity is eitherlower or higher than that of the referen ce.T hesubject must compare the two and indicate

whethe r the target light is brighter or dimmer.N o other cho ices are allowed.

We can ado pt Fechn er's Meth od ofConstant Stimuli again to perform this experiment. A computer will randomly choose theinte nsity level of the target light from a rangeand display that stimulus along with the fixedreferen ce stimulus.The subject's task is to compare the two stimuli, make a decision , and hitone of two buttons to register the respon se.This sequence is repeated many tim es until asufficient number of trials (say 50) have beenaccumulated for each intensity point. We canthen calculate the proportion (or percentage)of tr ials in whi ch the subject judged the targetlight to be brighter. Of course, we could j ustas well examine the proportion judged to bedimmer. Either way, the idea is to look at thedata and see how mu ch ofa change in physicalintensity was required for a detectable changein sensation. Since we gave the subject an equalnumber of bri ghter and dimmer intensities,one possibility is that all trul y dimmer intensitieswere judged correctly as were all trul y brighterintensities. In this case, the subjects theoretically behaved like an ideal detector because theynever failed in distinguishin g true differencesin stimulus intensities.

However, similar to wh at we saw earlierfor detection judgments, it turns out that wedo not behave as ideal detectors wh en it comesto difference judgments either. The psychome tri c function in Figure 1.4 (page 10) showsa plot of percentage brigluer responses againsttarget ligh t intensity. Again, as in Figure 1.3,performance data displays an ogive rather thana step function , indi cating that certain intensities generated mixed respon ses. The intensitythat produced 50% brightcr response s (pointa on the x-axis) can be taken as the point ofperceptual equivalence. In oth er words, at thisintensity our subject could not decide wh eth erthe target light was bri ghter or dimmer, andit was therefore perceptually equivalent to thereferen ce light.

Our task now is to use this data to determin e the difference threshold-that is, thatextra bit of physical intensity that needs to beadded to or subtracted from the target lightintensity at th is perceptual equivalence pointin ord er for there to be a just noticeabledifference OND) in sensation. This amo untwill in turn dep end on exactly wh at level ofno ticeable differen ce we wan t as our criterion. By convention, most psychophysicists use

Ernst Heinrich Weber (1795-1 878)© INTERFOTOIA1amy

4. WEBER'S LAW


become different ?This was precisely the question that Weber addressed in his experime ntswith weights, and in so doin g, he discovered afund amental relationship that has co me to bearhis name (Weber, 1996).

~I=k ·I

Multiple discrimination threshold experimentsLet us return to the difference thresholdexperiment with lights. Figure 1.5 shows thepsychometric functions that we wo uld likelyobtain if we co nducted this experime nt threetim es by setting the reference light at progressively higher intensities each tim e.T he psychometri c function s are correspo ndingly displacedto the right and becom e somewhat flatter.For each psychom etri c function , we can nowdetermine the difference th reshold .To keep itsimple, we will restrict th is analysis to j ust theincrem ent threshold .

As before, we wo uld first determine th etarget light int ensities that are perceptuallyequivalent in br ightness to th e reference ligh tfor all three cases (aj, az, a3) and th en find th eintensities produ cin g 75% brighter respo nses(b., bz, bj). Look ing closely at Figure 1.5, wecan see that th e increme nt threshold for the 'first psych ometric fun ction (b. minus a.) willbe less than that of th e seco nd fun ction, whichin turn will be less than th at of th e thi rd. Inothe r wo rds, the greate r th e intensity level atwhich we have to make a JND j udgme nt, th egreater the differen ce th reshold (~ I ) neededto attain that JN D. T he differen ce thresho ld isth erefore not co nstant but actually increasesin a linear fashion with stimulus inte nsity.T his is what Web er discovered , and the eq uation descr ibin g this relationship is known asWeb er's law :

Implications ofWeber's lawWe know from everyday experience that if asmall number of items is increm ented by j ustone, it is more likely that we will not ice thatdifference than if the same addition is made toa much larger set. Weber noti ced that if onelit candle was added to 60 others, then thataddition would be sufficient to cause a JN D inbrightness percepti on. However, if there were120 burning candles, then adding j ust one morewas no lon ger sufficient to cause a detectablechange in sensation.Thus, the requirem ent fora JND is that the increm ental (or decrem ent al)amount be scaled to the stimulus intensity.

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A typical psychometric function that is obtained in a difference threshold experiment where the subject has to judgetwo stimuli and determine whether the target was brighteror dimmer than the reference. The 25% and 75% brighterresponse levels are generally used as the points for a justnoticeable difference (JND) in sensation decrement andincrement, respectively.

100

the 75% br(~hter response level as the measure for a noti ceable increme nt in the stimulus (Gescheider, 1997). Thus, when the targetlight intensity is raised to point b in Figure 1.4,we will achieve th is result, and the differencebetween the two int ensities (b minus a) is takenas the difference threshold (~I). In othe r words,~I represents the extra bit of physical intensitythat we wo uld need to add in order to makea stimulus j ust noti ceably bri ghter. Exactlythe same logic can be used if we want to determin e the difference threshold for a redu ction insensation, exce pt now we use the 25% brighterresponse level (which corresponds to 75% dimmerjudgments).The target light int ensity nowneeds to be lowered to point c, and the difference between the two intensities (a minus c)is also a difference threshold (~I) . These twomeasures of difference threshold are usuallydistinguished by the terms increment thresholdand deaement threshold, respec tively, and areoften averaged to provide a composite value.

In the last experime nt, bri ghtness comparisonswere made to a reference light that was fixed ata parti cular int ensity.What happens if we nowchange the referen ce light to a higher leveland redo the experi me nt to find a new difference threshold? Do es the difference threshold value (~I) still remain the same or will it

......~-------

Target Light Intensity (I)


tl I

Astraight line isproduced if wemake a plot ofthe differencethreshold (~I) that was obtainedateach ofthe three intensity(I) levels. This isthe graphicalform ofWeber'slaw and hasbeen found tohold true for allsensory systems withinabroadrange ofintensities.The Weberfraction(k) is taken fromtheslope ofthis line.

SideNote 11.6Touch (heaviness) 0.02

Touch (vibration) 0.04

Taste 0.2

Smell 0.07

Loudness 0.3

Pitch 0.003

Brightness 0.08

Weber Fractions for Different Sensory Systems

no universal Weber fractio n that applies to allsensory systems. R ath er, there is considerablevariation suc h that certain sensory processesare very sensitive to change, wh ereas others are

Table 1.1

Sensory Dimension Weber Fraction (k)

Note. Small values ofk imply greater sensitivity indetecting changesof intensity. Adapted from "Psychophysics: I. Discrimination andDetection," by J. Engen, 1971 , in Woodworth & SChlossberg'sExperimental Psychology, Eds. J. W. Kling and L. A. Riggs, NewYork, NY: Holt, Rinehart & Winston; "On the Exponents in Stevens'Power Law and the Constant in Ekman's Law," byR. Teghtsoonian,1971 , Psychological Review, 78, pp. 71-80; "Differential Sensitivityfor Smell ," by W. S. Cain, 1977, Science, 195, pp. 796-798:"Psychological Dimensions and PerceptualAnalysis of Taste," by D.H.McBurney, 1978, inHandbook of Perception,Eds.E. C. Carterelleand M. P. Friedman, NewYork, NY:Academic Press.

75.....l!!-<::.~Cl:l

'" 50Olcac:'"1:'"a.

100

~~------------

o

Psychometric functions from difference threshold experiments in which the referencelight isset at progressively higher intensities.The lowest reference intensity (left curve)produces a small difference threshold, whereas the highest reference intensity (rightcurve) produces a much larger threshold . The bar lengths below the x-axis show therelative sizeof the differencethresholds for the three psychometric functions.

The difference threshold (tl I) is therefore nota constant value but some proportion (k) ofthe stimulus intensity (I).This prop ortion (k) isalso known as Weber's fraction .

Once the Web er fract ion is known, thedifference threshold can be easily calculatedfrom Web er 's law for any given intensi tyvalue. I3ut wh at is the value of k? This mustbe experimentally determined. The preferredway to do so is to determine the differencethresho ld at a numb er of different intensities,as we did in the experiment above. T he difference thresholds can then be plotted againstthe different values of int ensity to reveal astraight line (SideN ote 1.6).The slope of thi slinear function is th e Weber fraction (k). Forthe bri ghtness expe rime nt we just performed ,we wo uld have found th e value of k from theslope to be abo ut 0.08 . Thus, an 8% increase(or dec rease) in light intensity is sufficient toproduce a JND and allow us to detect thatchange in perceived bri ghtness.

Weber fractions fordifferent sensory systemsWe could have co nducted a similar differencethreshold experiment in any of the other sensory systems, such as taste, tou ch , hearin g, etc.,to determine their respective Weber fractions.This has indeed been done by psychophysicists since Weber's time , and some of the resultsare shown in Table 1.1. N ot ice that there is


not .Among the most acute of our sensory parame ters is the detection of pitc h where j ust a0.3% change in the frequency of sound is sufficient to cause a JND. On the other hand, thepercept ion of sound inte nsity (loudness) canrequire up to a 30% change in the stimulus forthat difference to be detected.

In general, the Weber fractions inTable 1.1 are accura te predicto rs of differe ncethresholds for a bro ad range of stimulus intensities. However, at the extreme situations ofvery high or low intensities, the value ofk cancha nge drama tically, suc h that the generalityofWeber 's law no lon ger applies (Gesche ide r,1984). This is tru e of all sensory dimensions.Alth ou gh the applicability of Weber's lawis limited to a certain range of intensities, itnevertheless remains one of mos t useful equation s in perceptual psycho logy.

5. FECHNER'S LAW

We rem arked earlier that one of Fechner'scentral goals was to obtai n the relationshipbetween sensory magnitude and stimulusinte nsity. We are now ready to complete thatstory. Fechner knew that to un cover the relations hip between those two parameters, it wasnecessary to know the way in whic h that function changed at progressively greater suprathreshold values (Fechner & Lowri e, 2008).As we have already seen, Weber 's law assertsthat highe r levels of suprath reshold intensityrequire a correspo ndingly greater change inintensity (ll l) to produce a change in sensation (ll S) that is j ust distinguishable UND) .But Fechner knew no thing abo ut the actual

magnitude of llS needed to produ ce a JND orwhe ther that value changed at different levelsof sensation.

Fechner's assumptionFechn er could not resolve this problem becauseit is simply impossible to measure sensations.N everth eless, he made a bold assumption.Fechn er proposed that all JNDs were producedby equal increment s in sensation regardless ofthe opera ting level (Fechner, 1860/1 966). Inother wo rds, exactly the same value of ll S wasneeded at all sensory magnitudes because theJND is a standard unit of change that representsa psychological constant. Fechn er was also wellaware of Weber 's results and the imp licationsthey had for his quest to determ ine the relation ship that he sought. Figure 1.6 (lefi side) showshow Fechn er 's assumption can be integratedwith Weber 's law. As shown, higher intensitylevels require a greater change in the physicalstimulus (ll l) to produ ce identical changesin sensation (llS) . In all of these cases, a JNDevent is presumed to occ ur through identicalchanges in sensation (Fechner's assumption)that are brought about by progressively greaterchanges in stimulus intensity (Weber's law).

Deriving the stimulus-sensation relationshipO nly one of the th ree possible functions thatwe explored in Figure 1.1, relating intensityand sensation, can acco unt for th is. Figure 1.6(right side) shows that the stimu lus-sensationrelationship mu st necessarily follow a logarithmic function . The intensity values from thedifference threshold experime nt in Figure 1.5are shown here on the x-ax is.The prog ressively

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-...~---------------The integration of Weber's law and Fechner's assumption implies that with increasing stimulusintensities, the difference threshold (~I) progressively increases but continues to be mapped ontoaconstant change insensation (~S) toproduceJNDS (left). Only the logarithmic function allows thiscondition to hold true (right). Fechner therefore concluded that the relationship between stimulusintensityand sensation isa logarithmic function .


greater change in ~I that was revealed in thatexperiment can now be related to Fechner 'sassumption of ~S being constant at all levelsfor a JND. Fechner could reach onl y on e co nclusion-the logarithmic function is the onl yone that will allow for ~I to increase accordingto Weber's law but still retain the same valuesof~S. Neither the linear nor exponential functions will permit this.

What we have just seen is a tour de forceof experimentation and insight. In the absenceofany direct means to study sensation, Fechnerwas still able to derive a fundamental relationship between sensation magnitude and stimulus intensity. As a tribute to his work , thatrelationship is now called Fe chner's law andis formally specified as

S = k • log (I)

where the constant k is related to, but not identical to, the constant in Weber's law. Fechner'slaw asserts that at low intensity levels, themagnitude of our sensations can change quiterapidly with small changes in stimulus intensity, whereas we become mu ch less sensitive athigher intensities. Indeed, at the very highestintensities, our perception of a stimulus shouldnot change appreciably, regardless of howmuch intensity is added.

These results were soon generalized acrossthe entire domain of perception such that therelationship between all physical events andconscious experience was taken to be largelylogarithmic in nature . This eventually turnedout to be a flawed conjecture, and indeed thelogarithmic function itself later became replacedby somewhat different functions as descriptors of the stimulus-sensation relationship.Neverth eless, the psychophysi cists of the 19thcentury continued to have a profound influen ceon perceptual psychology, even to this day, inboth theory and practice (SideN ote 1.7).

C. Modern PsychophysicsThe field of psychophysics flouri shed during Fechner and Weber's time. On the onehand, there was the sheer elegan ce by whichthe logarithmic relationship was established ,and on the other, there was the persuasivesimplicity of Fechner's assumption that JNDsrepresent fundamental and immutable unitsof sensory change. Fechner's law thus becamethe cornerstone of perceptual psychology, and

many psychophysicists simply became preocc upied with the logarithmic function as themaster descriptor of mental pro cesses. Nothingelse was acceptable.

And yet , there were many opponents aswell, some of who becam e quite influentialin their criticism of Fechnerian psychophysics (SideN ote 1.8). The main obj ection wasnot against the logarithmic relationship per sebut against the very notion that sensations canbe described by mathematical functions at all.One of the mo st scorn ful critics was WilliamJames, who believed that it was simply futileto put numbers on sensations (Richardson,2007) . Nothing about the empirical process,he argued, can allow any quantitative estimateof such private experiences as sensation, andtherefore any psychophysical law is fundamentally meaningless. In a classic rebuke, Jameswrote how terrible it would be if Fechnershould "saddle our Science forever with hispatient whimsies, and, in a world so full ofmore nutritious objects of attent ion, compelall future students to plough through the difficultie s, not onl y of his own works, but of thestill drier ones written in his refut ation ."

Fechner's supporters believed that thestimulus-sensation problem had been solved,whereas his critics believed that the probl emcould never be solved. Both intransigent attitudes in their own way produced a generaldecline ofinterest in the measurement ofsensation that lasted until the 1930s, when a Harvardpsychologist named Stanley S.Stevens began hispsychophysical work. Stevens boldly rejectedthe assertion that sensation cannot be measured.However, his approach was completely different from the German psychophysicists of the19th century. R ather than determine psychophysical laws through indirect procedures,Stevens proposed a set of direct methods forstudying sensation. And thu s began the era ofmodern psychophysics-an entirely new approachthat would galvanize the field and produce dramatic insights into sensory processing by the1950s, revealing psychophysical relationshipsthat in some cases did not even slightly resemble logar ithmic functions.

1. MAGNITUDE ESTIMATIONAND THE POWER LAW

Whereas Fechner believed that sensationscould only be measured indirectly throughdifference thresholds, Stevens believed that an

SideNote 11.7Fechner'stheory relating stimulus intensity tosensory experience marked the beginning ofexperimental psychophysics.He istherefore widely regardedas the father ofpsychophysics. Fechner himself was aneccentric character.The factthat he recorded the date ofhis psychophysical insight(22 October 1850) has resultedin Fechner Day celebrations onthis day insome psychologyquarters throughout the world.

SideNote 1_1_.8 _Some ofthe criticisms ofFechnerian psychophysicseven began toemerge from hiscontemporaries:

How much stronger orweaker one sensation isthan another, we are neverable tosay.Whether the sunisahundred orathousandtimes brighter than themoon,acannon ahundredora thousand times louderthan apistol , isbeyond ourpower toestimate.

Wilhelm Wundt, 1890

Stanley Smith Stevens(1906-1973)Harvard University Archives. Call # HUPStevens.Stanley S. (3)


SideNote 1--=1...:...9"-- _

Atypical instruction giventoasubject ina magnitudeestimation method might bethe following: "Youwill bepresentedwith aseries ofstimuli in irregular order.Yourtask istotell how intensetheyseem by assigning numbers tothem. Call thefirst stimulus anynumber that seems appropriatetoyou.Thenassignsuccessivenumbersinsuch awaythattheyreflect your subjectiveimpression" (Stevens, 1957).

exact relationship between stimulus and sensation co uld be directly obtained (Krueger,1989). Stevens was instrumental in establishinga set of pro cedures that are collectively knownas scaling. R ath er than taking the Fechnerianapproach of comparing stimuli and j udgi ngtheir differen ces, Stevens simply asked his subj ects to provide a dire ct rating of the sensationthat they expe rienced. This technique came tobe known as magnitude estimation.

Experimental design and outcomesThe subject is first presented with a standardstimulus, which is known as th e modulus, andtold that it represents a certain value, say 10.If for example the experiment required lou dness estimation, the subje ct would first experience the modulus and then provide a relativenumerical ratin g for othe r ton es of varyingintensity that are rand oml y presented (Stevens,

Table 1.2

Power Law Exponents for Different SensorySystems

Sensory Dimension Power LawExponent

Touch

Steady pressure (palm) 1.1

Vibration (250 Hz) 0.6

Temperature (cold) 1.0

Temperature (warmth) 1.6

Electricshock (fingers) 3.5

Taste

Sweet 1.3

Salt 1.4

Bitter 0.8

Smell

Coffee 0.55

Hearing

Loudness 0.67

Vision

Brightness (extended target) 0.33

Brightness (point source) 0.5

Estimated length (line) 1.0

Estimated area (square) 0.7

Note. The exponent values can be different for different aspectsof sensation within a particular system. Adapted from "On thePsychophysical Law,"by S.S.Stevens, 1957,PsychologicalReview,64,pp.153-181 .

1966). The numeri cal estimate represents thesubject's judgment of the sensation triggeredby that particular stimulus. In one variationof this method, first suggested to Stevens byhis wife, Gera ldine , subjects are not presentedwith a modulus to constrain their judgment s.R ather, they are free to develop their ownmodulus and assign numbers in proportion tothe sensation magnitude that they experie nce(Side N ot e 1.9).

A remarkable outcome of these experiments was the consistency with whi ch subjectsproduced their ratin gs and the similarity inthe trends observed among different individuals.The actual numbers ob tain ed were different across subje cts because they were free tochoose their own scale. But when the numberswere equated by takin g int o acco unt subjectvariability, it turned out that there was considerable agreeme nt amo ng different peoplewith regard to their sensory ratin gs for anygiven type of stimulus.

The magnitude estimation experime ntswere a direct challenge to Willi am Jam es' doctrine that sensations simply cannot be measured. Stevens showed tha t they ind eed canand that the data fit very nicel y into mathem atical functi ons that were co nsistent witha power law.The gene ral form of th e powerlaw is th e following:

S = k • I b

where S is the sensation experien ced by thesubject, I is the physical intensity of the stimulus, k is a so-called scaling constant that takesinto account the units used to represent thestimulus intensity, and b is th e expo nent (orpower) value . According to this relation ship,sensation is related to intensity raised to a certain power. But wh at is th e value of that poweror expone nt? It turned out that there was noon e general exponent value that served all ofthe senses. R ather, different sensory experiences are related to stimulus intensity by aparticular exponent (Stevens, 1957).Table 1.2provides some examples of power law exponents that were derived from experime ntson the various senses. As this table shows ,th ere is no uniformity in the expo ne nt values. Furthermore, for any given sense (taste isa good example), the actu al expo ne nt valuedepends on the particular aspect of that sensory dimension , for examp le, taste sensationsgenerated by salt, bitter, etc.


.....~-------

In one remarkable experimentby Borg, Diamant, Strom, andZotterman in1967, physiological recordings were madefrom the nerve that carriestaste information tothe braininapatient havingear surgeryunder local anesthesia.Thepatient was asked tomakemagnitudeestimations onseveral substances thatwereapplied tothe tongueat different concentrations.The resultsshowed that neural signalsinthetaste nerveand the subjective judgmentsofthepatientwere bothrelatedtoconcentration (intensity) by a power function withasimi lar exponent.

SideNote11.10

2.00.5 1.0 1.5Stimulus Intensity (I)

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2.0

physical stimulus becom es converte d into abiological signal (Stevens, 1962). According tothis idea, the neural output of sensory systemsmust follow a power law relationship with theincoming stimulus. The expo nent in th is caseis determined by the nature of the transformation at this site.

While there has been general supportfor th is notion from biological experime nts(SideN ote 1.10), there has also been a fairamo unt of criticism levelled at this so-calledsensory transducer theory . British psychologist E. C hristopher Poulton suggested thatpsychophysical magnitude function s are notonly related to low-level transformation processes but also to those at the high est levels ofthe mind whe re judgm ents are made on mental impressions (Poulto n, 1968). Accordin g toPoulton, differences in the power law exponent may be caused by variability in a number of different experime ntal situa tions thatin turn affect hum an judgment. Although thisissue is still not completely resolved , there hasbeen mu ch discussion on the impli cations ofthe power law and the facto rs that affect theexpo ne nt value . Scaling experi me nts, whichbecame an integral part of mod ern psychophysics, not only changed our understandingof how stimuli from the physical wo rld maponto our inn er world of percepti on but alsointroduced new ways of thinking about sensory processes.

Power law exponents

Althou gh sensatio n magnitude is related tostimulus intensity by the power law, the precise nature of that relationship is very mu chgovern ed by the exp onent. Table 1.2 showsthat for some sensory dimensions, the exponent is less than 1.0, whereas for others it isgreater. Figure 1.7 shows a graph of the twoextreme cases from Table 1.2- brightness forextended targets (0.33) and elect ric shoc k(3.5).The bri ghtness curve shows wh at is generally describ ed as a negatively accele ratingfunction . Brightness perception grows rapidlyat first with increasing light intensity, thoughfurther increments will gradua lly redu ce therate at whi ch perceived bri ghtness increases. Ina similar mann er, loudness perception is relatedto sound intensity by a negatively acceleratingfunction. But its expo nent value of 0.67 (seeTable 1.2) means that this relationship wo uldshow a somewhat steepe r rise with intensity(Stevens, 1966). N evertheless, the power lawrelationship for loudness perception is suchthat percept ion does not keep up with intensity. Indeed, to do uble loudness requires nearlya threefold increase in sound intensity, whereasfor brightness it requires nearly an eightfoldincrease in light inte nsity.

The power law relationship predictsquite different perceptual increme nts for ce rtain sensory param eters w he re the expo ne ntis greater than 1.0. For exa mple, as seen inFigure 1.7, th e sensation of electric shoc krises slowly at first but th en takes off dramatically with further increases in electric current . Certain other touch parameters, alongwith a few taste sensations, also display a similar expo ne nt ial relation ship . But wh at abo utthe case whe re the expo ne nt value is equalto 1.0, as with the visual impression of linelength ? This is shown by th e dashed line inFigure 1.7 . In suc h cases, there is an exac t perceptual relation ship with intensity such thatour mental impression changes exactly in stepwith changes in the stimulus.

Implications of the power law

Neuroscient ists and perceptual psychologists have postulated the origins of the powerfunction and the reason s why there can besuch large differen ces in th e exponent value.Stevens suggested that the power law reflectsthe operation of sensory systems at their lowest levels-that is, at the interface wh ere the

Fundamentals ofSensory Perception

SideNote 1....:.1 .::...c. 1:....:1'------ _

Psychophysical scaling procedures can be classifiedinto three general types. Inconfusion scaling,subjectsdetermine whether one sensation isgreater orless thananother. Fechner used this kindofindirect discriminative judgment inhis experiments.Thetechniqueofpartitionscalingrequires subjects tomake dir-ect judgments ofdifferences insensory magnitude byplacingthestimuli intoa limited num-ber of categories. Only the ratioscaling procedures, such asmagnitudeestimation, producemeasurements that can beplaced on a numerical scale.

2. PSYCHOPHYSICAL SCALING

The importance of magn itude estima tion as apsych ophysical techniqu e stems from th e factthat humans are remarkably good at bein gable to match numbers to what we perceive.As a result , several different scaling techniqueshave been developed to analyze our sensoryand perceptual functions in a qu antitativemann er (Side Note 1.11). With th e adve nt ofth ese techn iqu es, psych ologists soo n becam eint erested in measuring different aspec ts ofsensory func tion, not only within that particular domain but also in relati on to o the rsensory dim ension s (Baird & Noma, 1978).The technique of intramodal m atching,for example, produced new insights intohow sensi tive a partic ular senso ry system isto diverse kind s of stimulatio n. As we wi llsee in later chapters, mu ch of th at effort wasapplied in vision and hear ing to examine howperceived brightness was affected by differentco lours of lights or how perceived loudnesschanged for different ton es.

Cross-modal experiments

Stevens developed a rather unu sual pro cedure called cross- m o d ali ty m atching wh eresubjects were asked to compare stimuli fromone sensory modality to those of ano ther(e.g., loudness vs. bri ght ness, electr ic shock vs.vibration, etc.) (Stevens, 1966). What makesthis procedure unusual is that co mparisons arerequired not within a single sensory dim ension, wh ere the task is easier, but rather with

two enti rely different sensory experiences,whe re the task is to make a j udgme nt of equa lsensory magnitude. However, it turns out thatwe are also quite goo d at these kinds of comparisons (Luce, 1990).

Figure 1.8 shows the co llective results of10 different experime nts wh ere subjects wereasked to adj ust sound level until it match ed theperceived intensity ofa stimulus from anothersensory domain. The resulting equal sensation[unctions show different slo pes de pe ndi ngup on th e power fun ction for th e sensory parame ter that was bein g co mpare d. In fact, th eactual slope of th ese functions turned out tobe very close to the predi cted slope based onth e power law expo ne nts for loudness and th eparti cular senso ry param eter to whic h it wasbeing match ed. Thus, elec tr ic shock (whichhas a large expo ne nt value) shows a steep relation ship for cross-modal matching wi th lou dness, impl ying that small changes in elec triccurrent require large changes in sound sett ingfor a judgm ent of equality. The opposite istru e for cross- mo dal matches with bri ghtness(which has a small exponent value) . Theseresults not only validated the power law butalso showed the ut ility of psych ophysical scaling procedures in co mparing sensory function across different systems.

Prothetic and metathetic sensationsThe sensory expe riences that allow scalingsuch as tho se descr ibed above have a directunderlying relationship to the physical intensity of the stimulus. Perceptual qualities such

100

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40

RelativeIntensity of Stimulus

1IIIDIttr.. _Cross-modal matching between loudness and 10 other sensory stimuli. The slope of each equalsensation function isdetermined by comparingexponent values from the power functions ofloudnessand the particular stimulus. Adapted from "Matching Functions between Loudness and Ten OtherContinua,"by S.S.Stevens, 1966, Perception and Psychophysics, 1, pp. 5-8.


similarity is now represented by physical distance in a spatial map. This tech nique, whichis known as multi-dimensional scaling ,allows an investigator to peer into the underlying att ributes or qualities of th e stimulusthat prod uce similar or dissimilar perceptual expe riences . Multi-dimension al scalingis now well established as the tool of cho icefor pairwi se evaluatio ns of ent ities in suchdiverse fields as gene tics, linguistics, social sciences, and psych ology (Baird & N om a, 1978;Schiffman, R eynolds, & Young, 1981).

as brightn ess or loudness, for example, can beassociated with a numer ical value of physicalintensity. Sensory expe riences wh ere subjectscan make a judgment of "how mu ch" aretermed prothetic. However, there exists a different class of sensory experience that canno tbe directly linked to stimulus intensity. Colourperception is a good example,wh ere there is noquantitative difference between , say, the hues ofred or green.T hey produce two ent irely different kinds of percepti on , which thou gh linkedto the wavelength of light, canno t be scaled towavelength in a meanin gful way. Increasing thewavelength of light does not add to the magnitude of the sensory experience but rath erchanges it entirely. Such perceptual qualitiesare called metathetic.

[t turns out that prothetic pro cesses generally obey th e power law, but metath eti c processes do not (Gesc he ider, 1997). The reasonfor this is likely du e to th e way the two kindsof sensory dim ension s are processed by thebrain. Prot het ic percepti ons are beli eved torely on additive processes suc h that changes instimulus int ensity produce eithe r an increaseor decrease in the activity of the associatedsensory neurons. The collective beh aviour ofthis system is such that it follows the powerlaw.Metathet ic percepti on s, on th e othe r hand ,show a change in quality, and this in turn isassociated wi th th e substitution of one kind ofneural exc itatio n by ano the r.T he refore, in theabsence of an additive pro cess, th ere is littlescope for relatin g metath et ic experiences withthe stimulus in a quantitative mann er becausethere is no exac t relation ship between sensory impression and variation in the stimulus(Manning, 1979).

Multi-dimensional scalingPsychologists have had to devise some clevertechniq ues to analyze metath et ic percept s. lngeneral, these techniqu es rely on the noti on ofsimilarity or dissimilari ty (Bo rg & Groene n,2005). Consider colour percepti on as anexample. Subjects can be presented with thre ecolours at a time and asked to judge whichpair is the most similar-a procedure calledthe method oj triads.After enough data has beencollected with a sufficient nu mb er of colours,it is possible to represent the info rmation byway of a similarity map wh ere those colours that are perceived to be similar occupynearby position s, and tho se that are dissimilarare placed farthe r apart . T hus, psychological

3, SCALING OF NONSENSORYVARIABLES

O ur keen j udgme ntal abilities are not j ustrestr icted to the primary senses but extend tosome rathe r complex aspec ts ofhuman perception .The gene ral prin ciples of int ram odal andcross-mo dality matching may also be appliedto nonsensory variables wi thin the fields ofsocio logy, politi cal science , and esthetics. Thesame procedures that were used to scale lou dness and br ightness, for example, can also beapplied to questions such as the value of art,the imp ortance of certain occ upations, the seriousness of cri mes, etc. In other wo rds, a setof scaling meth ods can be employed in whatsome have called social psychophysics to establishmeasures of subjective magnitude in the areasof esthe tic preference or social/po litical opinion (Lodge, 198 1).

Discrimination scaling versus ratio scalingThe orig inal work in th is area actually beganwith Fechner and was later refined by Loui sT hursto ne in the 1920s (SideNote 1.12). T hebasic logic of Fechner 's sensory psychophysicswas used by Thurston e to study social issuessuch as preferen ces for nationalities and the seriousness of crimes (SideNote 1.13).T hurstonemad e the assumption that dispersions in j udgment represented a standard distance in subjective impression (T hurstone, 1959). His useof a nonsensory JND-like parameter producedfun ction s that retained the same math ematical quality as those seen in classical sensorypsychop hysics. Both T hursto ne and Fechn erthus made a fundamental assumption thateach increm ent in discrimination, measuredas a JND, produces equivalent increases in subj ective impression- in other wo rds, the variability in psychological un its is co nstant alonga linear psychological cont inuum. This kind

SideNote 11,12Fechner himself workedforsometime on problemsofesthetics and howtoapplytechniques from sensory psychophysics tomatters ofsocialopinion. In one experiment,heobtainedestheticjudgments fortwo versions of HansHolbein'sMadonna. Therewas quiteabitof controversy atthe time as towhichhad actually been paintedby Holbein.

SideNote 1_1_.1_3'-- _"Insteadofasking students todecidewhichoftwo weightsseemed tobe the heavier, itwas more interesting toask, forexample, whichoftwo nationalities theywouldgenerally prefertoassociatewith,or which theywouldprefer tohavetheir sistermarry, or whichoftwo offensesseemedto themtobe themoreserious" (Thurstone, 1959).


SideNote 1_1_.1_4 _If Fechnerhadchanged hisview and adopted Brentano'ssuggestion that the JND wasrelated tosensation level inamanner similar toWeber's law,then Fechner would actuallyhavebeen the first toderivethepower law function insensory science,which isnowwidelyaccepted.

of psychophysics became gene rally known asdiscrim ina tion scaling or confusion scaling(Torgerson, 1958).

T he alternative view that had led topsychophysical power functions was based onthe notion that equal units of discriminationalong the stimulus cont inuum did not represent equal distances but rath er equal ratiosalong the subjective continuum. The so-calledratio scaling procedures that were developedas a result, including Stevens' magnitude estimation technique, soo n found their way intostudies of social consensus as well (Ekman &

Sjobert, 1965). Among the more colourfulexamples in th is category are studies on thepoliti cal imp ortance of Swedish mon archs,the prestige of certain occ upations, the facto rsco ntributing to social status, the esthe tic valueof art and mu sic, the percept ions of nationalpower, and th e judged seriousness of certaincrimes (Chang & C hiou, 2007; Ekman, 1962;Vrij ,2000).

The above examples show how ratio scaling can be used to assess nonsensory variables.In a classic study, Thorsten Sellin and MarvinE. Wolfgan g showed that th ere is a gen eralconsensus across society on the perceivedseriousness of a variety of criminal offences(Sellin & Wolfgang, 1978). Using magnitudeestimation procedures, they showed that thetheft of progressively greater sums of mon eywas acco mpanied by growth in the j udgedseriousness. While this is hardly sur prising , itturned out that the power function for judgedseriousness grew with the amount stolen byan exponent value of on ly 0. 17.Thus, approx imately 60 times as mu ch mon ey needs to besto len in order to be perceived as being twiceas serious by most peopl e. Similarly, Sellin andWolfgang found that the judged seriousness ofcrime is related to jail tim e prescrib ed by thePennsylvania Penal Code by a power functionwith an expo ne nt value of0.7.These examplesillustrate how imp ortant societal issues can beaddressed by psychophysical scaling techniquesthat were ori ginally developed to study sensory processes.

Ekman's lawAs with sensory stimuli, discrimination scalingof nonsensory parameters produced logarithmic functions, wh ereas ratio scaling proceduresco nsistently yielded power function s. Goes taEkman at the University of Stockholm provided a theoretical account for this differen ce

(Ekman & Sjobert , 1965). Ekman prop osedthat detectable changes in sensation UND),rath er than being constant at all levels as proposed by Fechner, were actually related to sensation in a linear manner. In othe r words, therelationship between changes in sensation thatare j ust detectable at a parti cular sensatio n level(or magnitude) is exac tly analogo us to Weber 'slaw and can be stated as follows:

f1S = k • S

This relationship was actually prop osed as earlyas 1874 by Franz Brentano. By that tim e, however, the Fechneri an way of thinking so dom inated perceptual psychol ogy that Brent anosidea was largely ignored and remained withoutinfluence until Ekm an restored the validity ofthis principle in the 1950s.As a result, the relation ship is now known as Ekman's law.

Fechner's missed opportunityThe implications of Ekm an's law are quiteprofound.T he not ion that the JND is not constant at all levels of sensatio n marks a dramaticdeparture from the Fechneri an way of thinking. If we strictly adhere to Fechn er 's postulatethat the JND rem ains constant along the sensorycontinuum, then, as we saw earlier, logarithmicfunctions relating stimulus to sensatio n are thenatural conseque nce, given th e existence ofWeber 's law. If, however, Fechn er had appliedthe idea behind Weber's law to the sensoryco ntinuum as well and ado pted the view thatthe JND was not constant but rath er a constantratio of the sensory level, then he wou ld havederi ved the psychophysical power function . Inother wo rds, if both Weber 's law and Ekman'slaw are applied, then the math ematical outcome necessarily becomes Stevens' power law(SideN ote 1.14).

But is Ekman 's law valid? It has beenargued that since th e prop ortion ality rul e isgene rally tru e for th e physical sciences andsince it also applies in perceptual science byway ofWeber's law, it is reasonable to assum ethat a similar relation ship would hold tru efor th e sensory co ntinuum. Several empirica lstudies have provided suppo rt for th is view.For exa mple, R obert Teghtsooni an showedthat th e proportiona lity rule appe ared to bethe same for several different sensory expe riences (Teghtsoo nian, 1971). In other wo rds,th e value of k in Ekm an 's law, whic h wasfound to be 0.03, do es not change with thenature of th e sensory expe rience .This means

1I!lIDta.. _Background noise varies randomlyover time and therefore appears inthe form ofanormal distribution.When aweakstimulusispresent, the sensory magnitudes produced by itare added tonoiseandtherefore result inadistribution that isshifted tothe right.

that for all types of sensation, th e size of theJND expressed in subjective un its is approximately 3% of th e actual sensatio n magn itudeat any level.

4. SIGNAL DETECTION THEORY

To close this chapter, we return to the ideathat the threshold represents a fund amentalboundary between stimulus intensities that donot evoke sensation and those that do.We discussed earlier in Section B.2 that there is nosuch entity as a clear- cut, all-or- no ne absolutethreshold. R ath er, there is always some variability du e to inte rnal and externa l noise sothat the thresho ld in turn depends on thelikelihood that the signal exceeds this noiseto produ ce a detectable sensory event. Thismeans that the same stimulus may be detectedon some occasions and not on others. Theidea that eme rged from classical psychophysics is that the threshold itself can vary overtime. Modern psych ophysicists have soughtto identity the sources of this variability anddevelop new theoret ical foundation s that takeinto account nonsensory facto rs that can affectsignal detection .As we will later discover, thesedevelopments have revised our th inking abo utthe threshold co nce pt itself.

A major advance in this field was madein the 1950s by Wilson P. Tann er and JohnA. Swets who prop osed the use of statisticaldecision theor y to understand how humansbehave in a detection situation (Green &

Swets, 1989). This new model, called signaldetection theory (SDT) , uses statistical concepts that take into account cognitive factorsthat may influ ence a subject's decision-makin gprocess. Thus, th ere is not only a signal to bedetected, which in turn relies on the inh erentsensitivity of the sensory system, but also th edecision by the subject as to wh eth er a signalworthy of a positive response ind eed existed.

Basic foundations ofsignal detection theoryIn SDT, sensatio n magn itudes evoked by noise(N) and signal + noise (S + N ) are represent edas separate distr ibutions. A major source ofnoise is th e baseline firing of nerve cells thatproduces spo ntaneo us activity in sensory pathways. Because of the rand om nature of thisactivity, a probability plot of sensation magnitudes evoked by internal noise alone willappear in the form of a normal distribution, asshown in Figure 1.9. This rand om fluctuation


SensationMagnitUde

imp lies that sensory events triggered by noi sealone will vary with tim e. In an absolutethreshold experime nt, the subject is asked todetect a weak stimulus against this rand ombackground activity. Since the stimulus mustbe detected by the same noisynervous system, aprobability plot ofsensatio n magnitude evokedby the stimulus will also show a normal distr ibution because the signal must be added to thenoise distribution. Because of th is additivity,the combined signal + noise distribution mustalways lie to the right of the noise distributionalone, as shown in Figure 1.9.

The rand om variatio n in backgroundnoise poses an int eresting problem . When thestimulus to be detected is quite weak, the twodistributions will have considerable overlap,as is the case in Figure 1.9. Therefore, theremay be some instances wh ere the noise itselfmay be so high that it could be mistaken forthe signal, whereas in others the noise may beso weak that the signal is mistaken for noise(Swets, 1996). On each tri al, the subject musttherefore make a decision whe ther the evokedsensation was du e to a signal added to the noiseor to the noise alone. C learly there are two different processes at work here, and the subjectmust make a distinct ion between the effects ofone versus the othe r. But how can we parsethe effects of noise versus signal + no ise at thebehavioural level in a detection situatio n? Inothe r wo rds, how can we measure the relativeeffects of signal and noise through psychophysical meth ods?

Measuring the effects of signal and noiseIn early psychophysics experime nts, a stimulusof some intensity, however weak , was alwayspresent in each tria l. T he assumption was that


Table 1.3

Parameters Involved inthe Design and Executionofan SDT Experiment

the subject wo uld provid e a response basedsolely on whethe r the signal produced a detectable sensation. In terms of the SDT sche me, onlythe signal + noise parameter was being tested ,and psych om etri c functions therefore reflectedthe cumulative effects of that distribution (e.g.,see SideNote 1.5 on page 8).The way to testthe effects of noise alone in a detect ion experiment is to rand oml y give the subject a number of trials in which no stimulus is present.Allinstan ces of a YES respon se in such tria ls canthen be assumed to be the effects of noise alonebecause no signal was present. In other words,some internal process within the subject eitherproduced a sensation that coincided with thetria l and therefore led to a positive response or,alterna tively,an erroneo us j udgme nt was madein the belief that a sensory event had occ ur red.Either way, "no stimulus" trials allow researchers to get a hand le on the pervasive effects ofnoi se, regard less of its source, in that parti culardetection experime nt.

The possible outco mes in suc h a study areshown in Table 1.3. If a tri al did not containa stimulus, then the two possible responses ofthe subject can be categorized as follows.A NO

response is termed as a correct rejection andimpli es that at that mom ent in tim e, the noiselevel was not inte nse eno ugh for the subjectto judge that a detectable sensory event hadoccurred. A YES response on the other handimpli es j ust the opp osite and is term ed a false

alarm.T he subject indicated that a signal waspresent wh en in fact the sensation was onlyprodu ced by noise. If however a signal wasactually present in the tri al, then the effects ofsignal + noise in that event may be sufficientfor the subject to respo nd YES, which is termeda hit.The alterna tive possibility is that the subj ect responds NO, in whi ch case it is termed amiss because the subject failed to detect thesignal. Thus, there are only four possible outcomes in an SDT experime nt with two beingattr ibuted to the effects of the noise component and the other two to the effects of signal +noise (W ickens, 2001).

Criterion effects-general propertiesIf false alarms are th e product of noi se, and hit sare th e result of the combined effects ofsignaland noise, th en which point along the x-axisin Figure 1.9 can the se effects be attr ibutedto? In other words, how much sensation mu sttake place before th e relative effects of noiseand signal + noise yield a false alarm or a hit ,respectively? One of th e basic assumptionsof SDT is th at each subject establishes a setpoint or criterion <P) in a given detectionexperiment. That is, a certa in value of sensorymagn itude is chose n as a cut-off point th atin turn gove rns th e response. If on a parti cular tri al th e evoked sensation is gre ater thanthi s value, the response will be YES. If it failsto reach th at level, th e subject will respondNO. The mental process th at underli es eithe rdecision can in turn be triggered by noiseor signal + noi se. That is, on each tri al theevoked sensation can be attributed to eitherof th e two distributions, and th e subjec t mu stmake a judgm ent as to which one is co rrec t(Green & Swets, 1966).

The way that the criterion interacts withthe noise and signal + no ise distributions isshown in Figure 1.10. For clarity, the two distributions are vertically offset in this figure.Let us assume that the subject has ado pted acertain criterion value, as shown by the vertical line in this figure. If the sensory magnitude excee ds the criterion, then the subjectwill always respond )'ES. However, this decision may be eithe r a hit (stimulus was actuallypresent) or a false alarm (stimulus was absent) .The area under the noise distribution to theright of the criterion stipulates the probabilityof false alarms that will be seen in this experiment from noise tri als alone (SideN ote 1.15).Similarly, the area under the signal + noise

Absent NoiseCorrect Falserejection alarm

SignalPresent + Miss

Noise

ResponseSignal Distribution NO YES

Note. In an SOT experiment, the subject must answer either YES orNOas to whether a detectable or discriminable stimulus was perceived inagiventrial. However, thetrial mayor may not containastimulus. If thestimulus is absent, then the relativeeffects ofnoiseare being assessed, and the two possible answers are termed falsealarm and correct rejection. Ifastimulus ispresent inthe trial, thentheeffectsof thesignal + noise distribution are being assessed, andthetwo possible answersaretermed hitandmiss.

SideNote 1....:.1..:..... 1:....:5'--- _

Thelikelihood that a YESresponse will bedeterminedby noise alone isgiven by thecumulative probabilities ofallthe points onthe noise distribution that lieto the rightofthe criterion. Inmathematicalterms, this amounts todetermining the area under this portion of the noisedistribution.


NOresponses YESresponses

SideNote 1....::.1 ..::..... 1:....:6=--- _

We need not showthe ratesfor correct rejection since it issimply 1 minus the false alarmrate. Similarly, the miss rateneed not be shown since it isalways 1 minus the hitrate.

0.36

0.91

FalseAlarm

en u 30% 0.09:::J 0"5 0

E si:

~t5 :.:J 70% 0.64

The criterion level (~) established by each subject determines the sensation magnitude that mustoccur for a YES response. The interaction of B with the two distributions determines the relativeproportionofeach of thefourpossible outcomes inan SDT experiment. The noiseandsignal + noise.distributions are shown at different vertical levels for clarity.

~------------------

Criterion (B)

Sensation Magnitude

...

and simply defines th e sensory magnitude thatwill be required under the circumstances fora YES response. For any given pair of noiseand signal + noi se distributions, the criterionvalue will in turn spec ify th e rates of hits andfalse alarms (W ickens, 200 1).

Table 1.4

The Effects ofExpectation on DetectionPerformance inan SDT Experiment

Note. If the subject is awarethat the likelihood of stimulus appearance is low, she will adopt a conservative criterion that will in turnproduce low hitand false alarm rates. The opposite happens if thesubject hasahigh expectationofstimulusappearance becauseshewill then adopt a liberalcriterion.

Criterion effects-expectation

Is it possible for the subject to adopt a differentcriterion value ? Let us consider wh at wouldhappen if we conducted two experime nts, onein which we told the subjec t that a stimuluswill only be present on 30% of the trials and asecond experiment in which we to ld the subject that the stimulus will be present on 70%of the trials. In the first experiment, the subject will not expect a stimulus on the majority of trials and therefore will likely adopt aconservative criterion. In other words, thecriterion value will shift to the right of the oneshown in Figure 1.10, implying that the subject will only choose to respond YES whe nthe evoked sensory magnitude is quite large.In the second experime nt, a more liberal criterion will be ado pted, reflecting the higherprobability of stimulus appearance . The criterion will now move to the left of the oneshown in Figure 1.10. C ompared to the firstexperim ent, mu ch lower sensory magnitudeswill now be sufficient to elicit a YES respon sebecause the subject will expect more trialsto contain a stimulus. T hus, depending on aninherent expectation of stimu lus appearance,the subj ect will be either more or perhaps lessinclined to give a positive answer on each trial,even though none of the other parameters inthe experiment have chan ged .

Both situations will affect the hit and falsealarm rates. As we shift the criterion more andmore to the right (i.e., redu ced expec tation),there will be fewer instanc es of false alarmsas well as hits. This is shown by the data inTable 1.4 wh ere a stimulus appearance probability of 30%, and the acco mpanying rightward (conservative) criterion shift, results inrates of 0.09 and 0.36 for false alarms and hits,respectively (Side N ote 1.16).When the subjectis notified that stimulus appearance probability will be set at 70%, the accompanying leftward (liberal) criterion shift results in higherrates of false alarms and hits- 0.64 and 0.9 1,respectively.The bottom line is that the criterion level adopted by the subject is changeable

distribution to the right of the criter ion givesthe probability of hits that will be observed intrials that contained the stimulus. As we cansee in Figure 1.10, the number of hits will befar greater than false alarms in this parti cularsituation, given the nature of the two distributions and the criterion value that was ado ptedby the subjec t.

1I!IIIIIItla.~ _

Uberal

Icrite<iooJl7\\~

0.2 0.4 0.6 0.8 1.0Probability of False Alarm

..0.2

0.8

1.0

Criterion effects-motivationIn addition to stimulus expectation , th ere areother factors that can affect a subject's criterion and therefore also influence the dete ctionof weak stimu li. An especially powerful factoris motivation (Swets, 1996). Consider a situa tion where a subj ect is paid to parti cipate in astimulus detection experime nt in which th ereare neither pen alties for wrong answers (i.e.,false alarms) nor rewards for co rrect ones(i.e., hit s).The experimenter is ent irely at themercy of the subject, hoping that the subjectwill give a conscient ious effort despite bein gguaranteed a certain amount of money formerely participating. Let us make this experiment a little more interesting. As in all SDT

experiments, we give a certain number oftrial s that will contain a very weak stimulus (i.e., signal + noi se tri als) and others thatwill not (i.e., noi se- onl y tri als). But now wewill tell the subject that paym ent is co nt ingent upon performance in both sets of tri als.That is, ever y tim e there is a correct respon seto a signal + noi se tri al (hit), the subject willbe rewarded. However, there will be a penalty if an incorrect respon se is given in a noi setri al (false alarm). This way we will ensurethat the subject will not arbitrarily respond

-:;: 0.6o

~:Etile 0.4c..

The receiver operating characteristic (ROC) curve plots therelative effects of hits vs. false alarms for a signal of fixedintensity. Changes in criterion produce hit and false alarmrates that fall on different points of the ROC curve. A liberalcriterionappears toward the left end of the noiseand signal+ noisedistributions (seeinset),which inturn produces relatively high hit and false alarm rates.Aconservativecriterionproduces the opposite result and maps onto the bottom endofthe ROC curve.

The ROC curveIn a typical de tect ion experime nt, several hundred trials are given that fall either in the noise(stimulus absent) category or in the signal +noise (stimulus present) category. The actualproportion of trials in each category is set inadvance and communicated to the subject. Aswe have just seen, the subject establishes a criterion based on this information, whi ch in turnwill imp act performance. A convenient way ofillustrating tho se effects is by way of a receiveroperating characteristic (ROC) cur ve (Egan,1975; Green & Swets, 1966). An exampl e of anRO C curve that takes into account our resultsis shown in Figure I .II. So far, we have beeninterested in two outcomes-false alarm s andhits-that tell us how much the noise and signal+ noise distributions contribute to detectionperformance. An ROC curve plots the probabilities of these two factors with false alarmsrepresented on the x-axis and hits on the y-axis.Each point on an RO C curve is therefore specified by the subject's criterion since that determines the relative values of hits and false alarmsin an experiment.

The two experimental situations discussedon the previous page produced different criterion levels because ofdifferent stimulus expectation s. The resulting hit and false alarm ratesfrom Table 1.4 are shown in the RO C curve ofFigure 1.11. The experiment with the high erstimulus appearance probability (70%) produced a liberal criterion, whi ch on an ROC

plot appears as a point toward the upp er end ofthe curve. Had the stimulus appearance probability bee n set even higher, then this point toowould have edged farther up the RO C cur ve inresponse to the adoption of an even more liberal criterion. In contrast, the experiment withthe lower stimulus appearance probability (30%)produced a more conservative criterion, whi chon the RO C curve shows up as a point towardthe lower end. If we had chosen an even lowerstimulus appearance probability, then this pointwo uld have edged farther down the RO C curve.All intermediate values of stimulus appearancewould have produced hit and false alarm ratesthat map onto the RO C curve between the twothat have been outlined. The important feature of an RO C curve is that it illustrates theeffects ofdifferent criterion levels in a detectionexperiment. As the criterion shifts from low tohigh, the probabilities of hits and false alarmswill change and when plotted in relation toeach other will prod uce the RO C curve.



YES throughout the expe rime nt because ofthe false alarm pen alty or similarly respondNO throughout because th en rewards willnot accumulate. In short, we will now havea highly moti vated subject who will try veryhard to distingui sh the signal from noi se trials(Lu & Dosher, 2008) .

It turns out that th e way we set up th erewards and pen alt ies wi ll influ en ce th e subject 's criterion in th e same way th at we foundfor stimulus expec tanc ies.Table 1.5 shows twopossible payoff co nditions that may be used . Ifthe subject is told in advance that each hitwill be worth 50¢ and eac h false alarm willincur a penalty of 10¢, th en we will create agreate r tenden cy for YES votes because th edisparity in reward vs. pen alty will assure agreater payoff in th e lon g run . In o the r wo rds,the subject will ado pt a liberal cr iterion. Ifhowever we reverse th e paym ent conditions and imp ose a pen alty for false alarmsthat is mu ch greater than th e reward for hits,then th e subjec t wi ll tend to be very cautious and take fewe r risks. The subject nowadopts a co nservative crite rion. If we takethe hit and false alar m rates from th ese twositua tio ns and plot th em on an RO C cur ve,we will find a situa tio n analogous to that seenin Figure 1.11 .T he first payoff co nditio n willplace th e criterion value more tow ard the leftside of th e noise/signal + noise distr ibution sand therefore will produce hit and false alarmrates that will plot toward th e upper end ofthe RO C curve. The seco nd payoff co ndition will produce a crite rion more towardthe right side of th e two distributions, andthis wi ll yield a point on th e lower end ofthe RO C curve. If we employed othe r payoff co nditions, th en th e reward /pen alty ratiowould produce appro priate points elsewhe reon the RO C curve. In effect, we find thatmotivation al states induced by different payoff co nditio ns produce crite rion shi fts th atare similar to th ose we saw on th e previou spage for stimulus expec tancies.

The problem with thresholds

The two facto rs that we have co nsideredthus far-stimulus expec tancy and motivation-have nothing to do with the signal itself(SideNote 1.17). In the experime nts considered above, the signal strength was keptconstant th roughout, and the only parameter that changed was the non sensory factors.And yet, we have show n that these factors can

prod uce considerable response bias that inturn affects the probability of signal detection .T hese results call into question the very existence of thresholds that supposedly demarcatethe onset ofdetectable sensations because clearlysuch boundaries are susceptible to the effects ofnonsensory variables (King-Smith, 2005).

In classical psych ophysics, the physicalintensity of a stimulus that produced YES

respon ses 50% of the tim e was taken as theabsolute threshold of detection . Given whatwe now know abo ut the hit rate being susceptible to cr iterion effects, th e actual int ensity value producin g 50% YES respon sessho uld th erefore also vary. In other wo rds, thepsychom etri c functi ons th emselves sho uldchange with the subject's criterion, and therefore no single all-e nco mpassing thresholdvalue can be derived (SideNote 1.18). Giventhat detection performance relies so heavilyon the effects of non sensory facto rs, the veryco nce pt of an immutable absolute thresholdhas become meanin gless.

Signal intensity and detection sensitivityAccording to SDT, there is a certain inh erent sensitivity that applies to the opera tionof sensory systems. Human performance indetection experime nts is governed by thatsensitivity as well as various nonsensory factors. If the detectability of sensory events is

Table 1.5

Payoff Conditions forTwoDifferentSOT Experiments

S· I Payment Conditions forIgna

a YES Response

Experiment 1 Experiment 2

Absent-10¢ -50¢

(falsealarm)

Present •(hit)

Liberal Conservativecriterion criterion

Note. In thefirst experiment,hitsare rewardedat afar greater levelthanthe penalty for false alarms, leading tothe adoptionof aliberalcriterion. Inthe second experiment, the penalty for false alarms isfar greater than the reward for hits, leading to the adoption of aconservative criterion.

SideNote 11.17An often-used example canserve todistinguish the relative effects ofexpectancyand motivation. Aperson whoisincharge ofobserving aradarscopetodetectenemyaircraft is highly motivated toensurethat a true signal doesnot go undetected becausethecost for that failure istoo high.Thus, we have an individualwho will likelyadopt a liberalcriterion basedonthis factoralone. However, the likelihoodof asignal actually appearing isquitesmall sinceenemyaircraftusuallydo not pop uptoooften.Therefore the criterionwill tendtoshift toward more conservative levels that will reducethelikelihood ofahit.Nevertheless,given the importance ofsignaldetection (and thepenaltyfor amiss) , the probabilityfor ahit iskept highand must beaccompanied by a relativelyhigh falsealarm rateas well.

SideNote 1_1_.1_8'-- _Early psychophysicists wereaware that biasing factors werepresent in their absoluteanddifference threshold experi-ments and thatthese factorscouldinfluence theirdata. Oneway toreduce bias was tousehighly trained subjectswhocouldberelied upon to makeaccuratedetection jUdgments.Anothertechnique was theuseof so-called catch trials, inwhichnostimulus was present.Thefalsealarmrate taken fromthese trialswas thenused toscalethedata fromstimuluscontaining trials.

~undamentals ofSensory Perception

susceptible to higher-level mental functionsthat influence our j udgments, then how is itpossible to gather insight into de tec tion sensitivity that is uncontaminated by suc h factors?To answer th is, we have to take a closer look atthe noise and the signal + noise distributionsin relation to each othe r.

Thus far we have said very littl e abo utthe stimulus itself and have vaguely referredto it as a weak signal that is added to noiseand whose de tec tability is assessed by way ofa simp le" YES-NO" experiment. The signal +noise distribution that we have become familiar with is actually a reflection of two different parameters-signal int ensity and detectionsensitivity. To understand this, let us co nsiderthree different stimuli, each one bein g of aprogressively grea ter inte nsity. T he signa l +no ise distr ibut ion of each stimulus progressively shifts farther away from the noise distr ibuti on, which does no t cha nge becausethe underlying effects (e.g., random noise inth e nervou s system) are not disturbed. T his isshown in Figure 1. 12 wh ere the separatio nbetween the two distributions is quite small in

d'

the top panel (weak stimulus) and very largein the bottom one (strong stimulus) . A measure of the separation between the two distr ibution s is taken at their peaks and is denot edas d ' (pro no unce d d-prillle) (Swets, 1996).

The three pairs of distributions in Figure 1.12 can be interp reted ano the r way. Let usassume that the signal is now kept co nstant andinstead three different individuals are beingtested, each one having a different inherentsensitivity to the stim ulus.The more sensitive aperson is to this particular stimulus, the grea terthe sensatio n evoked by that stimulus. Sincethe signal + noise distr ibutio n is a probability plot of sensory magnitudes, a highly sensitive individual will have a distribution shiftedfarthe r to the right and away from the noisedistrib ut ion, as shown in the bo ttom panel ofFigure 1.12. In other words, the same stimuluswill generate greater sensory magnitudes in amore sensitive person and therefore produce amore rightward shifted signal + noise distribution. In this context, a large d' value is taken torepresent an individual wi th a high detectionsensitivity. The less sensitive the subject is to

Sensation Magnitude

~~-----------The relative positions ofthe noise and signal + noise distributions are determinedby signal intensity and detection sensitivity. The signal + noise distribution isprogressively shifted to the right and away from the noise distribution as signalstrength increases. A similareffect is seen if the signal is kept constant but thedetectorbecomes more sensitive.The relative separationof thetwo distributions istakenat their peaksand denoted as d'.


INVESTIGATION

SideNote 1-'.1-'.,1'-'9'-- _Byconvention, d' isexpressedas standard deviationunits ofthe noise distribution.Thus, d'valuesof0.5, 1.0,3.0, etc.,represent respective factors ofstandard deviation (or z-score).

1.00.80.6

levels can operate independently upon thesedistributions to produce different experimentaloutcomes of hit and false alarm rates.T his ideais illustrate d in Figure 1.13 where four different pairs of noise/ signal + noise distr ibutio ns are shown, each with a different d' valueranging from 0.5 to 3.0 (SideN ote 1.19) .T heaccompanying ROC cur ves show the expecteddetection performance if we apply a continuously variable criterion to each of these sets ofdistributions.

As an exampl e, let us consider the twoextreme cases. If d' = 3.0, then the large separation of noise and signal + noise distributionswill ensure that the hit rate far exceed s the

0.4

Probability of FalseAlarm

0.2

o

1.0 ~---::--::::==----::::::::::==------:::::::::::::;;;~

Cognitive Factors That Influence Perception

We see cognitive factorsat play all the time in our ability toperceive stimuli. In fact, two people can be inthe same place experiencing the same stimuli yet perceive different things. For example, say you aredriving with a friend and a dog runs out in the middle ofthe road.You as the driver are more likely tosee thedog first and react accordingly.Why? (See SideNote 1.17 for somehints.)

-....~-----------Afamily ofROCcurves that are generated by different values ofd'.The greater thesensitivity toa particular stimulus, the greater the separation of the noise and thesignal + noise distributions.A larged' value produces an ROCcurve that isbowedtoward the upper left. As the two distributions get closer (smaller d' values), andeventually overlap, the ROC curve flattensoutand becomesastraight line.

the stimulus, the closer the two distributionswill be with respect to each ot her, and accordingly d' will be smaller (Wic kens, 200 1).

-:i:o~zsctI.cec..

Sensitivity and d'

The importance ofd' is that it provides a numerical estimate of a person's sensitivity andtherefore allows comparisons among differentindividual s. Unlike th reshold values that canchange with criterion levels, it has been shownthat d' remains relatively robust and is unaffectedby nonsensory factors. In other words, d' as ameasure of sensitivity simply stipulates therelative separation of the noi se and the signal+ noise distributions. The different criterion


false alarm rate for mo dera te to liberal cr iterion levels (i.e., rightward criterio n placem ent).The RO C curve will bow upward to reflect afar greater proportio n of hits in co mparisonto false alarms . If however the two distributions are very close togeth er (e.g., d' = 0.5),then there will be a greater similarity in hitand f.1 lse alarm rates because of the closenessof the two distribution s. This situation willproduce a weakly bowed RO C curve . T hus, asthe noise/ signal + noise distribution s approacheach other, the RO C curves will progressivelyflatten out.The limit is reached wh en the twodistributions overlap each other (i.e., d' = 0)and produce a straight line. In this case, eitherthere is no signal or the subject is simply incapable of dete cting the stimulus. In eithe r event,detection performance will be random, andthere will be equal prob abiliti es of hits andfalse alarms regardless of the criterio n.

Procedural aspectsSDT has becom e highly popular amo ng perceptual psych ologists because it provides bothan estimate of the relative sensitivities of different individuals to a part icular stimulus and ameasure of how non sensory factors may influence the judgme nts of vario us subjec ts in itsde tec tion.The purpose in any SDT experime nttherefore is to obtain values of both d' and 13.Both of these parameters can be quite easilydetermined once we know the hit and falsealarm rates from a signal detection expe rime nt(Mc N icol, 2004). For any given subject, therewill be only on e RO C curve that will applyin that experime nt since the stimulus intensity is fixed and the individual has a parti cularinh erent sensitivity to that stimulus.The 11l1l11

erical descriptor of that sensitivity, d' , can beobtained by graphically determ inin g whichone of a family of RO C curves co ntains thesubject's hit and false alarm rates. The onlyvariable now is the criterio n. If the subjectemployed a liberal cr iterion, then this pointwo uld be located toward the upp er right ofthat part icular ROC curve . If a co nservative criterion was employed, then this point wo uld be

toward the lower left.We can obtain a measureof the cri terion used by the subject becauseall possible points will map onto a single RO C

curve that in turn will be governed by thatperson 's de tec tion sensitivity.

SDT provides insight no t only into theint rins ic sensitivity of the sensory system butalso into the mot ives, expectancies, and othe rhuman psychological factors that influencethe decision -making process (Macmillan &

Creelman, 2004). However, there may be situation s where a sensitivity measure is requ iredwithout the influen ce of such nonsensory factors. In such cases, the use of forced cho iceprocedures allows rapid estimation of only thesensitivity parameter. In the two-alternativeforced ch oic e (2AFC) procedure, two presenta tions are made on each trial.The subject istold that one of the present ations will containthe signal and the other will not . The task isto indicate which presentation contained thesignal.The impact of criterion effects is minimized beca use the subject knows that one ofthe two presentations will definitely contain astimulus. T he only experimental outcome toconsider then is the hit rate, which can fluc-'tuate between 0.5 (random guessing) to 1.0(perfect performance).The proportion of correct respon ses can then be used as a measure ofsensitivity because nonsensory factors do no taffect the hit rate in this situation.

A valuable feature of the 2AFC procedureis that the exper ime nter knows whe the r or notthe subject is responding correctly in a part icular trial. This has allowed more elaborate versions of this procedure to be develop ed . In thestaircase procedure, the stimulus level canbe varied in relation to the subject's responses.For example, stimulus int ensity may be continu ally increased as long as the subject is making incorrect responses. Similarly, the intensitycan be progressively decrease d when only correct responses are given. This alterna tion instimulus intensity is cont inued until a specifiednumber of response reversals take place. Thesignal inte nsity at this poi nt can be used as ameasure of sensitivity.

1. There is a rich history of scienti ficresearch on sensory perception, beginningwi th the German psychophysicists of the19th century. Their goal was to arrive ata quant itative relationship between stimulus inte nsities and sensation magnitudes.Knowin g the quantitative relationship hasseveral advantages, though it is difficult toobtain directly because of our inability tomeasure sensation. The approa ch taken bythe German scientists was to first obtaintwo parameters-the starting point andthe slope of the function. This informationco uld then be used to reveal the natureof the math ematical relationship betweenstimulus and sensation.

2. Fechner developed several psychophysical techniques to determine theabsolute threshold (w hich repre sents thestart ing point of the stimulus-s ensationrelation ship) and the difference threshold (whic h provides insight into howthe slope of the stimulus-sensation fun ction changes at suprathreshold levels).The Method of Constant Stimuli provides the most accurate data, wh ereas theMeth od of Adju stm ent is the easiest toco nduc t and produces the fastest result s.Psychophysical experime nts with the setechniques have shown that humans donot behave as ideal detectors but inste adshow a gradual progression of responsiveness wh en increasing some physical parame ter related to the stimulus.

3. Weber was interested in the gradation ofsensory experience by studying how thedifference threshold itself varied with thestimulus level. He found that the difference threshold is not constant but actuallyincreases linearly with stimulus intensity (known as I#bers lalV). To derive thestimulus-sensation relationship, Fechnermade the assumption that a detectablechange in sensation (LlS) caused by thedifference threshold (LlI) remained constant at all levels of sensory magnitude.T his insight, in conj unction with Weber'slaw, led Fechner to postulate that sensationmagnitude is related to stimulus intensityby way of a logarithmic function (knownas Fechner's law).

4. The era of modern psychophysics beganwith Stevens who believed that sensory


magnitudes could be directly determinedthrough quantitative methods. His technique of magnitude estimation led him toestablish the pOlVer law, which states thatsensor y magnitude is related to stimulusintensity raised to an exponent value thatis generall y less than 1.0, though somesensory experiences (e.g., electric shock)have an exponent greater than 1.0.

5. Psychophysical techniques can be usedto determine quantitative relationships within the same sensory system(intramodal matching) or across sensory systems (cross-modality matching).Whereas techniques such as magnitudeestimation can be used to assess sensations that have a dire ct relationship to thestimulus (prothetic sensations), a differentset of techniques such as multi-dimensionalscali"g must be used to assess those sensations that are entirely altered when astimulus parameter is changed (metathetic sensations).

6. The same psychophysical principles andtechniques used to understand sensory perception can also be used to assess variousnonsensory questions in the domains ofeconomics, marketing, sociology, and politics.A power law function is derived in allcases where the exponent value providesinsight into the underlying relationshipbetween the variables being probed.

7. Signal detection theory (SDT) is based onstatistical concepts that examine the possible relationships between the stimulus(signal) and the underlying noise. Theprobability distributions of the signal andsignal + noise profiles provide the basis forestimating the behaviour of individuals interms of their criterion level, expectation,and motivation in a psychophysical setting.The way in which noise and signal + noisecan affect detection performance is givenby the receiver operating characteristic (ROC)curve . SDT experiments have shown thatthere is no exact threshold value for anysensory parameter but rather the threshold is something that is affected by othernonsensory parameters. Consequently, amore reliable parameter is d', which provides a more robust numerical estimate ofa person 's sensitivity that is unaffected bynonsensory factors ,

metathetic, 17Meth od of Adjustment , 6Method of Constant Stimuli,

7Method of Limits, 6miss, 20multi-dimensional scaling, 17noise, 19ogive,7power law, 14prothetic, 17psychometric function , 7psychophysics, 6ratio scaling, 18receiver operating

characteristic (ROC), 22response bias, 23

6. What is the fund ament al differencebetween a prothetic and a metathetic sensation? Provide some examples other thanthe one s discussed in this chapter.

7. W hat would Weber's law have to looklike for the stimulus-sensation function tohave an exponential profile?

Fundamentals of SensoryPerception

absolute threshold, 6correct rej ection, 20criterion (P), 20cross-modality matching, 16d' (d-prime), 24difference threshold, 6discrimination scaling, 18Ekman's law, 18false alarm, 20Fechner's law, 13function,Shit, 20ideal detector, 7intramodal matchin g, 16just noticeable difference

OND),9magnitude estimation, 14

1. What are the three pri ncipal advantagesof obtaining a math ematical relationship between stimulus intensity and theresulting sensation magni tude?

2. What are the parameters that preventhuman subj ects from beh aving as idealdetectors?

3. What is the difference between the absolutethreshold and the dijferellce threshold? Whydid Weber have to undertake multipleexperiments on the difference thresholdto derive the law that bears his name?

4. What was the fundament al problem inFechn er's assumption on the cons tancy ofthe JND at all sensory magnitud es? CouldFechner have derived his law witho ut thisassumption?

5. How did modern psychophysics departfrom classical psychophysics in term s ofboth its methodology and its core und erlying principle?

8.

9.

scaling, 14sensory transducer theory, 15signal, 19signal detection theory (SOT),

19staircase procedure, 26step function, 7stimulus, 4sub threshold, 6suprathreshold, 6two-alternative forced choice

(2AFC),26

Weber's fraction (k), 11Weber's law, 10

How does Ekm an's law differ from theassump tion of JND constancy made byFechner? Is it possible to verify Ekm an'slaw with absolute certainty?

What are the key departures in the signaldetection theory model from the conceptof an all-or- none threshold? What arethe different variables that can affect thethreshold? W hat is the advantage of usingd' as a measure of sensitivity?

• Borg, I. , & Groenen, I~ (2005). Modernntultiditncusionat scaling: Theory and applications. New York, NY: Springer.

• Gescheider, G. A. (1997). Psychophysics:The [undamentals. Hillsdale, NJ: LawrenceErlbaurn .

• Green, D. M., & Swets, j. A. (1989). Sigl/aldetection theory and psychophysics. New York,NY: Peninsula Publishing.

• Heidelberger, M., & Klohr, C. (2004).N ature from within: Gustav Tlieodor Fechnerand his psychophysical wotldview. Pittsburgh,PA: University of Pittsburgh Press.


• Marks, L. E. (1974). Sel/sory processes:TIle ucui psychophysics. New York, NY:Academic Press.

• McNi col, D. (2004). A primer 4 signa!detection theory. Hillsdale, NJ: LawrenceErlbaum.

• R ichardson, R. D. (2007). Willialll[ames:11/the maelstrom 4 A merical/ Modernism. N ewYork, NY: Mariner Books.

• Stevens, S. S. (1986). Psychophysic:Introduction to its perceptual, neural, and socialprospects. New Brunswick, NJ:TransactionPublishers.

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