In the branch of experimental psychology focused on sense, sensation, and perception, which is called psychophysics, a just-noticeable difference or JND is the amount something must be changed in order for a difference to be noticeable, detectable at least half the time.[1] This limen is also known as the difference limen, difference threshold, or least perceptible difference.[2]
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Transcription
Voiceover: Imagine that we've got your arm here, and you got these nice big strong muscles, and you're holding in your hand a weight. Let's say that you're holding a two-pound weight. Here is a two-pound weight. Let's say that you are holding it in your hand and you want to lift it up. As you lift this two-pound weight, you notice that there is some resistance, and you definitely are able to notice that there is a weight in your hand. Let's say that we took this weight and you didn't know, let's say I grabbed the weight out of your hand and I replaced it with another weight that was 2.05 pounds. I've got this 2.05-pound weight, and it's the same exact shape and everything, and it's just .05 pounds heavier. Let's say that we replaced this guy with the 2.05-pound weight. Let's say that I asked you to lift this new 2.05-pound weight, and you might lift it, and you may notice that it's different, but most people in general would not notice any difference. They would just think it's the same exact two-pound weight. Basically, what I'm trying to say is that this .05-pound increase in the weight, for most people probably, would not be noticeable. Let's say that instead of giving you a 2.05-pound weight let's say that I gave you a weight that was 2.2 pounds, and let's say you close your eyes and I took this two-pound weight out of your hand, and I replaced it with this new 2.2-pound weight, and then I ask you to lift the new weight. Most people would probably notice this new increase, this new weight. Basically, what I'm trying to say is that a addition of .05 pounds probably wouldn't get noticed, whereas an addition of 0.2 pounds would get noticed. The threshold at which you're able to notice an increase or a change in weight or really any sensation so that threshold, where you go from not noticing a tiny little change to actually noticing a tiny little change is known as the just noticeable difference, noticeable difference. We can abbreviate this as JNT. In this case, the just noticeable difference, let's say for just sake of argument, is .2 pounds, .2 pounds. OK. Let's imagine that instead of starting with a two-pound weight, instead, we started with a five-pound weight, so five-pound weight. The five-pound weight is much heavier than the two-pound weight. In this case, if I replace the five-pound weight with a 5.2-pound weight, because it's a lot heavier and you're using a lot more muscle fibers in order to lift the five-pound weight, you may not notice the .2-pound increase. Whereas if I replaced the five-pound weight with a 5-1/2-pound weight, so 5.5-pound weight, and I asked you to lift it, you might notice the half a pound increase, but you might not notice the .2-pound increase. Basically, what's going on here is that since you're using more muscle fibers, you're using more sensory neurons, they're not as sensitive to small increases. They're not as sensitive to the 0.2-pound increase. You need a bigger just noticeable difference in order to actually be mentally aware of the change in weight. Basically, when you're holding five pounds, let's say for sake of argument, the just noticeable difference is a little bit higher than when you're holding two pounds. Now, these numbers we're just throwing around, and if you actually did this experimentally, the actual numbers might be different, but the concept generally would remain the same. In the five-pound weight category, the just noticeable difference is .5 pounds. From this, we can come up with an equation. Let's just define some variables. I, or the intensity of the stimulus, is equal to two pounds in this case and five pounds in this case. And delta I, so delta I, would be the just noticeable difference. It would be 5.5 pounds minus five pounds equals half a pound. For the five-pound example, I would be five, and delta I would be .5, and then in the two-pound example, I would be two, and delta I would be .2. Basically, there is actually a guy back in the day named Weber. Weber noticed in 1834 that the ratio of the increment threshold, the ratio of the increment threshold, which is this over here, to the background intensity, which is this over here, so this is the background intensity, is constant. If we were to take .2 divided by two, and if we were to take .5 divided by five, this ratio is actually equal, and it equals .1, and this ratio would be more or less fairly constant for a bunch of different weights. That's what Weber's law is. Weber, in 1834, realized that there is this relationship. We can write this as an equation. Delta I over I equals K. K is a constant for each individual person. There is this particular threshold, and the ratio, the background intensity to the incremental threshold is relatively constant, and that constant is this K value. This part of the equation over here is known as the Weber fraction. This works for sensory tactile stimuli like lifting a weight but it also works for auditory stimuli. Imagine you're in a quiet room. If you're in a quiet room with someone else, you can whisper. You can talk really, really softly and the person can hear you. But if you're at a rock concert, you have to be yelling at the top of your lungs in order for someone next to you to hear you. That's because the background intensity in a quiet room versus a concert is different, and so the delta I, which is whether you're just whispering or whether you're yelling, is different in accordance with the background intensity. That's what the Weber's law is basically saying. If we take this equation over here, let me just give myself a little bit of space. If we take this equation, Weber's law, and rearrange it, so we have delta I equals the background intensity times this constant, if we arrange it, we can see that this Weber's law predicts a linear relationship between the incremental threshold, which is this value over here, and the background intensity. In other words, as the background intensity gets bigger, the incremental threshold gets bigger. If we were to draw a little graph, if we were to draw a graph where the x-axis is the background intensity and the y-axis was the incremental, the difference threshold, what we would see would be this linear relationship. Using the concert example over here, a really, really big background intensity would result in a delta I, so this would be ... Let's say delta I in this case was how loud you were talking. The delta I would have to be a lot bigger than if you were in a quiet room, so quiet room. This law would generally hold true for almost any type of stimulus. It's a good rule of thumb. It's not exactly set in stone, but it is kind of how most of your different sensations operate, where if there is a bigger background intensity, you need a bigger difference threshold in order to actually perceive the sensation. In the real world, sometimes people add a different value. You got delta I over I equals K. This is the normal Weber's law. Some people will even add in another constant over here in order to take into account the baseline level of activity that needs to be surpassed in real-world situations. So this equation can be modified in order to more accurately represent what goes on in the real world.
Quantification
For many sensory modalities, over a wide range of stimulus magnitudes sufficiently far from the upper and lower limits of perception, the 'JND' is a fixed proportion of the reference sensory level, and so the ratio of the JND/reference is roughly constant (that is the JND is a constant proportion/percentage of the reference level). Measured in physical units, we have:
where is the original intensity of the particular stimulation, is the addition to it required for the change to be perceived (the JND), and k is a constant. This rule was first discovered by Ernst Heinrich Weber (1795–1878), an anatomist and physiologist, in experiments on the thresholds of perception of lifted weights. A theoretical rationale (not universally accepted) was subsequently provided by Gustav Fechner, so the rule is therefore known either as the Weber Law or as the Weber–Fechner law; the constant k is called the Weber constant. It is true, at least to a good approximation, of many but not all sensory dimensions, for example the brightness of lights, and the intensity and the pitch of sounds. It is not true, however, for the wavelength of light. Stanley Smith Stevens argued that it would hold only for what he called prothetic sensory continua, where change of input takes the form of increase in intensity or something obviously analogous; it would not hold for metathetic continua, where change of input produces a qualitative rather than a quantitative change of the percept. Stevens developed his own law, called Stevens' Power Law, that raises the stimulus to a constant power while, like Weber, also multiplying it by a constant factor in order to achieve the perceived stimulus.
The JND is a statistical, rather than an exact quantity: from trial to trial, the difference that a given person notices will vary somewhat, and it is therefore necessary to conduct many trials in order to determine the threshold. The JND usually reported is the difference that a person notices on 50% of trials. If a different proportion is used, this should be included in the description—for example one might report the value of the "75% JND".
Modern approaches to psychophysics, for example signal detection theory, imply that the observed JND, even in this statistical sense, is not an absolute quantity, but will depend on situational and motivational as well as perceptual factors. For example, when a researcher flashes a very dim light, a participant may report seeing it on some trials but not on others.
The JND formula has an objective interpretation (implied at the start of this entry) as the disparity between levels of the presented stimulus that is detected on 50% of occasions by a particular observed response,[3] rather than what is subjectively "noticed" or as a difference in magnitudes of consciously experienced 'sensations'. This 50%-discriminated disparity can be used as a universal unit of measurement of the psychological distance of the level of a feature in an object or situation and an internal standard of comparison in memory, such as the 'template' for a category or the 'norm' of recognition.[4] The JND-scaled distances from norm can be combined among observed and inferred psychophysical functions to generate diagnostics among hypothesised information-transforming (mental) processes mediating observed quantitative judgments.[5]
Music production applications
In music production, a single change in a property of sound which is below the JND does not affect perception of the sound. For amplitude, the JND for humans is around 1 dB.[6][7]
The JND for tone is dependent on the tone's frequency content. Below 500 Hz, the JND is about 3 Hz for sine waves, and 1 Hz for complex tones; above 1000 Hz, the JND for sine waves is about 0.6% (about 10 cents).[8]
The JND is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches.[9] The JND becomes smaller if the two tones are played simultaneously as the listener is then able to discern beat frequencies. The total number of perceptible pitch steps in the range of human hearing is about 1,400; the total number of notes in the equal-tempered scale, from 16 to 16,000 Hz, is 120.[9]
In speech perception
JND analysis is frequently occurring in both music and speech, the two being related and overlapping in the analysis of speech prosody (i.e. speech melody). While several studies have shown that JND for tones (not necessarily sine waves) might normally lie between 5 and 9 semitones (STs), a small percentage of individuals exhibit an accuracy of between a quarter and a half ST.[10] Although JND varies as a function of the frequency band being tested, it has been shown that JND for the best performers at around 1 kHz is well below 1 Hz, (i.e. less than a tenth of a percent).[11][12][13] It is, however, important to be aware of the role played by critical bandwidth when performing this kind of analysis.[12]
When analysing speech melody, rather than musical tones, accuracy decreases. This is not surprising given that speech does not stay at fixed intervals in the way that tones in music do. Johan 't Hart (1981) found that JND for speech averaged between 1 and 2 STs but concluded that "only differences of more than 3 semitones play a part in communicative situations".[14]
Note that, given the logarithmic characteristics of Hz, for both music and speech perception results should not be reported in Hz but either as percentages or in STs (5 Hz between 20 and 25 Hz is very different from 5 Hz between 2000 and 2005 Hz, but the same when reported as a percentage or in STs).
Marketing applications
Weber's law has important applications in marketing. Manufacturers and marketers endeavor to determine the relevant JND for their products for two very different reasons:
- so that negative changes (e.g. reductions in product size or quality, or increase in product price) are not discernible to the public (i.e. remain below JND) and
- so that product improvements (e.g. improved or updated packaging, larger size or lower price) are very apparent to consumers without being wastefully extravagant (i.e. they are at or just above the JND).
When it comes to product improvements, marketers very much want to meet or exceed the consumer's differential threshold; that is, they want consumers to readily perceive any improvements made in the original products. Marketers use the JND to determine the amount of improvement they should make in their products. Less than the JND is wasted effort because the improvement will not be perceived; more than the JND is again wasteful because it reduces the level of repeat sales. On the other hand, when it comes to price increases, less than the JND is desirable because consumers are unlikely to notice it.
Haptics applications
Weber's law is used in haptic devices and robotic applications. Exerting the proper amount of force to human operator is a critical aspects in human robot interactions and tele operation scenarios. It can highly improve the performance of the user in accomplishing a task.[15]
See also
- Absolute threshold
- ABX test
- Color difference
- Limen
- Minimal clinically important difference
- Mutatis mutandis
- Psychometric function
- Sensor resolution
- Visual perception
- Weber–Fechner law
References
Citations
- ^ "Weber's Law of Just Noticeable Difference". University of South Dakota.
- ^ Judd 1931, pp. 72–108.
- ^ Torgerson 1958.
- ^ Booth & Freeman 1993.
- ^ Richardson & Booth 1993.
- ^ Middlebrooks & Green 1991.
- ^ Mills 1960.
- ^ Kollmeier, Brand & Meyer 2008, p. 65.
- ^ a b Olson 1967, pp. 171, 248–251.
- ^ Bachem 1937.
- ^ Ritsma 1965.
- ^ a b Nordmark 1968.
- ^ Rakowski 1971.
- ^ 't Hart 1981, p. 811.
- ^ Feyzabadi et al. 2013, pp. 309, 319.
Sources
- Bachem, A. (1937). "Various Types of Absolute Pitch". The Journal of the Acoustical Society of America. 9 (2): 146–151. Bibcode:1937ASAJ....9..146B. doi:10.1121/1.1915919. ISSN 0001-4966.
- Booth, D.A.; Freeman, R.P.J. (1993), "Discriminative measurement of feature integration", Acta Psychologica, 84 (1): 1–16, doi:10.1016/0001-6918(93)90068-3, PMID 8237449
- Feyzabadi, Seyedshams; Straube, Sirko; Folgheraiter, Michele; Kirchner, Elsa Andrea; Kim, Su Kyoung; Albiez, Jan Christian (2013). "Human Force Discrimination during Active Arm Motion for Force Feedback Design". IEEE Transactions on Haptics. 6 (3): 309–319. doi:10.1109/TOH.2013.4. ISSN 1939-1412. PMID 24808327. S2CID 25749906.
- Judd, Deane B. (1931). "Chromaticity sensibility to stimulus differences". JOSA. 22 (2): 72–108. doi:10.1364/JOSA.22.000072.
- Kollmeier, B.; Brand, T.; Meyer, B. (2008). "Perception of Speech and Sound". In Jacob Benesty; M. Mohan Sondhi; Yiteng Huang (eds.). Springer handbook of speech processing. Springer. ISBN 978-3-540-49125-5.
- Middlebrooks, John C.; Green, David M. (1991). "Sound Localization by Human Listeners". Annual Review of Psychology. 42 (1): 135–159. doi:10.1146/annurev.ps.42.020191.001031. ISSN 0066-4308. PMID 2018391.
- Mills, A. W. (1960). "Lateralization of High‐Frequency Tones". The Journal of the Acoustical Society of America. 32 (1): 132–134. Bibcode:1960ASAJ...32..132M. doi:10.1121/1.1907864. ISSN 0001-4966.
- Nordmark, Jan O. (1968). "Mechanisms of Frequency Discrimination". The Journal of the Acoustical Society of America. 44 (6): 1533–1540. Bibcode:1968ASAJ...44.1533N. doi:10.1121/1.1911293. ISSN 0001-4966. PMID 5702028.
- Olson, Harry F. (1967). Music, Physics and Engineering. Dover Publications. ISBN 0-486-21769-8.
- Rakowski, A. (1971), "Pitch discrimination at the threshold of hearing", Proceedings of the Seventh International Congress on Acoustics, Budapest, vol. 3 20H6, p. 376
- Richardson, N.; Booth, D.A. (1993), "Multiple physical patterns in judgements of the creamy texture of milks and creams", Acta Psychologica, 84 (1): 93–101, doi:10.1016/0001-6918(93)90075-3, PMID 8237459
- Ritsma, R. J. (1965), "Pitch discrimination and frequency discrimination", Proceedings of the Fifth International Congress on Acoustics, Liège, vol. B22
- 't Hart, Johan (1981). "Differential sensitivity to pitch distance, particularly in speech". The Journal of the Acoustical Society of America. 69 (3): 811–821. Bibcode:1981ASAJ...69..811T. doi:10.1121/1.385592. ISSN 0001-4966. PMID 7240562.
- Torgerson, Warren S. (1958). Methods of Scaling. John Wiley.