Principles of Perceptual Measurement

In this chapter . .. A SCIENTIFIC BASIS OF PERCEPTUAL MEASUREMENT • You will discover the main controversies that arose instudies todetermine the relationship between physical stimuli and the sensations they evoke within us. B CLASSICAL PSYCHOPHYSICS You will also learn how todescribe and give examples ofthe human ability to 1. Psychophysical Methods estimate sensations. 2. Absolute Threshold • You will examine famous classical psychophysicists, such as Gustav Fechner 3. Difference Threshold and Ernst Weber, and the experimental methods they designed to study 4. Weber's Law sensory perception . You will become familiar with psychometric function 5. Fechner's Law and how it can be affected by both sensory and nonsensory parameters . C MODERN PSYCHOPHYSICS • You will become familiar with the difference threshold, which determines how 1. Magnitude Estimation and the much extra stimulus is needed in order tojustnotice a change. You will also Power Law become familiar with Webers law, which states that the difference threshold 2. Psychophysical Scaling does not remain constant as the stimulus increases in intensity; and Fechner's 3. Scaling of Nonsensory Variables law, which was found tobe flawed but transformed the field ofsensory science 4. Signal Detection Theory and remains influential to this day. • You will learn about Stanley S. Stevens, who began the era ofmodern psycho­ physics.You will also learn about the method of magnitude estimation, which led tothe development ofthe power law. • You will study the difference between prothetic and metathetic stimuli and how they are assessed. Finally, you will become famil iar with differences in human sensitivity to stimuli and how researchers use techniques to compare those differences in terms ofz-scores,

Tru e SciCIlCC investigates and bri1 t,

We are co nstantly being bombarded by energy indi viduals, and therefore the data can be sci­ from the physical wo rld, whether it is in the entifically validated (Gescheider, 1997). We form of visual, auditory, tactile, or chemose n­ will return to this deb ate and explore the sory stimulation. T hese stimuli are very real issues on both sides later in this chapter. But and can be measured . The inte nsity of light first, it is necessary to learn some thing abo ut reflected by an object, for example, can be the experimental approaches to studying sen­ exactly determined with a device called a ra di­ sory processes, the kinds ofproblems to which ometer.T his device will spec ify the intensity in a they can be applied, and the infor mation they set of units for wh ich it has been calibrated. In reveal about the op eration of the brain. What general, all physical stimuli that we are capable will follow is a set of core concepts that will ofperceiving can be spec ified in real terms that surface throughout this book as we examine give us a value acco rding to some dim ension of each of the sensory systems in detail. its physical reality. But what abo ut the psychological events that evoke within us an appreciation of that .A. Scientific Basis of physical stim ulus ? Can the resulting perceptual experience also be measured?That depends on Perceptual Measurement wh o is doing the measurin g. If it happens to be The most obvious question to begin with is anyone other than the perceiver, the answer of "Why take a scientific approach to this prob­ course is /l 0 . Percepti on is a very private experi­ lem?" That is, what do we hop e to gain by ence, and since it cannot be exposed to anyone developing and applying a set of rigorous else, it canno t be directly measured by any­ experi me ntal procedures to the study of per­ one else either. Consider the followin g. Most ception? The reason most psychologists would of us wo uld be able to correctly identify the first offer is that it satisfies an intellectual curios­ colour of a stoplight. But does that mean we ity. Perception is such a mysterious and almost . are all expe rien cing an identi cal psychological magical phenomenon that a first step toward event, or could it be that each ofus experiences learning anything about it is to establish a quan­ some thing slightly different but that we have all tifiable relationship between the two variables been taught to call it red since childhood? We in this process-the physical stimulus and the SideNote 1...;:.1.:.... 1=--- _ may never know the answer to this. resulting perceptual impression (SideNote 1.1). If an outsider is not capable of measur­ Since it is impossible to open up the mind and Although the terms sensation and perceptionare often used ing our own percepti on s, then are we? Are observe the process of percepti on , one advan­ interchangeably, it is import- we capable of determining, say, the psycho­ tage of knowing this relationship is that it may ant to establish the distinction logical int ensity of a sound that is experienced offer clues about the nature of the brain, the between them atthe outset. in our mind, giving it a value, and compar­ way it processes information, and, ultim ately, Sensoryprocesses capture ing its perceived inte nsity with a different how the biological operations within it lead to information from the physical sound or a different type of sensation alto­ sensation and perception. world and transform them gether? R em arkably, the answer is yes. And it into biologicalsignals that Quantitative relationships and their benefits are interpreted by the brain. turns out that we are actually quite goo d at it In so doing , the brain creates even though perceptions do not reside in the There are several additional advantages to a perceptual representation very real world ofphysics (Stevens, 1986). And understanding the math ematical relation ship inourmind that allows us to therein lies a rath er thorny probl em . Many between the physical and perceptual wo rlds. appreciate the physical world . psychologists have asserted that even makin g One is that it provid es an estimate of the per­ Thus, perception represents the attempt at measuring a perceptual event is ceptual quality of a stimulus in numer ical terms a singleunified awareness of fruitl ess because it is not a measurable thing and and thu s allows comparisons with other stim­ astimulus that in turn arises therefore can never be verified (He idelberger uli. Say for example that a new perfume has from the sensation produced j ust been developed and the co mpany wishes by our sensory systems. & Klohr, 200 4). To say that this issue has generated some to test its aromatic acceptance by the publi c lively debate in the past wou ld be an under­ before spending millions of dollars on its pro­ stateme nt. This is largely because of the moti on . By applying a set of experime ntal pro­ opposite view held by some experime ntal cedures, which we will soon learn, it is possible psychologists that the perceived intensity of to obtain a numerical index of its impact on sensations can indeed be reliably estimated the sense of sme ll and then use this to provide by the perceiver. Furthermore, the informa­ a meanin gful comparison with the perceptual tion so obtained is generally consistent across impression made by other perfumes. Such data Chapter 1 Principles of Perceptual Measurement can predict the likely social acceptability ofthe shown in Figure 1.1. new produ ct and therefore can be used by the The simplest is a linear function. For any compa ny's executives to make imp ortant com­ given increase in physical intensity, th ere is a mercia l decisions (Lodge, 198 1). certain inc reme nt in th e perceived intensity. Quant itative relation ships also have the T he prop ortion between th e two remai ns advantage that they allow co mparisons amo ng co nstant across the who le range . In other individuals and even species.The later chapters wo rds, th e slope remai ns co nstant .This is not of this book will cover many details about our the case for th e other two possibiliti es shown limits and capacities in processing informatio n in Figure 1.1. In an expo nent ial relation ship, from the physical world, how they vary with the perceived sensation intensity changes age, and, where appropriate, how they co mpare very slow ly at low values of physical intensity. with other animals. The factors that are used But after a certain point, th e function takes in such comparisons are always math emat­ off such that even small changes in stimulus ical descriptors of the system in question . An intensity produce a dramatic increase in per­ extension of this idea is the comparison amo ng ception. In an exponential fun ction, th erefore, the different sensory modalities-a so-called th e slope itself progressively increases with cross-modal comparison-r-io see if any similarities physical int ensity. The opp osite is true of a exist among them (Luce, 1990). For example, if logarithmic function where the slope is very we perceive warmth on the skin in some defin­ large at th e beginning such that perceived able way to the temperature ofthe object, then intensities can change dramatically wi th small how does this relation ship co mpare to the way changes in stimulus int ensity. However, this in which we perceive the loudness ofsound as effect diminishes and th e functio n tails off a function of its physical intensity? Before we at higher stimulus intensities. A logarithmic explore such sophisticated Issues, we need to function th erefore displays a decreasing slope address a basic question . over its entire range. According to th is math­ ema tical description, a sensory system wo uld Is there a general relationship between no lon ger be additionally responsive to fur­ physical stimulus and perception? th er increments in stimulus int ensity beyond This is one of the fundame ntal questions of a certain point. perceptual psycho logy and one to which much There are two general approac hes to effort has been directed over the last 150 years. obtaining the precise relationship between Th e early experime ntalists wh o approached physical events and perceptual experience.The this problem were motivated in findin g a first is to simply ask human subjects to rate general formula that could describe all sen­ the perceived intensity of a certain stimulus, sory systems.What might such a formula look say the loudness of a sound, at various physical like-or, rath er, wh at kind ofa function could intensities (Gescheider, 1984). It would then be relate the physical intensity ofa stimulus to its possible to plot the two sets of values and deter­ perceived magnitude? We kn ow from every­ min e whi ch of the general functi ons shown in day experience that this will be an increasing Figure 1.1 best describes the transformation function. That is, as the physical intensity ofthe of a physical input-in this case, sound-into stimulus increases, so will our percepti on of it. a perceptual event. We will look at the infor­ But that could happen in a number ofways, as mation revealed by this kind of approac h later

~ Linear ~ Exponential ~ Logarithmic "C.a'" "C.a'" "C.a'" '2 '2 '2 Cl Cl Cl :E'" :E'" :E'" c: c: c: 0 0 0 ~ ~ ~ '"c: '"c: '"c: en'" en'" en'" StimulusIntensity (I) Stimulus Intensity (I) StimulusIntensity (I)

.....Threepossiblefunctionsthatmay relate the physical intensityofastimulus (I) totheperceived intensity ofsensation (S) . Fundamentals of Sensory Perception

in this chapter. The second approach is a bit We have j ust describ ed th e genera l out­ more convoluted because it requires a measure line of a scientific approach that had been of the smallest change in stimulus input that formulated by th e Ge rman physicist Gustav causes a j ust discriminable change in sensation. Fechner in 1860. Fechner wan ted to deter­ To understand how this can reveal anything mine th e relationship between mind and imp ortant , we have to examine the ideas first bod y and set out to establish not only a guid­ proposed by the experime ntal psychologists of ing principle but also a set of experimental the 19th century. T hey had understood that meth ods that were to be used in thi s new a math ematical relation ship between physical field called psychophysics. H e believed that and perceptual qualities could be established by there existed a general relation ship between obtaining two basic charac ter istics or descrip­ physical and perceptual qualities, that it was tors of that function-the starting point and similar for all types of sensations, and that it GustavTheodor Fechner the slope. co uld be obtained by knowin g the stimu­ (1801-1887) lus energy at which the output can just be © INTERFoTO/Alamy detected or discr iminated-that is, th e abso­ B. Classical Psychophysics lute threshold and the difference threshold (Heidelberger & Klohr, 2004). Fechner was Looki ng again at Figure 1.1, we see that all no t just int erested in knowin g these thresholds three func tions do not begin at the origin but because th ey wo uld reveal some thing abo ut are displaced somewhat to the right . This is th e opera tio nal sensitivity of senso ry systems because we are unable to detect very low lev­ but because he believed that they represented els of stimulus intensity. Although a stimulus fun dame ntal param eters in the grand formula is physically present, the biological elements of percepti on. that are involved in capturi ng th e stimulus and transforming it into a sensory experience do 1. PSYCHOPHYSICAL METHODS not normally fun ction well if the physical int ensity is too low (Engen, 1971). R ath er, the It is possible to apply anyone of three gen ­ intensity has to reach a cer tain minimum level, eral meth ods that were develop ed by Fechner the so-ca lled absolute threshold, befo re it to obtain absolute and difference thresholds is registered by the brain as a sensory event. (Gescheider, 1997). T he simplest of these is Stimulus intensities below this poin t are called th e Method of Adjustment where a human subthreshold and will not produ ce detectable subject is to ld to simply adj ust the physical sensation. So the first item that has to be deter­ inte nsity ofa stimulus until it is barely de tect­ min ed is th e absolute threshold, which wo uld able. T he initial' inte nsity wo uld be set either \hen \ e\\ U 'S. \.h e \,Q\n\. (~Q\n 'Nn \ <:n \.0 b c ~\\~ a.bovt.: 0 1' b c\o 'N t.hTC ~ho\ d . a nd t.he ...\.\hic c't plotting our function. wo uld acco rdingly change the value until the We would next want to know what stimulus is just perceptible or when the sensa­ happens beyond this point in the so-called tion j ust disappears. Alth ou gh this procedure suprathreshold region wh ere sensatio n takes is very fast and actively engages the subject in place. For this, we will have to determine how the psychophysical experime nt, the Me thod the slope changes as a function of physical of Limits is preferable if speed is not an issue intensity. Furthermore, th e slope wo uld have beca use this technique provides more reli­ to be determined not just for one suprathresh­ able estimates. H ere, the subject is present ed old point but also for several others in order wi th a stimulus whose inte nsity is chosen to see how it is changin g. O ne possible way from an ascending or descending series . If to obtain this inform ation is by knowing just an ascending series is used, the intensity of how small a change in stimulus inte nsity is the stimulus is initially set at a subthreshold required to produce a discrimin able change in value and inc reased by a fixed amo unt in suc­ sensation.This so-ca lled difference threshold cessive trials until th e subject reports that it is can be used to estimate how the slope changes perceived. Alternatively, if a descending series at suprathreshold levels. And once we know is used,a suprath reshold intensity value is grad­ this, we can determine which function best ually reduce d until the percept disappears.T he describ es the transform ation ofphysical stimuli transition points from several such ascending in the real wo rld into psychological events that and descending series prov ide a reasonable we experience as percept ion . estima te of the threshold. Chapter 1 Principles of Perceptual Measurement

Both the Meth od of Limits and the to produce detectable sensation, and so our Meth od of Adju stment allow th e subject to subject sho uld consistently respond NO when have an idea of wh at the next stimulus will be asked if some thing is visible.However, once we like compared to the last one.T his predictabil­ reach an intensity that is sufficient to trigger ity in stimulus presentation makes both ofthese sensatio n, the subject should then co nsisten tly methods less accurate. A more suitable pro­ respond YES. The transition between these cedure is the Method of Constant Stimuli two response levels can then be defined as the where the intensity values are rand oml y absolute threshold .The subject is presumed to chosen from a preset range and presented to behave like an ideal detector in such a scen­ the subject. N either th e experime nter nor the ario- that is, all subthreshold intensities fail to subject usually knows the value of the next produce a detectable sensory event, wh ereas stimulus to be present ed. T he subject merely all suprathresho ld ones consistently produce a replies whether or not a sensation occ ur red positive sensatio n. Furthermore, the subject is and a frequency chart is established based on absolutely perfect in being able to distinguish the responses collected from many presenta­ betwe en these two conditions. tions at each intensity. As an example, let us consider an experi­ Humans are not ideal detectors ment on the visual system where we will In reality, however, our respon ses are quite SideNote 1..:.1.:.:.2=-- _ attempt to obtain the absolute threshold for different. As Figure 1.3 (page 8) shows, the detecting light using the M eth od of Constant response curve that wou ld eme rge from an Asimple psychophysics setup inwhich ahuman subject Stimuli. Such experime nts are typically con­ actual experime nt wo uld look more like an observes computer-generated ducted with a sophisticated optical setup. S-shaped function or ogive.Althou gh we reli­ stimuli ona monitor froma However, we will simplify the experime nt so ably detect very high intensities and always fail fixeddistance.The response that the stimulus will be under computer con­ to detect very low ones, it appears that the inter­ isindicatedwith thepress of trol and presented on a mon itor. The subjec t vening inte nsity levels cause some uncertainty abuttonand sent tothe com­ will view the stimulus from a fixed distance as to whet her or not a sensory event occ ur red. puter, which stores this infor­ and after each trial will indicate a response to According to Figure 1.3, it is clear that as the mation for lateranalysis. the compute r. This is a typical setup for most intensity increases,there isa progressive increase modern psychophysical experime nts on vision in the likelihood that it will be detected. (SideNote 1.2). After each stimulus presenta­ This so-called psychometric function pro­ tion , the subject hits either a YES or a NO but­ vides a typical profile of how our sensory sys­ ton to indicate wh ether a sensation occ ur red, tems respond as a function of physical intensity that is, whether light was detected or not. For (Falmagne, 2002). And as such, it is clear that any given trial, the stimulus intensity will be randoml y chosen by the computer from a pre­ SideNote 11.3 defined set ofvalues.T he lowest intensity value 100 One probleminundertaking a must be one that is never detected, whereas threshold experiment with the the highest value should always be detected.In 80 Methodof Constant Stimuli '" this way,the threshold intensity will be located '"c: is choosing an appropriate '"0 c. range ofstimulus intensities. somewhere within this range (SideNote 1.3). '" At the end of the experime nt, each intensity a:'" 60 Optimally, the threshold should will have been present ed an equal number of !i! be somewhere inthe middle '0 of this range. Sincethisisthe times, and a summary of the frequency of YES Cl 40 '" parameterbeing determined responses to each stimulus intensity will be 'E'" Absolute '"~ experimentally, it becomes provided by the computer. / threshold c..'" 20 difficult to construct a range around an unknown value. One 0 way toget around this istodo 2. ABSOLUTE THRESHOLD a"quick and dirty" Method of 2 3 4 5 Adjustment experiment, which Before looking at the data that such an experi­ Stimulus Intensity (I) will give an approximate value ment might generate, let us co nsider what the ~------for the threshold. response profile would look like based simply The expected response profile in an absolute threshold on intuition. One likely possibility is shown experiment looks likeastep function.All stimulus intensities in Figure 1.2 wh ere the respon se curve looks up toacertain point will failtoproducesensation, whereas all like what is called a step fu nction.All intensi­ intensities beyond that pointwill always do so. The absolute ties below a certain point wo uld be too weak threshold is the intensity at whichthis transitionoccurs. Fundamentals of Sensory Perception

100 Conventional approaches tothreshold estimation Given that we are not ideal detectors, then 80 whic h intensity value do we take from '"Q) '"c: Figure 1.3 to represent the absolute thresh­ c.0 Q) old? Because there is a gradual increm ent in a:'" 60 ~ stimulus detectabiliry with increasing physical '0 int ensity,there actu ally is no well-defined point Q) Cl 40 co th at can serve as the thresho ld. We therefore 'E eQ) have to adopt an arbitrary response level that Q) c... 20 can be used to obtain the threshold (Engen, 1971). By convention, psycho physicists have 0 used the 50% response level for that purpose 2 3 4 5 (SideNote 1.5).Therefore, the physical inten­ StimulusIntensity (I) sity that produces th is respon se is taken to be 1I!!lIDt..~ the absolute threshold . An experime nter can SideNote 1....:.1 ..:....4=-- _ _ certainly use a different criterion so lon g as Cognitive factors can arise from The actual response profile (psychometric fun ction) that is obtained in an absolutethreshold experiment. Theabsolute it is made clear which respon se level that is. noise inthe decision-making For examp le, it is possible to use the 60% YES process. For example, a sub- threshold isusually taken as theintensity atwhich the stimu­ value as the definitio n of threshold sensa­ jectmay actually perceive the lus was detected on 50% of the trials. stimulus butopttorespond tion. In that case, the stim ulus intensity tha t NO due toreduced confidence. produces this would be taken as the absolute Alternatively, a suolect may threshold ofdetec tio n. W hat this means is that we do not behave as ideal detectors, leadin g to not actually have perceived the in reality there is no ali-or-none condition for the natural qu estion ofwhy this is so. stimulus but chose torespond stimulus detection . R ath er, our thresholds can Under mo st circumstances, our sensory YES due toeagerness. Cognitive fluctu ate a little, and therefore the noti on of systems have to deal with several sources factorsareextremely important a threshold now becomes defined in a more in psychophysical experiments of un certainty (Ma rks, 1974). These facto rs statistical mann er. and will be discussed later in become espec ially critical at very low physical Since Fechner's time, th ere has been Section C.4. int ensities where detection threshold s typ­ much effort at determining absolute threshold ically arise. O ne such source is th e stimulus values for different sensory systems under dif­ itself. There is usually some variability in the ferent conditions (Gescheider, 1997; Stevens, intensity of a stimulus simply because no SideNote 11-'1....:..5=--- _ 1986). T hese results have shown that we are physical device can provide perfect del ivery ind eed extremely sensitive creatures, and Let us assume that the sensa­ at a spec ified int ensity, espec ially whe n it is under some conditions, the laws of physics tion produced by astimulus has very low. This stimulus is th en captu red by a anormal probability distribution often impose th e limits to detection . Here are sensory system th at adds further noise to th e due tothe effects ofnoise.The some examples of how well we do. detection probability ofasignal signal. It is a biological fact that our nervou s system is inh erentl y noisy, which becomes 701/c1z-a dimpling of the skin by as little as is given by the cumulative 5 probabilities-thatis, the area espec ially probl em atic at th e lim its of sen­ 10- ern is sufficient to be detected. under the distribution-up to sory function where the noise interferes wi th Smell-under op timal co nditions, the absorp­ thatpoint.The ogive psycho­ signal detection to produce instances of mis­ tion of on ly 40 molecules by detectors in the metric fun ction resultsfrom percept ion . And finally, once this somewhat nose is sufficie nt to produce a detectable smell. the cumulative probabilities variable stimulus has been delivered and th en determined inthismanner at Hearillg-detection threshold is so small that it captu red by our noi sy senso ry system, we still progressively greater values represents moveme nt of the eardru m by only have to make a judgm ent as to wheth er it ofsensation magnitude.The 10-10 cm.This is smaller than th e diameter of was perceived. That judgment can be influ ­ 0.5(or 50%) level inthe ogive a hydrogen molecul e. corresponds tothe mean ofthe ence d by a number of physical, emo tional, distribution, which is why it is and cognitive facto rs (Side Note 1.4). While Visioll-the eye can be exposed to as little as usedtoestimate thethreshold. the magnitude of th ese would certainly vary 54-1 48 ph ot on s to produce a detectable sen­ among different peopl e, th ese factors can also sation oflight. Ifl osses in transmiss ion through vary wi th time within an indi vidu al subject. the eye are co nsidered, it turns out tha t this Togeth er, th ese different sources of variabil­ represents the absorp tion of a single pho ton ity-from stimulus to subject- ma ke our in abo ut 5 to 14 detector cells of the retina. sensory systems behave quite differentl y from These figures attest to th e remarkable bio­ SensationMagnitude an ideal detector. logical co nstruc tion ofour senso ry systems. Chapter 1 Principles of Perceptual Measurement

3. DIFFERENCE THRESHOLD whether the target light is brighter or dimmer. N o other cho ices are allowed. As noted before, one of Fechner's central goals We can ado pt Fechn er's Meth od of was to understand the relationship between the Constant Stimuli again to perform this experi­ physical and mental worlds-in other wo ~ds , ment. A computer will randomly choose the the way in whi ch stimuli of different physical inte nsity level of the target light from a range intensities produce different amounts of sen­ and display that stimulus along with the fixed sation, or sensory magnitude. The absolute referen ce stimulus.The subject's task is to com­ threshold gives only on e point in that profile, pare the two stimuli, make a decision , and hit that is, the starting point for any of the possible one of two buttons to register the respon se. relationships that are shown in Figure 1.1. But This sequence is repeated many tim es until a this is obviously not enough to determine what sufficient number of trials (say 50) have been the rest of the function would look like. For accumulated for each intensity point. We can this Fechner needed to have an idea of what then calculate the proportion (or percentage) the 'slope of the func tion was at suprathreshold of trials in whi ch the subject judged the target levels and how that slope changed with light to be brighter. Of course, we could j ust increasing intensity (Engen , 1971; Manning & as well examine the proportion judged to be R.osenstock, 1967) .If the slope remains con­ dimmer. Either way, the idea is to look at the stant, then the relationship between sensory data and see how mu ch ofa change in physical magnitude and stimulus intensity is de s cribe~ intensity was required for a detectable change by a linear function. However, if the slope IS in sensation. Since we gave the subject an equal either increasing or decreasing, then the func­ number of bri ghter and dimmer intensities, tion becomes either an exponential or a loga­ one possibility is that all trul y dimmer intensities rithmi c one, respectively. were judged correctly as were all trul y brighter A clue as to which of these possible func­ intensities. In this case, the subjects theoretic­ tions correctly describes the transformation of ally behaved like an ideal detector because they physical to mental events came to Fechn er from never failed in distinguishing true differences a series of experiments on difference thresh­ in stimulus intensities. olds that were carried out by a co nte mpor­ However, similar to wh at we saw earlier ary German physiologist named Ern st Weber. for detection judgments, it turns out that we Weber had been interested in determining do not behave as ideal detectors wh en it comes the gradations ofsensory experience at supra­ to difference judgments either. The psycho­ threshold levels (Weber, 1996). The question me tric function in Figure 1.4 (page 10) shows now was no longer whether or not a stimulus a plot of percentage brigluer responses against was perceived but rather how mu ch it needed target light intensity. Again, as in Figure 1.3, to change in order to produce a detectable performance data displays an ogive rather than change in sensation.T he differen ce in physical a step function , indicating that certain intensi­ intensity that was required to accomplish this ties generated mixed respon ses. The intensity became known as the dt[fcrc//cc threshold.Weber that produced 50% brightcr response s (point worked mainly with the discrimination of a on the x-axis) can be taken as the point of object weights, carrying out a series of careful perceptual equivalence. In oth er words, at this experime nts on the smallest detectable change intensity our subject could not decide wh eth er for a series ofdifferent starting weights. the target light was bri ghter or dimmer, and it was therefore perceptually equivalent to the Adifference threshold experiment Ernst Heinrich Weber (1795-1 878) referen ce light. on the visual system © INTERFOTOIA1amy Our task now is to use this data to deter­ Let us illustrate the principles that Weber min e the difference threshold-that is, that developed using discrimination of light inten­ extra bit of physical intensity that needs to be sities as an example. We can set up a psycho­ added to or subtracted from the target light physical experiment as before but now ask the intensity at this perceptual equivalence point subje ct to examine two stimuli-a referen ce in ord er for there to be a just noticeable light, whose intensity is always kept constant, difference OND) in sensation. This amo unt and a target light , whose int ensity is either will in turn dep end on exactly wh at level of lower or higher than that of the referen ce.T he no ticeable difference we wan t as our criter­ subject must compare the two and indicate ion. By convention, most psychophysicists use Fundamentals of Sensory Perception

100 become different ?This was precisely the ques­ tion that Weber addressed in his experime nts with weights, and in so doing, he discovered a '- 75 fund amental relationship that has co me to bear ~ .c: his name (Weber, 1996). ;§ :g, 50 Multiple discrimination threshold experiments .sc '"e Let us return to the difference threshold 0..'" experiment with lights. Figure 1.5 shows the 25 psychometric functions that we wo uld likely obtain if we co nducted this experime nt three o tim es by setting the reference light at progres­ c a b sively higher intensities each tim e.T he psycho­ Target LightIntensity (I) metri c function s are correspo ndingly displaced ~------to the right and becom e somewhat flatter...... A typical psychometric fun ction that is obtained in a differ­ For each psychom etri c function , we can now ence threshold experiment where the subject has to judge determine the difference threshold .To keep it two stimuli and determine whether the target was brighter simple, we will restrict this analysis to j ust the or dimmerthan the reference. The 25% and 75% brighter increm ent threshold . response levelsare generally used as the points for a just noticeable difference (JND) in sensation decrement and As before, we wo uld first determine th e increment, respectively. target light int ensities that are perceptually equivalent in br ightness to th e reference light for all three cases (aj, az, a3) and th en find th e the 75% br(~hter response level as the meas­ intensities produ cin g 75% brighter respo nses ure for a noticeable increme nt in the stimu­ (b., bz, bj). Looking closely at Figure 1.5, we lus (Gescheider, 1997). Thus, when the target can see that th e increme nt threshold for the ' light intensity is raised to point b in Figure 1.4, first psychometric fun ction (b. minus a.) will we will achieve this result, and the difference be less than that ofth e seco nd fun ction, which between the two int ensities (b minus a) is taken in turn will be less than th at of th e thi rd. In as the difference threshold (~ I). In other words, other wo rds, the greater th e intensity level at ~I represents the extra bit of physical intensity which we have to make a JND j udgme nt, th e that we wo uld need to add in order to make greater the difference threshold ( ~ I ) needed a stimulus j ust noticeably bri ghter. Exactly to attain that JND. T he difference thresho ld is the same logic can be used if we want to deter­ th erefore not co nstant but actually increases min e the difference threshold for a redu ction in in a linear fashion with stimulus inte nsity. sensation, exce pt now we use the 25% brighter T his is what Weber discovered , and the eq ua­ response level (which corresponds to 75% dim­ tion descr ibin g this relationship is known as merjudgments).The target light int ensity now Web er's law : needs to be lowered to point c, and the differ­ ence between the two intensities (a minus c) ~I=k ·I is also a difference threshold (~ I) . These two measures of difference threshold are usually Implications ofWeber's law distinguished by the terms increment threshold We know from everyday experience that if a and deaement threshold, respec tively, and are small number of items is increm ented by j ust often averaged to provide a composite value. one, it is more likely that we will notice that difference than if the same addition is made to a much larger set. Weber noticed that if one 4. WEBER'S LAW lit candle was added to 60 others, then that In the last experime nt, brightness comparisons addition would be sufficient to cause a JND in were made to a reference light that was fixed at brightness percepti on. However, if there were a particular int ensity.What happens if we now 120 burning candles,then adding j ust one more change the reference light to a higher level was no lon ger sufficient to cause a detectable and redo the experi me nt to find a new dif­ change in sensation.Thus, the requirem ent for ference threshold? Do es the difference thresh­ a JND is that the increm ental (or decrem ent al) old value (~ I) still remain the same or will it amount be scaled to the stimulus intensity. Chapter 1 Principles of Perceptual Measurement

100

75 .... .l!! -<:: . ~ Cl:l '"Ol 50 c:ca 1:'" a.'"

o

Target Light Intensity (I) ~~------Psychometric functions from difference threshold experiments in which the reference light isset at progressively higher intensities. The lowest reference intensity (left curve) produces a small difference threshold, whereas the highest reference intensity (right curve) produces a much larger threshold . The bar lengths below the x-axis show the relative sizeof the differencethresholds for the three psychometric functions.

The difference threshold (tl I) is therefore not no universal Weber fractio n that applies to all a constant value but some proportion (k) of sensory systems. R ath er, there is considerable the stimulus intensity (I).This prop ortion (k) is variation such that certain sensory processes also known as Weber's fraction. are very sensitive to change, wh ereas others are Once the Weber fraction is known, the difference threshold can be easily calculated Table 1.1 from Weber's law for any given intensity value. I3ut wh at is the value of k? This must Weber Fractions for Different Sensory Systems be experimentally determined. The preferred way to do so is to determine the difference Sensory Dimension Weber Fraction (k) thresho ld at a numb er of different intensities, Touch(heaviness) 0.02 as we did in the experiment above. T he dif­ SideNote 11.6 Touch (vibration) 0.04 ference thresholds can then be plotted against Astraight line isproduced if we the different values of int ensity to reveal a Taste 0.2 make a plot ofthe difference straight line (SideN ote 1.6).The slope of thi s threshold (~ I ) that was obtained linear function is th e Weber fraction (k). For Smell 0.07 ateach ofthe three intensity (I) levels. This isthe graphical the bri ghtness experime nt we just performed, Loudness 0.3 we wo uld have found th e value of k from the form ofWeber'slaw and has been found tohold true for all slope to be abo ut 0.08. Thus, an 8% increase Pitch 0.003 sensory systems withinabroad (or decrease) in light intensity is sufficient to Brightness 0.08 range ofintensities.The Weber produce a JND and allow us to detect that fraction(k) is taken fromthe change in perceived bri ghtness. Note. Small values ofk imply greater sensitivity indetecting changes slope ofthis line. of intensity. Adapted from "Psychophysics: I. Discrimination and Weber fractions fordifferent sensory systems Detection ," by J. Engen, 1971 , in Woodworth & SChlossberg's We could have co nducted a similar difference Experimental Psychology, Eds. J. W. Kling and L. A. Riggs, New threshold experiment in any of the other sen­ York, NY: Holt, Rinehart & Winston; "On the Exponents in Stevens' tlI Power Law and the Constant in Ekman's Law," byR. Teghtsoonian , sory systems, such as taste, tou ch, hearin g, etc., 1971 , Psychological Review, 78, pp. 71-80;"Differential Sensitivity to determine their respective Weber fractions. for Smell ," by W. S. Cain, 1977, Science, 195, pp. 796-798: This has indeed been done by psychophysi­ "Psychological Dimensions andPerceptualAnalysis of Taste," by D. cists since Weber's time, and some ofthe results H.McBurney, 1978,inHandbook of Perception, Eds.E.C. Carterelle are shown in Table 1.1. N otice that there is and M. P. Fri edman, NewYork, NY:Academic Press. Fundamentals of Sensory Perception

not .Among the most acute ofour sensory par­ magnitude ofllS needed to produ ce a JND or ame ters is the detection of pitc h where j ust a whether that value changed at different levels 0.3% change in the frequency ofsound is suf­ ofsensation. ficient to cause a JND. On the other hand, the percept ion of sound inte nsity (loudness) can Fechner's assumption require up to a 30% change in the stimulus for Fechn er could not resolve this problem because that difference to be detected. it is simply impossible to measure sensations. In general, the Weber fractions in N everth eless, he made a bold assumption. Table 1.1 are accurate predicto rs of difference Fechn er proposed that all JNDs were produced thresholds for a bro ad range ofstimulus inten­ by equal increments in sensation regardless of sities. However, at the extreme situations of the operating level (Fechner, 1860/1 966). In very high or low intensities, the value ofk can other wo rds, exactly the same value ofll S was change drama tically, such that the generality needed at all sensory magnitudes because the ofWeber's law no lon ger applies (Gescheide r, JND is a standard unit ofchange that represents 1984). This is tru e of all sensory dimensions. a psychological constant. Fechn er was also well Alth ou gh the applicability of Weber's law aware of Weber's results and the implications is limited to a certain range of intensities, it they had for his quest to determ ine the relation ­ nevertheless remains one ofmost useful equa­ ship that he sought. Figure 1.6 (lefi side) shows tion s in perceptual psychology. how Fechn er's assumption can be integrated with Weber's law. As shown, higher intensity levels require a greater change in the physical 5. FECHNER'S LAW stimulus (ll l) to produ ce identical changes We rem arked earlier that one of Fechner's in sensation (llS). In all of these cases, a JND central goals was to obtai n the relationship event is presumed to occur through identical between sensory magnitude and stimulus changes in sensation (Fechner's assumption) inte nsity. We are now ready to complete that that are brought about by progressively greater story.Fechner knew that to un cover the rela­ changes in stimulus intensity (Weber's law). tions hip between those two parameters, it was necessary to know the way in whic h that func­ Deriving the stimulus-sensation relationship tion changed at progressively greater supra­ O nly one of the three possible functions that threshold values (Fechner & Lowri e, 2008). we explored in Figure 1.1, relating intensity As we have already seen, Weber's law asserts and sensation, can acco unt for this. Figure 1.6 that higher levels of suprathreshold intensity (right side) shows that the stimu lus-sensation require a correspo ndingly greater change in relationship mu st necessarily follow a logarith­ intensity (ll l) to produce a change in sensa­ mic function . The intensity values from the tion (ll S) that is j ust distinguishable UND) . difference threshold experime nt in Figure 1.5 But Fechner knew no thing abo ut the actual are shown here on the x-ax is.The prog ressively

LIS Sensation § --- LIS Q) LIS LIS LIS 'C / LIS I :Er::: Cl ::;:'" r::: ._ / ~ LIS .- . en r::: -I' enQ) L11 L11 L11 L11 Stimulus (

a, ti, a,b, a 3 b3 Stimulus Intensity (I) -...~------The integration of Weber's law and Fechner's assumption implies that with increasing stimulus intensities, the difference threshold (~I) progressively increases but continues to be mapped onto a constant change in sensation (~S) toproduceJNDS (left). Only the logarithmic function allows this condition to hold true (right). Fechner therefore concluded that the relationship between stimulus intensityand sensationis a logarithmic fun ction . Chapter 1 Principles of Perceptual Measurement greater change in ~I that was revealed in that many psychophysicists simply became pre­ experiment can now be related to Fechner's occupied with the logarithmic function as the assumption of ~S being constant at all levels master descriptor of mental pro cesses. Nothing for a JND. Fechner could reach onl y on e co n­ else was acceptable. clusion-the logarithmic function is the onl y And yet, there were many opponents as one that will allow for ~I to increase according well, some of who becam e quite influential to Weber's law but still retain the same values in their criticism of Fechnerian psychophys­ of~S . Neither the linear nor exponential func­ ics (SideN ote 1.8). The main obj ection was SideNote 11.7 tions will permit this. not against the logarithmic relationship per se Fechner'stheory relating stimu­ What we have just seen is a tour de force but against the very notion that sensations can lus intensity tosensory experi­ ofexperimentation and insight. In the absence be described by mathematical functions at all. ence marked the beginning of ofany direct means to study sensation, Fechner One of the mo st scorn ful critics was William experimental psychophysics. was still able to derive a fundamental relation­ James, who believed that it was simply futile He istherefore widely regarded as the father ofpsychophys­ ship between sensation magnitude and stimu­ to put numbers on sensations (Richardson, ics. Fechner himself was an lus intensity. As a tribute to his work, that 2007) . Nothing about the empirical process, eccentric character.The fact relationship is now called Fe chner's law and he argued, can allow any quantitative estimate that he recorded the date of is formally specified as of such private experiences as sensation, and his psychophysical insight therefore any psychophysical law is fundamen­ (22 October 1850) has resulted S k • log (I) = tally meaningless. In a classic rebuke, James in Fechner Day celebrations on this day insome psychology where the constant k is related to, but not iden­ wrote how terrible it would be if Fechner quarters throughout the world. tical to, the constant in Weber's law. Fechner's should "saddle our Science forever with his law asserts that at low intensity levels, the patient whimsies, and, in a world so full of magnitude of our sensations can change quite more nutritious objects of attent ion, compel SideNote 1_1_.8 _ rapidly with small changes in stimulus inten­ all future students to plough through the dif­ sity, whereas we become mu ch less sensitive at ficultie s, not onl y ofhis own works, but ofthe Some ofthe criticisms of higher intensities. Indeed, at the very highest still drier ones written in his refutation." Fechnerian psychophysics intensities, our perception ofa stimulus should Fechner's supporters believed that the even began toemerge from his contemporaries: not change appreciably, regardless of how stimulus-sensation problem had been solved, much intensity is added. whereas his critics believed that the problem How much stronger or weaker one sensation is These results were soon generalized across could never be solved. Both intransigent atti­ than another, we are never tudes in their own way produced a general the entire domain of perception such that the able tosay.Whether the sun relationship between all physical events and decline ofinterest in the measurement ofsensa­ isahundred orathousand conscious experience was taken to be largely tion that lasted until the 1930s, when a Harvard times brighter than the logarithmic in nature . This eventually turned psychologist named Stanley S.Stevens began his moon,a cannon ahundred out to be a flawed conjecture, and indeed the psychophysical work. Stevens boldly rejected ora thousand times louder logarithmic function itself later became replaced the assertion that sensation cannot be measured. than apistol ,isbeyond our power toestimate. by somewhat different functions as descrip­ However, his approach was completely differ­ tors of the stimulus-sensation relationship. ent from the German psychophysicists of the Wilhelm Wundt, 1890 Neverth eless, the psychophysi cists of the 19th 19th century. R ather than determine psycho­ century continued to have a profound influen ce physical laws through indirect procedures, on perceptual psychology, even to this day, in Stevens proposed a set of direct methods for both theory and practice (SideN ote 1.7). studying sensation. And thu s began the era of modern psychophysics-an entirely new approach that would galvanize the field and produce dra­ Modern Psychophysics matic insights into sensory processing by the C. 1950s, revealing psychophysical relationships The field of psychophysics flouri shed dur­ that in some cases did not even slightly resem­ ing Fechner and Weber's time. On the one ble logarithmic functions. hand, there was the sheer elegan ce by which the logarithmic relationship was established, 1. MAGNITUDE ESTIMATION and on the other, there was the persuasive AND THE POWER LAW simplicity of Fechner's assumption that JNDs Stanley Smith Stevens represent fundamental and immutable units Whereas Fechner believed that sensations (1906-1973) of sensory change. Fechner's law thus became could only be measured indirectly through Harvard University Archives. Call # HUP the cornerstone of perceptual psychology, and difference thresholds, Stevens believed that an Stevens. Stanley S. (3) Fundamentals of Sensory Perception

exact relationship between stimulus and sen­ 1966). The numeri cal estimate represents the sation co uld be directly obtained (Krueger, subject's judgment of the sensation triggered 1989). Stevens was instrumental in establishing by that particular stimulus. In one variation a set ofpro cedures that are collectively known of this method, first suggested to Stevens by as scaling.R ath er than taking the Fechnerian his wife, Gera ldine , subjects are not presented approach of comparing stimuli and j udgi ng with a modulus to constrain their judgments. their differen ces, Stevens simply asked his sub­ R ather, they are free to develop their own jects to provide a direct rating of the sensation modulus and assign numbers in proportion to that they experienced. This technique came to the sensation magnitude that they experie nce SideNote 1--=1...:...9"-- _ be known as magnitude estimation. (Side N ot e 1.9). A remarkable outcome of these experi­ Atypical instruction given Experimental design and outcom es ments was the consistency with whi ch subjects toa subject ina magnitude estimation method might be The subject is first presented with a standard produced their ratin gs and the similarity in the following:"Youwill be stimulus, which is known as th e modulus, and the trends observed among different individ­ presentedwith a series of told that it represents a certain value, say 10. uals.The actual numbers ob tained were differ­ stimuli inirregular order.Your If for example the experiment required lou d­ ent across subje cts because they were free to task istotell how intensethey ness estimation, the subje ct would first experi­ choose their own scale. But when the numbers seem by assigning numbers to ence the modulus and then provide a relative were equated by takin g int o acco unt subject them. Call thefirst stimulus any numerical ratin g for other ton es of varying variability, it turned out that there was con­ number that seems appropriate toyou.Thenassign successive intensity that are rand oml y presented (Stevens, siderable agreeme nt amo ng different people numbersinsuch awaythat with regard to their sensory ratin gs for any they reflect your subjective Table 1.2 given type of stimulus. impression " (Stevens, 1957). The magnitude estimation experime nts Power Law Exponents for Different Sensory were a direct challenge to Willi am Jam es' doc­ Systems trine that sensations simply cannot be meas­ ured. Stevens showed tha t they ind eed can Sensory Dimension Power Law and that the data fit very nicel y into math­ Exponent em atical functions that were co nsistent with Touch a power law.The general form of th e power Steady pressure (palm) 1.1 law is th e following: Vibration (250 Hz) 0.6 S = k • I b Temperature (cold) 1.0 Temperature (warmth) 1.6 where S is the sensation experienced by the Electricshock (fingers) 3.5 subject, I is the physical intensity ofthe stimu­ Taste lus, k is a so-called scaling constant that takes Sweet 1.3 into account the units used to represent the Salt 1.4 stimulus intensity, and b is th e expo nent (or power) value. According to this relation ship, Bitter 0.8 sensation is related to intensity raised to a cer­ Smell tain power. But wh at is th e value ofthat power Coffee 0.55 or exponent? It turned out that there was no on e general exponent value that served all of Hearing the senses. R ather, different sensory experi­ Loudness 0.67 ences are related to stimulus intensity by a Vision particular exponent (Stevens, 1957).Table 1.2 Brightness (extended target) 0.33 provides some examples of power law expo­ nents that were derived from experime nts Brightness (point source) 0.5 on the various senses. As this table shows , Estimated length (line) 1.0 th ere is no uniformity in the expo nent val­ Estimated area (square) 0.7 ues. Furthermore, for any given sense (taste is a good example), the actu al expo nent value Note. The exponent values can be different for different aspects of sensation within a particular system. Adapted from "On the depends on the particular aspect of that sen­ Psychophysical Law," by S.S.Stevens, 1957,PsychologicalReview, sory dimension , for examp le, taste sensations 64,pp.153-181 . generated by salt, bitter, etc. Chapter 1 Principles of Perceptual Measurement

Power law exponents 2.0 Althou gh sensatio n magnitude is related to stimulus intensity by the power law, the pre­ cise nature of that relationship is very mu ch §: 1.5 govern ed by the exp onent. Table 1.2 shows .a'C'" that for some sensory dimensions, the expo­ '2 Cl nent is less than 1.0, whereas for others it is ~ 1.0 c: greater. Figure 1.7 shows a graph of the two o ~ extreme cases from Table 1.2- brightness for '"c:

2. PSYCHOPHYSICAL SCALING two entirely different sensory experiences, where the task is to make a j udgme nt ofequa l The importance of magnitude estima tion as a sensory magnitude. However, it turns out that psychophysical techniqu e stems from th e fact we are also quite goo d at these kinds of com­ that humans are remarkably good at bein g parisons (Luce, 1990). able to match numbers to what we perceive. Figure 1.8 shows the collective results of As a result , several different scaling techniques 10 different experime nts wh ere subjects were have been developed to analyze our sensory asked to adj ust sound level until it matched the and perceptual functions in a qu antitative perceived intensity ofa stimulus from another SideNote 1....:.1 .::...c. 1:....:1'------_ mann er (Side Note 1.11). With th e adve nt of sensory domain. The resulting equal sensa­ th ese techn iqu es, psychologists soo n becam e Psychophysical scaling pro­ tion[unctions show different slopes de pendi ng cedures can be classified int erested in measuring different aspec ts of up on th e power fun ction for th e sensory par­ into three general types. In sensory function, not only within that par­ ame ter that was bein g co mpare d. In fact, th e confusion scaling, subjects ticular domain but also in relati on to other actual slope of th ese functions turned out to determine whether one sensa­ sensory dim ension s (Baird & Noma, 1978). be very close to the predi cted slope based on tion isgreater orless than The technique of intramodal m atching, th e power law expo nents for loudness and th e another. Fechner used this kind for example, produced new insights into parti cular senso ry param eter to whic h it was ofindirect discriminative judg­ how sensitive a partic ular senso ry system is mentinhis experiments.The being matched. Thus, elec tric shock (which to diverse kind s of stimulatio n. As we will tech niqueofpartitionscaling has a large expo nent value) shows a steep rela­ requires subjects tomake dir- see in later chapters, mu ch of th at effort was tion ship for cross-modal matching with lou d­ ect judgments ofdifferences in applied in vision and hearing to examine how ness, impl ying that small changes in elec tric sensory magnitude byplacing perceived brightness was affected by different current require large changes in sound setting thestimuli intoalimited num- colours of lights or how perceived loudness for a judgm ent of equality. The opposite is ber of categories. Only the ratio changed for different ton es. scaling procedures, such as tru e for cross- mo dal matches with bri ghtness magnitude estimation, produce (which has a small exponent value) . These­ Cross-modal experiments measurements that can be results not only validated the power law but placed on a numerical scale. Stevens developed a rather unu sual pro ced­ also showed the ut ility ofpsychophysical scal­ ure called cross- m o d ality m atching wh ere ing procedures in co mparing sensory func­ subjects were asked to compare stimuli from tion across different systems. one sensory modality to those of ano ther (e.g., loudness vs. bri ght ness, electr ic shock vs. Prothetic and metathetic sensations vibration, etc.) (Stevens, 1966). What makes The sensory experiences that allow scaling this procedure unusual is that co mparisons are such as tho se described above have a direct required not within a single sensory dim en­ underlying relationship to the physical inten­ sion, wh ere the task is easier, but rather with sity of the stimulus. Perceptual qualities such

100

80 iii' :s a; > C1l -' 60 'Cc: :::> 0 tI) 40

Rel ativeIntensityof Stimulus 1IIIDIttr.. _ Cross-modal matching between loudness and 10 other sensory stimuli. The slope of each equal sensation function isdetermined by comparingexponent values from the power fun ctions ofloudness and the particular stimulus. Adapted from "Matching Functions between Loudness and Ten Other Continua,"by S. S. Stevens, 1966, Perception and Psychophysics, 1, pp. 5-8. Chapter 1 Principles of Perceptual Measurement

as brightn ess or loudness, for example, can be similarity is now represented by physical dis­ associated with a numerical value of physical tance in a spatial map. This tech nique, which intensity. Sensory experiences wh ere subjects is known as multi-dimensional scaling, can make a judgment of "how mu ch" are allows an investigator to peer into the under­ termed prothetic. However, there exists a dif­ lying attributes or qualities of th e stimulus ferent class of sensory experience that canno t that prod uce similar or dissimilar percep­ be directly linked to stimulus intensity. Colour tual experiences . Multi-dimension al scaling perception is a good example,wh ere there is no is now well established as the tool of cho ice quantitative difference between , say, the hues of for pairwi se evaluatio ns of ent ities in such red or green.T hey produce two entirely differ­ diverse fields as genetics, linguistics, social sci­ ent kinds of percepti on , which thou gh linked ences, and psychology (Baird & N om a, 1978; to the wavelength of light, canno t be scaled to Schiffman, R eynolds, & Young, 1981). wavelength in a meanin gful way. Increasing the wavelength of light does not add to the mag­ 3, SCALING OF NONSENSORY nitude of the sensory experience but rath er VARIABLES changes it entirely. Such perceptual qualities are called metathetic. O ur keen j udgme ntal abilities are not j ust [t turns out that prothetic pro cesses gen­ restricted to the primary senses but extend to erally obey th e power law, but metath etic pro­ some rather complex aspec ts ofhuman percep­ cesses do not (Gesc heider, 1997). The reason tion .The general prin ciples of intram odal and for this is likely du e to th e way the two kinds cross-mo dality matching may also be applied of sensory dim ension s are processed by the to nonsensory variables within the fields of brain. Prot hetic percepti ons are believed to socio logy, politi cal science, and esthetics. The rely on additive processes such that changes in same procedures that were used to scale lou d­ stimulus int ensity produce either an increase ness and br ightness, for example, can also be or decrease in the activity of the associated applied to questions such as the value of art, sensory neurons. The collective behaviour of the imp ortance of certain occupations, the ser­ this system is such that it follows the power iousness of crimes, etc. In other wo rds, a set law.Metathetic percepti on s, on th e other hand , of scaling meth ods can be employed in what show a change in quality, and this in turn is some have called social psychoph ysics to establish associa ted with th e substitution of one kind of measures of subjective magnitude in the areas SideNote 11,12 neural excitatio n by ano ther.T herefore, in the of esthetic preference or social/political opin­ Fechner himself workedfor absence of an additive pro cess, th ere is little ion (Lodge, 198 1). sometime on problemsof scope for relatin g metath etic experiences with esthetics and howtoapplytech ­ the stimulus in a quantitative mann er because Discrimination scaling versus ratio scaling niques from sensory psycho­ there is no exac t relation ship between sen­ The orig inal work in this area actually began physicstomatters ofsocial opinion. In one experiment,he sory impression and variation in the stimulus with Fechner and was later refined by Louis obtained estheticjudgments for (Manning, 1979). T hursto ne in the 1920s (SideNote 1.12). T he two versions of HansHolbein 's basic logic of Fechner's sensory psychophysics Madonna. Therewas quiteabit Multi-dimensional scaling was used by Thurston e to study social issues of controversy atthe time as to Psychologists have had to devise some clever such as preferences for nationalities and the ser­ wh ich had actually been painted techniq ues to analyze metath etic percepts. ln iousness of crimes (SideNote 1.13).T hurstone by Holbein. general, these techniqu es rely on the noti on of mad e the assumption that dispersions in j udg­ similarity or dissimilari ty (Bo rg & Groenen, ment represented a standard distance in sub­ 2005). Consider colour percepti on as an jective impression (T hurstone, 1959). His use SideNote 1_1_.1_3'-- _ example. Subjects can be presented with thre e of a nonsensory JND-like parameter produced "Insteadofasking students to colours at a time and asked to judge which fun ction s that retained the same math emat­ decidewhichoftwo weights pair is the most similar-a procedure called ical quality as those seen in classical sensory seemed tobe the heavier,it the methodoj triads.After enough data has been psychop hysics. Both T hursto ne and Fechn er was moreinteresting to ask,for collected with a sufficient nu mb er of colours, thus made a fundamental assumption that example, wh ichoftwo national ­ ities theywouldgenerally prefer it is possible to represent the info rmation by each increm ent in discrimination, measured toassociatewith,or which they way of a similarity map wh ere those col­ as a JND, produces equivalent increases in sub­ wouldprefer tohavetheir sister ours that are perceived to be similar occupy jective impression- in other wo rds, the vari­ marry, or whichoftwo offenses nearby position s, and tho se that are dissimilar ability in psychological un its is co nstant along seemedto themto be the more are placed farther apart . T hus, psychological a linear psychological continuum. This kind serious" (Thurstone, 1959). Fundamentals of Sensory Perception

of psychophysics became generally known as (Ekman & Sjobert , 1965). Ekman prop osed discrim ination scaling or confusion scaling that detectable changes in sensation UND), (Torgerson, 1958). rath er than being constant at all levels as pro­ T he alternative view that had led to posed by Fechner, were actually related to sen­ psychophysical power functions was based on sation in a linear manner. In other words, the the notion that equal units of discrimination relationship between changes in sensation that along the stimulus continuum did not rep­ are j ust detectable at a particular sensatio n level resent equal distances but rath er equal ratios (or magnitude) is exactly analogo us to Weber's along the subjective continuum. The so-called law and can be stated as follows: ratio scaling procedures that were developed f1S k • S as a result, including Stevens' magnitude esti­ = mation technique, soo n found their way into This relationship was actually prop osed as early studies of social consensus as well (Ekman & as 1874 by Franz Brentano. By that tim e, how­ Sjobert, 1965). Among the more colourful ever, the Fechnerian way of thinking so dom ­ examples in this category are studies on the inated perceptual psychol ogy that Brent anos politi cal imp ortance of Swedish mon archs, idea was largely ignored and remained without the prestige of certain occ upations, the facto rs influence until Ekm an restored the validity of co ntributing to social status, the esthetic value this principle in the 1950s.As a result, the rela­ of art and mu sic, the percept ions of national tion ship is now known as Ekman's law. power, and th e judged seriousness of certain crimes (Chang & C hiou, 2007; Ekman, 1962; Fechner's missed opportunity Vrij ,2000). The implications of Ekm an's law are quite The above examples show how ratio scal­ profound.T he not ion that the JND is not con­ ing can be used to assess nonsensory variables. stant at all levels ofsensatio n marks a dramatic In a classic study, Thorsten Sellin and Marvin departure from the Fechnerian way of think­ E. Wolfgang showed that th ere is a gen eral ing.If we strictly adhere to Fechn er's postulate consensus across society on the perceived that the JND rem ains constant along the sensory seriousness of a variety of criminal offences continuum, then, as we saw earlier, logarithmic (Sellin & Wolfgang, 1978). Using magnitude functions relating stimulus to sensatio n are the estimation procedures, they showed that the natural consequence, given th e existence of theft of progressively greater sums of mon ey Weber's law. If, however, Fechn er had applied was acco mpanied by growth in the j udged the idea behind Weber's law to the sensory seriousness. While this is hardly sur prising, it co ntinuum as well and ado pted the view that turned out that the power function for judged the JND was not constant but rath er a constant seriousness grew with the amount stolen by ratio of the sensory level, then he wou ld have an exponent value of on ly 0. 17.Thus, approxi­ derived the psychophysical power function . In mately 60 times as mu ch mon ey needs to be other wo rds, if both Weber's law and Ekman's stolen in order to be perceived as being twice law are applied, then the math ematical out­ as serious by most people. Similarly, Sellin and come necessarily becomes Stevens' power law SideNote 1_1_.1_4 _ Wolfgang found that the judged seriousness of (SideN ote 1.14). crime is related to jail tim e prescrib ed by the But is Ekman's law valid? It has been If Fechnerhad changed his view and adopted Brentano 's Pennsylvania Penal Code by a power function argued that since th e prop ortion ality rul e is suggestion that the JND was with an expo nent value of0.7.These examples gene rally tru e for th e physical sciences and related tosensation level ina illustrate how important societal issues can be since it also applies in perceptual science by manner similar toWeber'slaw, addressed by psychophysical scaling techniques way ofWeber's law, it is reasonable to assum e then Fechner would actually that were ori ginally developed to study sen­ that a similar relation ship would hold tru e have been the first toderive sory processes. for th e sensory co ntinuum. Several empirical the powerlaw function in studies have provided suppo rt for this view. sensory science,which isnow Ekman 's law widelyaccepted. For example, R obert Teghtsooni an showed As with sensory stimuli, discrimination scaling that th e proportiona lity rule appe ared to be of nonsensory parameters produced logarith­ the same for several different sensory experi­ mic functions, wh ereas ratio scaling procedures ences (Teghtsoo nian, 1971). In other wo rds, co nsistently yielded power function s. Goes ta th e value of k in Ekm an's law, whic h was Ekman at the University of Stockholm pro­ found to be 0.03, do es not change with the vided a theoretical account for this difference nature of th e sensory experience .This means Chapter 1 Principles of Perceptual Measurement

that for all types of sensation, th e size of the JND expressed in subjective un its is approxi­ mately 3% of th e actual sensatio n magnitude at any level.

4. SIGNAL DETECTION THEORY To close this chapter, we return to the idea that the threshold represents a fund amental boundary between stimulus intensities that do SensationMagnitUde not evoke sensation and those that do.We dis­ 1I!lIDta.. _ cussed earlier in Section B.2 that there is no Background noise varies randomlyover time and therefore appears inthe form ofanormal distribu­ such entity as a clear- cut, all-or- no ne absolute tion.When aweakstimulusispresent,the sensory magnitudes produced by itare added to noiseand threshold. R ath er, there is always some vari­ therefore result inadistribution that isshifted tothe right. ability du e to inte rnal and external noise so that the threshold in turn depends on the likelihood that the signal exceeds this noise implies that sensory events triggered by noi se to produ ce a detectable sensory event. This alone will vary with tim e. In an absolute means that the same stimulus may be detected threshold experime nt, the subject is asked to on some occasions and not on others. The detect a weak stimulus against this rand om idea that eme rged from classical psychophys­ background activity. Since the stimulus must ics is that the threshold itself can vary over be detected by the same noisynervous system, a time. Modern psychophysicists have sought probability plot ofsensatio n magnitude evoked to identity the sources of this variability and by the stimulus will also show a normal distri­ develop new theoretical foundation s that take bution because the signal must be added to the into account nonsensory factors that can affect noise distribution. Because of this additivity, signal detection .As we will later discover, these the combined signal + noise distribution must developments have revised our thinking abo ut always lie to the right of the noise distribution the threshold co nce pt itself. alone, as shown in Figure 1.9. A major advance in this field was made The rand om variatio n in background in the 1950s by Wilson P. Tann er and John noise poses an int eresting problem . When the A. Swets who prop osed the use of statistical stimulus to be detected is quite weak, the two decision theor y to understand how humans distributions will have considerable overlap, behave in a detection situation (Green & as is the case in Figure 1.9. Therefore, there Swets, 1989). This new model, called signal may be some instances wh ere the noise itself detection theory (SDT) , uses statistical con­ may be so high that it could be mistaken for cepts that take into account cognitive factors the signal, whereas in others the noise may be that may influence a subject's decision-makin g so weak that the signal is mistaken for noise process. Thus, th ere is not only a signal to be (Swets, 1996). On each trial, the subject must detected, which in turn relies on the inh erent therefore make a decision whether the evoked sensitivity of the sensory system, but also th e sensation was du e to a signal added to the noise decision by the subject as to wh eth er a signal or to the noise alone. Clearly there are two dif­ worthy ofa positive response ind eed existed. ferent processes at work here, and the subject must make a distinction between the effects of Basic foundations ofsignal detection theory one versus the other. But how can we parse In SDT, sensatio n magnitudes evoked by noise the effects of noise versus signal + no ise at the (N) and signal + noise (S + N ) are represent ed behavioural level in a detection situatio n? In as separate distributions. A major source of other wo rds, how can we measure the relative noise is th e baseline firing of nerve cells that effects of signal and noise through psycho­ produces spo ntaneo us activity in sensory path­ physical meth ods? ways.Because of the rand om nature of this activity, a probability plot of sensation mag­ Measuring the effects of signal and noise nitudes evoked by internal noise alone will In early psychophysics experime nts, a stimulus appear in the form ofa normal distribution, as of some intensity, however weak , was always shown in Figure 1.9. This rand om fluctuation present in each trial. T he assumption was that Fundamentals of Sensory Perception

the subject wo uld provid e a response based alarm.T he subject indicated that a signal was solely on whether the signal produced a detect­ present wh en in fact the sensation was only able sensation. In terms of the SDT scheme, only produ ced by noise. If however a signal was the signal + noise parameter was being tested, actually present in the trial, then the effects of and psychom etri c functions therefore reflected signal + noise in that event may be sufficient the cumulative effects ofthat distribution (e.g., for the subject to respo nd YES, which is termed see SideNote 1.5 on page 8).The way to test a hit.The alterna tive possibility is that the sub­ the effects ofnoise alone in a detection experi­ ject responds NO, in whi ch case it is termed a ment is to rand oml y give the subject a num­ miss because the subject failed to detect the ber of trials in which no stimulus is present.All signal. Thus, there are only four possible out­ instan ces of a YES respon se in such trials can comes in an SDT experime nt with two being then be assumed to be the effects of noise alone attributed to the effects of the noise compon­ because no signal was present. In other words, ent and the other two to the effects of signal + some internal process within the subject either noise (W ickens, 2001). produced a sensation that coincided with the trial and therefore led to a positive response or, Criterion effects-general properties alterna tively,an erroneo us j udgme nt was made If false alarms are th e product ofnoi se, and hit s in the belief that a sensory event had occ ur red. are th e result ofthe combined effects ofsignal Either way,"no stimulus" trials allow research­ and noise, th en which point along the x-axis ers to get a hand le on the pervasive effects of in Figure 1.9 can the se effects be attributed noi se, regardless of its source, in that particular to? In other words, how much sensation mu st detection experime nt. take place before th e relative effects of noise The possible outco mes in such a study are and signal + noise yield a false alarm or a hit, shown in Table 1.3. If a trial did not contain respectively? One of th e basic assumptions a stimulus, then the two possible responses of of SDT is th at each subject establishes a set the subject can be categorized as follows.A NO point or criterion

distribution to the right of the criter ion gives Criterion (B) the probability of hits that will be observed in ... trials that contained the stimulus. As we can NOresponses YESresponses see in Figure 1.10, the number of hits will be far greater than false alarms in this parti cular situation, given the nature of the two distribu­ tions and the criterion value that was ado pted by the subject.

Criterion effects-expectation Is it possible for the subject to adopt a different criterion value ? Let us consider wh at would happen if we conducted two experime nts, one in which we told the subjec t that a stimulus will only be present on 30% of the trials and a second experiment in which we told the sub­ ject that the stimulus will be present on 70% of the trials. In the first experiment, the sub­ ject will not expect a stimulus on the major­ ity of trials and therefore will likely adopt a

conservative criterion. In other words, the Sensation Magnitude criterion value will shift to the right of the one shown in Figure 1.10, implying that the sub­ ~------( ~) ject will only choose to respond YES when The criterion level established by each subject determines the sensation magnitude that must the evoked sensory magnitude is quite large. occur for a YES response. The interaction of B with the two distributions determines the relative proportionofeach of thefourpossible outcomesinan SDT experiment. The noiseandsignal + noise. In the second experime nt, a more liberal cri­ distributions are shown at different verticallevelsfor clarity. terion will be ado pted, reflecting the higher probability of stimulus appearance. The cri­ terion will now move to the left of the one shown in Figure 1.10. Compared to the first and simply defines th e sensory magnitude that experim ent, mu ch lower sensory magnitudes will be required under the circumstances for will now be sufficient to elicit a YES respon se a YES response. For any given pair of noise because the subject will expect more trials and signal + noi se distributions, the criterion to contain a stimulus. T hus, depending on an value will in turn spec ify th e rates of hits and inherent expectation of stimu lus appearance, false alarms (W ickens, 200 1). the subject will be either more or perhaps less inclined to give a positive answer on each trial, even though none of the other parameters in the experiment have chan ged . Table 1.4 Both situations will affect the hit and false The Effects ofExpectation on Detection alarm rates.As we shift the criterion more and Performance inan SDT Experiment more to the right (i.e., redu ced expec tation), there will be fewer instanc es of false alarms as well as hits. This is shown by the data in False Table 1.4 wh ere a stimulus appearance prob­ Alarm ability of 30%, and the acco mpanying right­ ward (conservative) criterion shift, results in en u :::J 0 30% 0.09 0 0.36 rates of0.09 and 0.36 for false alarms and hits, "5 si: E ~ respectively (Side N ote 1.16).When the subject t5 :.:J 70% 0.64 0.91 SideNote 1....::.1 ..::..... 1:....:6=--- _ is notified that stimulus appearance probabil­ ity will be set at 70%, the accompanying left­ We need not showthe rates Note. If the subject is awarethat the likelihood of stimulus appear­ for correct rejection since it is ward (liberal) criterion shift results in higher ance is low, she will adopt a conservative criterion that will in turn simply 1 minus the false alarm rates of false alarms and hits- 0.64 and 0.91, produce low hitandfalse alarm rates. The opposite happens if the rate. Similarly, the miss rate respectively.The bottom line is that the criter­ subject has ahigh expectationofstimulusappeara nce because she need not be shown since it is ion level adopted by the subject is changeable will then adopt a liberalcriterion. always 1 minus the hitrate . Fundamentals of Sensory Perception

The ROC curve Criterion effects-motivation In a typical detection experime nt, several hun­ In addition to stimulus expectation , th ere are dred trials are given that fall either in the noise other factors that can affect a subject's criter­ (stimulus absent) category or in the signal + ion and therefore also influence the dete ction noise (stimulus present) category. The actual of weak stimu li. An especially powerful factor proportion of trials in each category is set in is motivation (Swets, 1996). Consider a situa ­ advance and communicated to the subject. As tion where a subj ect is paid to participate in a we have just seen, the subject establishes a cri­ stimulus detection experime nt in which th ere terion based on this information, whi ch in turn are neither pen alties for wrong answers (i.e., will impact performance. A convenient way of false alarms) nor rewards for co rrect ones illustrating tho se effects is by way ofa receiver (i.e., hits).The experimenter is entirely at the operating characteristic (ROC) cur ve (Egan, mercy of the subject, hoping that the subject 1975; Green & Swets, 1966).An exampl e of an will give a conscientious effort despite bein g RO C curve that takes into account our results guaranteed a certain amount of money for is shown in Figure I .II. So far, we have been merely participating. Let us make this experi­ interested in two outcomes-false alarms and ment a little more interesting. As in all SDT hits-that tell us how much the noise and signal experiments, we give a certain number of + noise distributions contribute to detection trials that will contain a very weak stimu­ performance. An ROC curve plots the prob­ lus (i.e., signal + noi se trials) and others that abilities of these two factors with false alarms will not (i.e., noi se- onl y trials). But now we represented on the x-axis and hits on the y-axis. will tell the subject that paym ent is co ntin­ Each point on an ROC curve is therefore speci­ gent upon performance in both sets of trials. fied by the subject's criterion since that deter­ That is, every tim e there is a correct respon se mines the relative values ofhits and false alarms to a signal + noi se trial (hit), the subject will in an experiment. be rewarded. However, there will be a pen­ The two experimental situations discussed alty if an incorrect respon se is given in a noi se on the previous page produced different criter­ trial (false alarm). This way we will ensure ion levels because ofdifferent stimulus expecta­ that the subject will not arbitrarily respond tion s. The resulting hit and false alarm rates from Table 1.4 are shown in the ROC curve of Figure 1.11. The experiment with the higher 1.0 stimulus appearance probability (70%) pro­ duced a liberal criterion, whi ch on an ROC 0.8 plot appears as a point toward the upp er end of the curve. Had the stimulus appearance prob­ Uberal ability bee n set even higher, then this point too :;:- 0.6 crit o I e

YES throughout the experime nt because of prod uce considerable response bias that in the false alarm penalty or similarly respond turn affects the probability of signal detection . NO throughout because th en rewards will T hese results call into question the very exist­ not accumulate. In short, we will now have ence of thresholds that supposedly demarcate a highly motivated subject who will try very the onset ofdetectable sensations because clearly hard to distinguish the signal from noi se trials such boundaries are susceptible to the effects of (Lu & Dosher, 2008) . nonsensory variables (King-Smith, 2005). It turns out that th e way we set up th e In classical psychophysics, the physical rewards and penalties will influ en ce th e sub­ intensity of a stimulus that produced YES ject's criterion in th e same way th at we found respon ses 50% of the tim e was taken as the for stimulus expec tancies.Table 1.5 shows two absolute threshold of detection . Given what possible payoffco nditions that may be used . If we now know abo ut the hit rate being sus­ SideNote 11.17 the subject is told in advance that each hit ceptible to cr iterion effects, th e actual int en­ An often-used example can will be worth 50¢ and eac h false alarm will sity value producin g 50% YES respon ses servetodistinguish the rela­ incur a penalty of 10¢, th en we will create a sho uld th erefore also vary. In other wo rds, the tive effects ofexpectancy greater tenden cy for YES votes because th e psychom etri c functions th emselves sho uld and motivation. Aperson who disparity in reward vs. pen alty will assure a change with the subject's criterion, and there­ isin charge ofobserving a greater payoffin th e lon g run. In other wo rds, fore no single all-e nco mpassing threshold radarscopetodetect enemy the subject will ado pt a liberal criterion. If value can be derived (SideNote 1.18). Given aircraft is highly motivated to however we reverse th e paym ent condi­ that detection performance relies so heavily ensurethat a true signal does not go undetected becausethe tions and imp ose a penalty for false alarms on the effects of non sensory facto rs, the very cost for that failure istoo high. that is mu ch greater than th e reward for hits, co nce pt of an immutable absolute threshold Thus, we have an individual then th e subject wi ll tend to be very cau­ has become meanin gless. who will likely adopt a liberal tious and take fewe r risks. The subject now criterion basedonthisfactor adopts a co nservative criterion. If we take Signal intensity and detection sensitivity alone. However,the likelihood the hit and false alarm rates from th ese two According to SDT, there is a certain inh er­ of a sig nal actually appearing is quite small sinceenemyaircraft situatio ns and plot th em on an ROC cur ve, ent sensitivity that applies to the opera tion usually do not pop uptoooften. we will find a situa tio n analogous to that seen of sensory systems. Human performance in Therefore the criterionwilltend in Figure 1.11 .T he first payoff co nditio n will detection experime nts is governed by that toshifttoward more conserva­ place th e criterion value more tow ard the left sensitivity as well as various nonsensory fac­ tivelevels that will reducethe side of th e noise/signal + noise distr ibution s tors. If the detectability of sensory events is likelihood ofa hit.Nevertheless, and therefore will produce hit and false alarm given theimportance ofsignal rates that will plot toward th e upper end of detection (andthepenaltyfor a Table 1.5 the RO C curve. The seco nd payoff co ndi­ miss) ,the probabilityfor a hit is kept highand must beaccom­ tion will produce a criterion more toward Payoff Conditions forTwoDifferent SOT Experiments panied by a relativelyhigh false the right side of th e two distributions, and alarm rateas well. this will yield a point on th e lower end of ·I Payment Conditions for the RO C curve. If we employed othe r pay­ SIgna a YES Response off co nditions, th en th e reward /penalty ratio would produce appro priate points elsewhere Experiment 1 Experiment 2 SideNote 1_1_.1_8'-- _ on the ROC curve. In effect, we find that Early psychophysicists were motivation al states induced by different pay­ Absent aware that biasing factors were -10¢ -50¢ off co nditio ns produce criterion shi fts th at (falsealarm) present in their absoluteand are similar to th ose we saw on th e previou s difference threshold experi- ments and thatthesefactors page for stimulus expec tancies. Present couldinfluencetheirdata. One (hit) way toreduce bias wastouse The problem with thresholds highly trained subjectswho The two factors that we have co nsidered Liberal Conservative could be relied upon to make • accuratedetection jUdgments. thus far-stimulus expec tancy and motiva­ criterion criterion tion-have nothing to do with the signal itself Anothertechnique wasthe useof so-called catch trials, in (SideNote 1.17). In the experime nts con­ Note. In thefirst experiment,hitsare rewardedat afar greater level whichnostimulus was present. sidered above, the signal strength was kept thanthe penalty for false alarms, leading tothe adoptionof aliberal Thefal sealarmrate taken from constant throughout, and the only param­ criterion . Inthe second experiment, the penalty for false alarms is these trialswas then used to eter that changed was the non sensory factors. far greater than the reward for hits, leading to the adoption of a scalethedata fromstimu lus­ And yet, we have show n that these factors can conservative criterion. containing trials. ~undamentals of Sensory Perception

susceptible to higher-level mental functions the top panel (weak stimulus) and very large that influence our j udgments, then how is it in the bottom one (strong stimulus) . A meas­ possible to gather insight into detection sensi­ ure of the separation between the two distri­ tivity that is uncontaminated by such factors? bution s is taken at their peaks and is denot ed To answer this, we have to take a closer look at as d ' (pro no unce d d-prillle) (Swets, 1996). the noise and the signal + noise distributions The three pairs of distributions in Fig­ in relation to each other. ure 1.12 can be interp reted ano ther way.Let us Thus far we have said very little abo ut assume that the signal is now kept co nstant and the stimulus itself and have vaguely referred instead three different individuals are being to it as a weak signal that is added to noise tested, each one having a different inherent and whose de tectability is assessed by way of sensitivity to the stim ulus.The more sensitive a a simp le"YES-NO" experiment. The signal + person is to this particular stimulus, the greater noise distribution that we have become fam­ the sensatio n evoked by that stimulus. Since iliar with is actually a reflection of two differ­ the signal + noise distributio n is a probabil­ ent parameters-signal int ensity and detection ity plot of sensory magnitudes, a highly sensi­ sensitivity. To understand this, let us co nsider tive individual will have a distribution shifted three different stimuli, each one bein g of a farther to the right and away from the noise progressively greater inte nsity. T he signal + distrib ution, as shown in the bottom panel of no ise distribut ion of each stimulus progres­ Figure 1.12. In other words, the same stimulus sively shifts farther away from the noise dis­ will generate greater sensory magnitudes in a tributi on, which does no t change because more sensitive person and therefore produce a the underlying effects (e.g., random noise in more rightward shifted signal + noise distribu­ th e nervou s system) are not disturbed. T his is tion. In this context, a large d' value is taken to shown in Figure 1. 12 wh ere the separatio n represent an individual with a high detection between the two distributions is quite small in sensitivity. The less sensitive the subject is to

d'

Sensation Magnitude ~~------The relative positions ofthe noise and signal + noise distributions are determined by signal intensity and detection sensitivity. The signal + noise distribution is progressively shifted to the right and away from the noise distribution as signal strength increases. A simi lar effect is seen if the sig nal is kept constant but the detectorbecom es more sensitive .The relative separationof thetwo distributionsis takenat their peaks and denoted as d'. Chapter 1 Principles of Perceptual Measurement

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

the stimulus, the closer the two distributions levels can operate independently upon these will be with respect to each ot her, and accord­ distributions to produce different experimental ingly d' will be smaller (Wic kens, 200 1). outcomes of hit and false alarm rates.T his idea is illustrate d in Figure 1.13 where four dif­ Sensitivity and d' ferent pairs of noise/ signal + noise distribu­ The importance ofd' is that it provides a num­ tio ns are shown, each with a different d' value erical estimate of a person's sensitivity and ranging from 0.5 to 3.0 (SideN ote 1.19).T he therefore allows comparisons among different accompanying ROC cur ves show the expected SideNote 1-'.1-'.,1'-'9'-- _ individuals. Unlike th reshold values that can detection performance if we apply a continu­ By convention, d' isexpressed change with criterion levels, it has been shown ously variable criterion to each ofthese sets of as standard deviation units of that d' remains relatively robust and is unaffected distributions. the noise distribution.Thus, d' by nonsensory factors. In other words, d' as a As an exampl e, let us consider the two valuesof0.5, 1.0, 3.0, etc., measure of sensitivity simply stipulates the extreme cases. If d' = 3.0, then the large separa­ represent respective factors of relative separation of the noi se and the signal tion of noise and signal + noise distributions standard deviation (or z-score). + noise distributions. The different criterion will ensure that the hit rate far exceed s the

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

:i:- o ­~ zs .cctI c..e

o 0.2 0.4 0.6 0.8 1.0 Probability of FalseAlarm -....~------Afamily ofROCcurves that are generated by different values ofd'.The greater the sensitivity toa particu lar stimulus, the greater the separation of the noise and the signal + noise distributions.Alarged' value produces an RO Ccurve that isbowed toward the upperleft. As the two distributions get closer (smaller d' values), and eventually overlap,the ROC curve flattensoutand becomesastraight line. Fundamentals of Sensory Perception

false alarm rate for mo derate to liberal criter­ toward the lower left.We can obtain a measure ion levels (i.e., rightward criterio n placement). of the criterion used by the subject because The RO C curve will bow upward to reflect a all possible points will map onto a single RO C far greater proportio n of hits in co mparison curve that in turn will be governed by that to false alarms . If however the two distribu­ person 's detection sensitivity. tions are very close togeth er (e.g., d' = 0.5), SDT provides insight not only into the then there will be a greater similarity in hit intrinsic sensitivity of the sensory system but and f.1 lse alarm rates because of the closeness also into the motives, expectancies, and other of the two distribution s. This situation will human psychological factors that influence produce a weakly bowed ROC curve . T hus, as the decision -making process (Macmillan & the noise/ signal + noise distribution s approach Creelman, 2004). However, there may be situa­ each other, the ROC curves will progressively tion s where a sensitivity measure is requ ired flatten out.The limit is reached wh en the two without the influence of such nonsensory fac­ distributions overlap each other (i.e., d' = 0) tors. In such cases, the use of forced cho ice and produce a straight line. In this case, either procedures allows rapid estimation ofonly the there is no signal or the subject is simply incap­ sensitivity parameter. In the two-alternative able of dete cting the stimulus. In either event, forced ch oic e (2AFC) procedure, two pres­ detection performance will be random, and entations are made on each trial.The subject is there will be equal prob abilities of hits and told that one of the present ations will contain false alarms regardless of the criterio n. the signal and the other will not . The task is to indicate which presentation contained the Procedural aspects signal.The impact of criterion effects is mini­ SDT has becom e highly popular amo ng per­ mized beca use the subject knows that one of ceptual psychologists because it provides both the two presentations will definitely contain a an estimate of the relative sensitivities of dif­ stimulus. T he only experimental outcome to ferent individuals to a particular stimulus and a consider then is the hit rate, which can fluc-' measure of how non sensory factors may influ­ tuate between 0.5 (random guessing) to 1.0 ence the judgme nts of vario us subjec ts in its (perfect performance).The proportion of cor­ de tection.The purpose in any SDT experime nt rect respon ses can then be used as a measure of therefore is to obtain values of both d' and 13. sensitivity because nonsensory factors do no t Both of these parameters can be quite easily affect the hit rate in this situation. determined once we know the hit and false A valuable feature of the 2AFC procedure alarm rates from a signal detection experime nt is that the exper ime nter knows whether or not (Mc N icol, 2004). For any given subject, there the subject is responding correctly in a particu­ will be only on e RO C curve that will apply lar trial. This has allowed more elaborate ver­ in that experime nt since the stimulus inten­ sions of this procedure to be develop ed. In the sity is fixed and the individual has a particular staircase procedure, the stimulus level can inh erent sensitivity to that stimulus.The 11l1l11­ be varied in relation to the subject's responses. erical descriptor of that sensitivity, d', can be For example, stimulus int ensity may be con­ obtained by graphically determ inin g which tinu ally increased as long as the subject is mak­ one of a family of ROC curves co ntains the ing incorrect responses. Similarly, the intensity subject's hit and false alarm rates. The only can be progressively decrease d when only cor­ variable now is the criterio n. If the subject rect responses are given. This alterna tion in employed a liberal criterion, then this point stimulus intensity is continued until a specified wo uld be located toward the upp er right of number of response reversals take place. The that particular ROC curve . If a co nservative cri­ signal inte nsity at this poi nt can be used as a terion was employed, then this point wo uld be measure ofsensitivity. Chapter 1 Principles of Perceptual Measurement

1. There is a rich history of scientific magnitudes could be directly determined research on sensory perception, beginning through quantitative methods. His tech­ with the German psychophysicists of the nique of magnitude estimation led him to 19th century. Their goal was to arrive at establish the pOlVer law, which states that a quantitative relationship between stimu­ sensor y magnitude is related to stimulus lus inte nsities and sensation magnitudes. intensity raised to an exponent value that Knowin g the quantitative relationship has is generall y less than 1.0, though some several advantages, though it is difficult to sensory experiences (e.g., electric shock) obtain directly because of our inability to have an exponent greater than 1.0. measure sensation. The approa ch taken by 5. Psychophysical techniques can be used the German scientists was to first obtain to determine quantitative relation­ two parameters-the starting point and ships within the same sensory system the slope ofthe function.This information (intramodal matching) or across sen­ could then be used to reveal the nature sory systems (cross-modality matching). of the math ematical relationship between Whereas techniques such as magnitude stimulus and sensation. estimation can be used to assess sensa­ 2. Fechner developed several psycho­ tions that have a dire ct relationship to the physical techniques to determine the stimulus (prothetic sensations), a different absolute threshold (w hich repre sents the set oftechniques such as multi-dimensional starting point of the stimulus-s ensation sca li"g must be used to assess those sen­ relation ship) and the difference thresh­ sations that are entirely altered when a old (whic h provides insight into how stimulus parameter is changed (meta­ the slope of the stimulus-sensation fun c­ thetic sensations). tion changes at suprathreshold levels). 6. The same psychophysical principles and The Method of Constant Stimuli pro­ techniques used to understand sensory per­ vides the most accurate data, wh ereas the ception can also be used to assess various Meth od of Adju stm ent is the easiest to nonsensory questions in the domains of conduct and produces the fastest results. economics, marketing, sociology, and pol­ Psychophysical experime nts with these itics.A power law function is derived in all techniques have shown that humans do cases where the exponent value provides not behave as ideal detectors but instead insight into the underlying relationship show a gradual progression ofresponsive­ between the variables being probed. ness wh en increasing some physical par­ ame ter related to the stimulus. 7. Signal detection theory (SDT) is based on statistical concepts that examine the pos­ 3. Weber was interested in the gradation of sible relationships between the stimulus sensory experience by studying how the (signal) and the underlying noise. The difference threshold itself varied with the probability distributions of the signal and stimulus level. He found that the differ­ signal + noise profiles provide the basis for ence threshold is not constant but actually estimating the behaviour of individuals in increases linearly with stimulus inten­ terms of their criterion level, expectation, sity (known as I#bers lalV). To derive the and motivation in a psychophysical setting. stimulus-sensation relationship, Fechner The way in which noise and signal + noise made the assumption that a detectable can affect detection performance is given change in sensation (LlS) caused by the by the receiver operating characteristic (ROC) difference threshold (Ll I) remained con­ curve . SDT experiments have shown that stant at all levels of sensory magnitude. there is no exact threshold value for any T his insight, in conjunction with Weber's sensory parameter but rather the thresh­ law, led Fechner to postulate that sensation old is something that is affected by other magnitude is related to stimulus intensity nonsensory parameters. Consequently, a by way of a logarithmic function (known more reliable parameter is d', which pro­ as Fechner's law). vides a more robust numerical estimate of 4. The era of modern psychophysics began a person's sensitivity that is unaffected by with Stevens who believed that sensory nonsensory factors, Fundamentals of SensoryPerception absolute threshold, 6 metathetic, 17 scaling, 14 correct rejection, 20 Method of Adjustment, 6 sensory transducer theory, 15 criterion (P), 20 Method of Constant Stimuli, signal, 19 cross-modality matching, 16 7 signal detection theory (SOT), d' (d-prime), 24 Method of Limits, 6 19 difference threshold, 6 miss, 20 staircase procedure, 26 discrimination scaling, 18 multi-dimensional scaling, 17 step function, 7 Ekman's law, 18 noise, 19 stimulus, 4 false alarm, 20 ogive,7 subthreshold, 6 Fechner's law, 13 power law, 14 suprathreshold, 6 function,S prothetic, 17 two-alternative forced choice hit, 20 psychometric function , 7 (2AFC),26 ideal detector, 7 psychophysics, 6 Weber's fraction (k), 11 intramodal matching, 16 ratio scaling, 18 Weber's law, 10 just noticeable difference receiver operating OND),9 characteristic (ROC), 22 magnitude estimation, 14 response bias, 23

1. What are the three pri ncipal advantages 6. What is the fund amental difference of obtaining a math ematical relation­ between a prothetic and a metathetic sen­ ship between stimulus intensity and the sation? Provide some examples other than resulting sensation magni tude? the one s discussed in this chapter. 2. What are the parameters that prevent 7. W hat would Weber's law have to look human subjects from beh aving as ideal like for the stimulus-sensation function to detectors? have an exponential profile? 3. What is the difference between the absolute 8. How does Ekm an's law differ from the threshold and the dijferellce threshold? Why assump tion of JND constancy made by did Weber have to undertake multiple Fechner? Is it possible to verify Ekm an's experiments on the difference threshold law with absolute certainty? to derive the law that bears his name? 9. What are the key departures in the signal 4. What was the fundamental problem in detection theory model from the concept Fechn er's assumption on the constancy of of an all-or-none threshold? What are the JND at all sensory magnitud es? Could the different variables that can affect the Fechner have derived his law without this threshold? W hat is the advantage of using assumption? d' as a measure ofsensitivity? 5. How did modern psychophysics depart from classical psychophysics in terms of both its methodology and its core und er­ lying principle? Chapter 1 Principles of Perceptual Measurement

• Borg, I., & Groenen, I~ (2005). Modern • Marks, L. E. (1974). Sel/sory processes: ntultiditncusionat scaling: Theory and applica­ TIle ucui psychophysics. New York, NY: tions. NewYork, NY: Springer. Academic Press. • Gescheider, G. A. (1997). Psychophysics: • McNi col, D. (2004). A primer 4 signa! The [undamentals. Hillsdale, NJ: Lawrence detection theory. Hillsdale, NJ: Lawrence Erlbaurn . Erlbaum. • Green, D. M., & Swets,j. A. (1989). Sigl/al • R ichardson, R. D. (2007). Willialll [ames: 11/ detection theory and psychophysics. NewYork, the maelstrom 4 A merical/ Modernism. New NY: Peninsula Publishing. York, NY: Mariner Books. • Heidelberger, M., & Klohr, C. (2004). • Stevens, S. S. (1986). Psychophysic: N ature from within: Gustav Tlieodor Fechner Introduction to its perceptual, neural, and social and his psychophysical wotldview. Pittsburgh, prospects. New Brunswick, NJ:Transaction PA: University ofPittsburgh Press. Publishers.