Just noticeable difference
Encyclopedia
In psychophysics
, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest detectable difference between a starting and secondary level of a particular sensory stimulus. It is also known as the difference limen or the differential threshold.
where
is the original intensity of stimulation, 
is the addition to it required for the difference 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, of 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.
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 (Torgerson, 1958), 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 (Booth & Freeman, 1993). 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 (Richardson & Booth, 1993).
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 product. Marketers use the j.n.d to determine the amount of improvement they should make in their products. Less than the j.n.d is wasted effort because the improvement will not be perceived; more than the j.n.d is again wasteful because it reduces the level of repeat sales. On the other hand, when it comes to price increases, less than the j.n.d is desirable because consumers are unlikely to notice it.
Psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they effect. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual...
, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest detectable difference between a starting and secondary level of a particular sensory stimulus. It is also known as the difference limen or the differential threshold.
Explanation
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 how thee 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 stimulation, is the addition to it required for the difference to be perceived (the jnd), and k is a constant. This rule was first discovered by Ernst Heinrich WeberErnst Heinrich Weber
Ernst Heinrich Weber was a German physician who is considered one of the founders of experimental psychology.Weber studied medicine at Wittenberg University...
(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 Fechner
Gustav Theodor Fechner , was a German experimental psychologist. An early pioneer in experimental psychology and founder of psychophysics, he inspired many 20th century scientists and philosophers...
, so the rule is therefore known either as the Weber Law or as the Weber–Fechner law
Weber–Fechner law
The Weber–Fechner law is a confusing term, because it combines two different laws. Some authors use the term to mean Weber's law, and others Fechner's law. Fechner himself added confusion to the literature by calling his own law Weber's 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
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
of sounds. It is not true, however, of the wavelength of light. Stanley Smith Stevens
Stanley Smith Stevens
Stanley Smith Stevens was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory and is credited with the introduction of Stevens' power law. Stevens authored a milestone textbook, the 1400+ page "Handbook of Experimental Psychology" . He was also one of the founding organizers...
argued that it would hold only for what he called prothetic sensory continua
Continuum (theory)
Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...
, 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.
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 (Torgerson, 1958), 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 (Booth & Freeman, 1993). 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 (Richardson & Booth, 1993).
Marketing applications of the j.n.d
Weber’s law has important applications in marketing. Manufacturers and marketers endeavor to determine the relevant j.n.d 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 j.n.d) 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 j.n.d).
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 product. Marketers use the j.n.d to determine the amount of improvement they should make in their products. Less than the j.n.d is wasted effort because the improvement will not be perceived; more than the j.n.d is again wasteful because it reduces the level of repeat sales. On the other hand, when it comes to price increases, less than the j.n.d is desirable because consumers are unlikely to notice it.
See also
- Absolute thresholdAbsolute thresholdIn neuroscience and psychophysics, an absolute threshold is the smallest detectable level of a stimulus. However, at this low level, subjects will sometimes detect the stimulus and at other times not. Therefore, an alternative definition of absolute threshold is the lowest intensity at which a...
- LimenLimenIn physiology, psychology, or psychophysics, a limen or a liminal point is a threshold of a physiological or psychological response.Liminal, as an adjective, means situated at a sensory threshold, hence barely perceptible....
- Minimal negation operator
- Psychometric functionPsychometric functionA psychometric function describes the relationship between a parameter of a physical stimulus and the responses of a person who has to decide about a certain aspect of that stimulus. Usually these sensory decisions take the form of a two-alternative forced choice . The psychometric function usually...
- Sensor resolution
- Visual perceptionVisual perceptionVisual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...