In the branch of
experimental psychology
Experimental psychology refers to work done by those who apply experimental methods to psychological study and the underlying processes. Experimental psychologists employ human participants and animal subjects to study a great many topics, in ...
focused on
sense
A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of Stimulus (physiology), stimuli. (For example, in the human body, the brain which is part of the cen ...
,
sensation
Sensation (psychology) refers to the processing of the senses by the sensory system.
Sensation or sensations may also refer to:
In arts and entertainment In literature
*Sensation (fiction), a fiction writing mode
*Sensation novel, a British ...
, and
perception
Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system ...
, which is called
psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, m ...
, 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.
This
limen
In physiology, psychology, or psychophysics, a limen or a liminal point is a sensory threshold of a physiological or psychological response. It is the boundary of perception. On one side of a limen (or threshold) a stimulus is perceivable, on the ...
is also known as the difference limen, difference threshold, or least perceptible difference.
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
Ernst Heinrich Weber (24 June 1795 – 26 January 1878) was a German physician who is considered one of the founders of experimental psychology. He was an influential and important figure in the areas of physiology and psychology during his lif ...
(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
Gustav Theodor Fechner (; ; 19 April 1801 – 18 November 1887) was a German physicist, philosopher, and experimental psychologist. A pioneer in experimental psychology and founder of psychophysics (techniques for measuring the mind), he inspired ...
, so the rule is therefore known either as the Weber Law or as the
Weber–Fechner law
The Weber–Fechner laws are two related hypotheses in the field of psychophysics, known as Weber's law and Fechner's law. Both laws relate to human perception, more specifically the relation between the actual change in a physical stimulus and ...
; 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
Stanley Smith Stevens (November 4, 1906 – January 18, 1973) was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory, studying psychoacoustics, and he is credited with the introduction of Stevens's power law. Stevens author ...
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
Stevens' power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus. It is often considered to supersede ...
, 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
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (ca ...
, 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, 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 Psychological distance is the degree to which people feel removed from a phenomenon. Distance in this case is not limited to the physical surroundings, rather it could also be abstract. Distance can be defined as the separation between the self and ...
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. 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.
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
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).
The JND is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches. The JND becomes smaller if the two tones are played
simultaneously
Simultaneity may refer to:
* Relativity of simultaneity, a concept in special relativity.
* Simultaneity (music), more than one complete musical texture occurring at the same time, rather than in succession
* Simultaneity, a concept in Endogene ...
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.
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. 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. It is, however, important to be aware of the role played by critical bandwidth when performing this kind of analysis.
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".
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
Marketing is the process of exploring, creating, and delivering value to meet the needs of a target market in terms of goods and services; potentially including selection of a target audience; selection of certain attributes or themes to emph ...
. 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.
See also
*
Absolute threshold
In neuroscience and psychophysics, an absolute threshold was originally defined as the lowest level of a stimulus – light, sound, touch, etc. – that an organism could detect. Under the influence of signal detection theory, absolute threshold ...
*
ABX test An ABX test is a method of comparing two choices of sensory stimuli to identify detectable differences between them. A subject is presented with two known samples (sample , the first reference, and sample , the second reference) followed by one unkn ...
*
Color difference
In color science, color difference or color distance is the separation between two colors. This metric allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of great ...
*
Limen
In physiology, psychology, or psychophysics, a limen or a liminal point is a sensory threshold of a physiological or psychological response. It is the boundary of perception. On one side of a limen (or threshold) a stimulus is perceivable, on the ...
*
Minimal clinically important difference The minimal important difference (MID) or minimal clinically important difference (MCID) is the smallest change in a treatment outcome that an individual patient would identify as important and which would indicate a change in the patient's managem ...
*
Mutatis mutandis
''Mutatis mutandis'' is a Medieval Latin phrase meaning "with things changed that should be changed" or "once the necessary changes have been made". It remains unnaturalized in English and is therefore usually italicized in writing. It is used i ...
*
Psychometric function
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and ...
*
Sensor resolution
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
*
Visual perception
Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum reflecte ...
*
Weber–Fechner law
The Weber–Fechner laws are two related hypotheses in the field of psychophysics, known as Weber's law and Fechner's law. Both laws relate to human perception, more specifically the relation between the actual change in a physical stimulus and ...
References
Citations
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Perception
Psychophysics