The branch of psychology that deals with the relationships between physical stimuli and sensory response.
psychophysical psy'cho·phys'i·cal adj.psychophysically psy'cho·phys'i·cal·ly adv.
psychophysicist psy'cho·phys'i·cist (-fĭz'ĭ-sĭst) n.
psychophysics
Dictionary:
psy·cho·phys·ics (sī'kō-fĭz'ĭks)  |
n. (used with a sing. verb)
psychophysically psy'cho·phys'i·cal·ly adv.
psychophysicist psy'cho·phys'i·cist (-fĭz'ĭ-sĭst) n.
psychophysically psy'cho·phys'i·cal·ly adv.
psychophysicist psy'cho·phys'i·cist (-fĭz'ĭ-sĭst) n.
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Psychophysics originally meant the study of the sensations evoked by physical stimuli. As an example to illustrate the distinction between a stimulus and a sensation, the amount of light reflected by this page is its luminance, and can be measured with a light meter such as photographers use; the sensation evoked by that reflected light is the experienced brightness of the page, and may be deceptively related to the luminance, as photographers know well. Psychophysics is concerned with the brightness of the stimulus, and its other subjective qualities, and, secondly, with the relation of that brightness to the physical luminance.
The term 'psychophysics' was introduced by Gustav Fechner in his Elemente der Psychophysik (1860), in which he conceived an indirect method of measuring sensations. If a luminance L2 can just be distinguished as greater than L1, then, to a close approximation, L2/L1 is constant; this is Weber's law (formulated as the Weber–Fechner law). If one supposes that all just-noticeable differences (e.g. between L1 and L2) are subjectively equivalent, then the sensation (in this case, of brightness) must increase as the logarithm of the physical stimulus magnitude, for if L2/L1, is constant, so also is log L2 − log L1.
Fechner's logarithmic measure was universally accepted until the 1930s, at which time it was questioned for a purely practical reason. At that time the decibel scale for the measurement of auditory intensity was newly developed. On this scale 20 dB represents a tenfold increase in the amplitude of modulation of sound pressure, or a hundredfold increase in acoustic power, and, since the range of acoustic powers to which the ear may be exposed is typically 1 : 1012, a logarithmic scale is convenient. Decibel measurements are always relative to a reference point, which is usually taken as about equal to the faintest sound that the ear can detect. So, a naive application of Fechner's law would suggest that 50 dB should sound half as loud as 100 dB, but it is generally agreed that 50 dB sounds much quieter than that. To enable acoustic engineers to communicate meaningfully with their customers, the 1930s saw some research on how people assign numbers to ratios of sound levels and this research led to the development of the sone scale by S. S. Stevens in 1936. Loudness in sones grows as the 0.3 power of the physical sound power.
Subsequently, in the 1950s, S. S. Stevens and his collaborators developed the methods and ideas of the 1930s to devise power law scales of the sensations, evoked by more than 30 different sensory attributes, substantially those for which Weber's law holds. When subjects judge the ratios of stimuli, the numbers assigned vary as N = aXβ, where X is the magnitude of the stimulus being judged and β is an exponent characteristic of the attribute. This exponent varies from 0.33 for luminance to 3.5 for electric shock.
Inspired by Fechner's use of the just-noticeable difference as a unit of sensation, there has evolved a very great body of experimental work and practical knowledge about human discrimination of all kinds of sensory attributes, and following from Stevens's power law, there has developed a comparable body of facts and figures about human judgement. For practical purposes, psychophysics has come to refer to these two large accumulations of data and models. But, notwithstanding its long history, basic theoretical principles are only just beginning to emerge.
On mature consideration it can be seen that sensation is not, in fact, measurable independently of the physical stimulus from which it is derived. Fechner's logarithmic transform exists only as a mathematical construction, having no operational validity, and conformity to Stevens's power law depends on getting the experiment 'right'. These two assertions can be supported by a demonstration and a simple experiment.
Panel a of Fig. 1 shows a black-and-white sectored disc which, when spun rapidly, appears as in panel b. Intermittent illumination interrupted at a sufficiently rapid rate is not distinguishable from uniform illumination of the same time-average illuminance. So the centre and periphery of the rotating disc must have the same luminance — but their brightnesses are manifestly different. Now if the boundary between the centre and periphery of the rotating disc is covered with an opaque annulus (panel c), the brightnesses of the centre and the periphery are immediately seen to be equal. Remove the annulus (panel b) and they are again different. This phenomenon is known as the Craik–Cornsweet illusion. It depends on the kinky profile of luminance at the boundary of the figure, which may be appreciated from the shape of the black sector on the stationary disc. There is an abrupt step in luminance which is easily perceived, and two ramps which are not. And so the centre appears darker than the periphery. When this profile is obscured by the annulus, centre and periphery appear equally bright. It follows that we do not see relative brightness only from a comparison of the two luminances in question, but from the perceived change in luminance at the boundary. That is, the sensation of brightness is obtained by a differential process from the physical stimulus. This idea was first proposed as long ago as 1865, by Ernst Mach.
The Craik–Cornsweet illusion is known to have analogues in the attributes of sound intensity and frequency, and in the length and spacing of lines. It is probably a general feature of human sensory perception. And the differential process which it reveals explains Weber's law, why the just-noticeable difference increases in direct proportion to the stimulus magnitude. The logarithmic transform is a matter of the imagination only.
If our sensory experience is differentially coupled to the physical world, what of Stevens's power law? An elegant experiment by W. R. Garner addresses this point. Thirty subjects listened to a standard tone at 90 dB and then a comparison tone. The comparison tone was to be judged 'more' or 'less' than half as loud as the standard, and from each subject's judgements of a series of such comparisons was estimated that intensity of tone that would have been judged 'more' and 'less' equally often — a subjective half-loudness value. One group of subjects listened to comparison tones varying between 75 and 85 dB, and having half-loudness values within that range. Another group listened to comparison tones between 65 and 75 dB which all had half-loudness values within that range; and likewise for a third group listening to tones between 55 and 65 dB. Only one subject complained that the comparison tones presented did not straddle the half-loudness value, and she was happily reassigned to the third group.
It is apparent that most people have no idea what 'half as loud' means. Not wishing to appear foolish, the subjects in Garner's experiment assumed that some comparison tones must be more, and some less, than half as loud as the standard (else the experiment made no sense) and adjusted their criteria of judgement accordingly. They were conned. Their judgements depended on the immediate context rather than on the loudness of the stimulus. In experiments on the estimation of sensations the influence of context is very powerful and the accuracy of judgement is typically poorer by one to two orders of magnitude compared to that accuracy revealed in the measurement of just-noticeable differences. The accuracy of judgement of single stimuli has been found, with many different attributes, to be equivalent to the identification of no more than five different stimulus levels.
In conclusion, there is no way to measure sensation that is distinct from measurement of the physical stimulus. Sometimes we are deceived — Fig. 1 presents an example — and such examples present intriguing problems to the experimental psychologist. Attempts to 'measure' sensation have taught us that judgements of quantity are astonishingly poor. For this reason photographers use exposure meters, and cars are fitted with speedometers, so that the driver merely has to judge that the needle is adjacent to the mark representing 30 mph, rather than 25 or 35 — a 'yes or no' kind of judgement that is reliable. We habitually make our judgements of quantity with the aid of a measuring instrument, a ruler or scale pan, and, in practice, problems arise only with those attributes which we feel intuitively ought to admit a continuum of values, but for which no measuring instrument exists — attributes like the merit of essays written in an examination or the aesthetic value of a painting. Such problems are nicely illustrated by the auction prices of Old Master paintings. The authenticity of such a painting can often be determined with great reliability, but sometimes the provenance is reappraised and the market value of the painting, physically the same, with its aesthetic qualities entirely unchanged, can vary at least thirtyfold in consequence. In the auction room aesthetic merit is of very little account, precisely because it cannot be accurately assessed; in its stead, provenance, a 'yes and no' matter, is almost everything.
Fig. 1. The Craik–Cornsweet illusion. Plates b and c have been made from the same photographic negative which was taken while the sectored disc was rotated at high speed. The inner disc has the same average luminance as the outer annulus, but in plate b it appears darker because only the sharp step in luminance at the boundary is perceptible.
(Published 1987)
The term 'psychophysics' was introduced by Gustav Fechner in his Elemente der Psychophysik (1860), in which he conceived an indirect method of measuring sensations. If a luminance L2 can just be distinguished as greater than L1, then, to a close approximation, L2/L1 is constant; this is Weber's law (formulated as the Weber–Fechner law). If one supposes that all just-noticeable differences (e.g. between L1 and L2) are subjectively equivalent, then the sensation (in this case, of brightness) must increase as the logarithm of the physical stimulus magnitude, for if L2/L1, is constant, so also is log L2 − log L1.
Fechner's logarithmic measure was universally accepted until the 1930s, at which time it was questioned for a purely practical reason. At that time the decibel scale for the measurement of auditory intensity was newly developed. On this scale 20 dB represents a tenfold increase in the amplitude of modulation of sound pressure, or a hundredfold increase in acoustic power, and, since the range of acoustic powers to which the ear may be exposed is typically 1 : 1012, a logarithmic scale is convenient. Decibel measurements are always relative to a reference point, which is usually taken as about equal to the faintest sound that the ear can detect. So, a naive application of Fechner's law would suggest that 50 dB should sound half as loud as 100 dB, but it is generally agreed that 50 dB sounds much quieter than that. To enable acoustic engineers to communicate meaningfully with their customers, the 1930s saw some research on how people assign numbers to ratios of sound levels and this research led to the development of the sone scale by S. S. Stevens in 1936. Loudness in sones grows as the 0.3 power of the physical sound power.
Subsequently, in the 1950s, S. S. Stevens and his collaborators developed the methods and ideas of the 1930s to devise power law scales of the sensations, evoked by more than 30 different sensory attributes, substantially those for which Weber's law holds. When subjects judge the ratios of stimuli, the numbers assigned vary as N = aXβ, where X is the magnitude of the stimulus being judged and β is an exponent characteristic of the attribute. This exponent varies from 0.33 for luminance to 3.5 for electric shock.
Inspired by Fechner's use of the just-noticeable difference as a unit of sensation, there has evolved a very great body of experimental work and practical knowledge about human discrimination of all kinds of sensory attributes, and following from Stevens's power law, there has developed a comparable body of facts and figures about human judgement. For practical purposes, psychophysics has come to refer to these two large accumulations of data and models. But, notwithstanding its long history, basic theoretical principles are only just beginning to emerge.
On mature consideration it can be seen that sensation is not, in fact, measurable independently of the physical stimulus from which it is derived. Fechner's logarithmic transform exists only as a mathematical construction, having no operational validity, and conformity to Stevens's power law depends on getting the experiment 'right'. These two assertions can be supported by a demonstration and a simple experiment.
Panel a of Fig. 1 shows a black-and-white sectored disc which, when spun rapidly, appears as in panel b. Intermittent illumination interrupted at a sufficiently rapid rate is not distinguishable from uniform illumination of the same time-average illuminance. So the centre and periphery of the rotating disc must have the same luminance — but their brightnesses are manifestly different. Now if the boundary between the centre and periphery of the rotating disc is covered with an opaque annulus (panel c), the brightnesses of the centre and the periphery are immediately seen to be equal. Remove the annulus (panel b) and they are again different. This phenomenon is known as the Craik–Cornsweet illusion. It depends on the kinky profile of luminance at the boundary of the figure, which may be appreciated from the shape of the black sector on the stationary disc. There is an abrupt step in luminance which is easily perceived, and two ramps which are not. And so the centre appears darker than the periphery. When this profile is obscured by the annulus, centre and periphery appear equally bright. It follows that we do not see relative brightness only from a comparison of the two luminances in question, but from the perceived change in luminance at the boundary. That is, the sensation of brightness is obtained by a differential process from the physical stimulus. This idea was first proposed as long ago as 1865, by Ernst Mach.
The Craik–Cornsweet illusion is known to have analogues in the attributes of sound intensity and frequency, and in the length and spacing of lines. It is probably a general feature of human sensory perception. And the differential process which it reveals explains Weber's law, why the just-noticeable difference increases in direct proportion to the stimulus magnitude. The logarithmic transform is a matter of the imagination only.
If our sensory experience is differentially coupled to the physical world, what of Stevens's power law? An elegant experiment by W. R. Garner addresses this point. Thirty subjects listened to a standard tone at 90 dB and then a comparison tone. The comparison tone was to be judged 'more' or 'less' than half as loud as the standard, and from each subject's judgements of a series of such comparisons was estimated that intensity of tone that would have been judged 'more' and 'less' equally often — a subjective half-loudness value. One group of subjects listened to comparison tones varying between 75 and 85 dB, and having half-loudness values within that range. Another group listened to comparison tones between 65 and 75 dB which all had half-loudness values within that range; and likewise for a third group listening to tones between 55 and 65 dB. Only one subject complained that the comparison tones presented did not straddle the half-loudness value, and she was happily reassigned to the third group.
It is apparent that most people have no idea what 'half as loud' means. Not wishing to appear foolish, the subjects in Garner's experiment assumed that some comparison tones must be more, and some less, than half as loud as the standard (else the experiment made no sense) and adjusted their criteria of judgement accordingly. They were conned. Their judgements depended on the immediate context rather than on the loudness of the stimulus. In experiments on the estimation of sensations the influence of context is very powerful and the accuracy of judgement is typically poorer by one to two orders of magnitude compared to that accuracy revealed in the measurement of just-noticeable differences. The accuracy of judgement of single stimuli has been found, with many different attributes, to be equivalent to the identification of no more than five different stimulus levels.
In conclusion, there is no way to measure sensation that is distinct from measurement of the physical stimulus. Sometimes we are deceived — Fig. 1 presents an example — and such examples present intriguing problems to the experimental psychologist. Attempts to 'measure' sensation have taught us that judgements of quantity are astonishingly poor. For this reason photographers use exposure meters, and cars are fitted with speedometers, so that the driver merely has to judge that the needle is adjacent to the mark representing 30 mph, rather than 25 or 35 — a 'yes or no' kind of judgement that is reliable. We habitually make our judgements of quantity with the aid of a measuring instrument, a ruler or scale pan, and, in practice, problems arise only with those attributes which we feel intuitively ought to admit a continuum of values, but for which no measuring instrument exists — attributes like the merit of essays written in an examination or the aesthetic value of a painting. Such problems are nicely illustrated by the auction prices of Old Master paintings. The authenticity of such a painting can often be determined with great reliability, but sometimes the provenance is reappraised and the market value of the painting, physically the same, with its aesthetic qualities entirely unchanged, can vary at least thirtyfold in consequence. In the auction room aesthetic merit is of very little account, precisely because it cannot be accurately assessed; in its stead, provenance, a 'yes and no' matter, is almost everything.
Fig. 1. The Craik–Cornsweet illusion. Plates b and c have been made from the same photographic negative which was taken while the sectored disc was rotated at high speed. The inner disc has the same average luminance as the outer annulus, but in plate b it appears darker because only the sharp step in luminance at the boundary is perceptible.
(Published 1987)
— Donald R. J. Laming
- Bibliography
- Gescheider, G. A. (1985). Psychophysics: Method, Theory, and Application (2nd edn.).
- Laming, D. (1986). Sensory Analysis.
| Wikipedia: Psychophysics |
Psychophysics is a discipline within psychology that investigates the relationship between physical stimuli and their subjective correlates, or percepts. Psychophysics has been described variously as “the scientific study of the relation between stimulus and sensation”[1] or, more completely, as “the analysis of perceptual processes by studying the effect on a subject’s experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions.”[2] It is a general-purpose theory that can be applied to any sensory system. The techniques of "classical" psychophysics are still widely used, although the theoretical background is heavily influenced by signal detection theory.[3]. A broader area of research uses Likert scales to match more complex cognitive attributes than sensations to numerical categorical scales. Although this area of research is largely ignorant or naive to the psychometric issues of psychophysics it represents an enormous body of implementation of the basic theory. A more scientifically rigorous bridge between these two areas of traditional discrimination psychophysics and Likert categorical scaling is offered by Steven's power law approach to magnitude estimation, magnitude production, and cross-modality matching.
Contents |
History
Many of the classical techniques and theory of psychophysics were formulated in 1860 when Gustav Theodor Fechner published Elemente der Psychophysik.[4]. He coined the term "psychophysics", described research relating physical stimuli with how they are perceived, and set out the philosophical foundations of the field. Fechner wanted to develop a theory that could relate matter to the mind, by describing the relationship between the world and the way it is perceived. He was influenced by the work of German physiologist Ernst Heinrich Weber [5][6] Fechner's work formed the basis of psychology as a science. Wilhelm Wundt, the founder of the first laboratory for psychological research, built upon Fechner's work.
More modern approaches are divided into three large camps: Likert scaling, signal detection theory and power law theory. Power law theory is named after psychophysicist Stanley Smith Stevens (1906–1973). Although the idea of a power law had been suggested by 19th century researchers, Stevens is credited with reviving the law, creating new methods of magnitude estimation, magnitude production, and cross modality matching to create its scales and publishing a body of psychophysical data to support it.
Some authors[7] have argued that the medieval scientist Alhazen should be considered the founder of psychophysics. Although al-Haytham made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and such claims have been rebuffed.[8]
Thresholds
Psychophysicists usually employ experimental stimuli that can be objectively measured, such as pure tones varying in intensity, or lights varying in luminance. All the senses have been studied: vision, hearing, touch (including skin and enteric perception), taste, smell, and the sense of time. Regardless of the sensory domain, there are three main areas of investigation: absolute thresholds, discrimination thresholds, and scaling.
A threshold (or limen), is the point of intensity at which the participant can just detect the presence of, or difference in, a stimulus. Stimuli with intensities below the threshold are considered not detectable (hence: sub-liminal). Stimuli at values close enough to a threshold will often be detectable some proportion of the time; therefore, a threshold is considered to be the point at which a stimulus, or change in a stimulus, is detected some proportion p of the time. There are two kinds of thresholds: absolute[9] and difference.[6]
Detection
An absolute threshold is the level of intensity of a stimulus at which the subject is able to detect the presence of the stimulus some proportion of the time (a p level of 50% is often used). An example of an absolute threshold is the number of hairs on the back of one's hand that must be touched before it can be felt - a participant may be unable to feel a single hair being touched, but may be able to feel two or three as this exceeds the threshold. Absolute threshold is also often referred to as detection threshold.
Discrimination
A difference threshold is the magnitude of the difference between two stimuli of differing intensities that the participant is able to detect some proportion of the time (again, 50% is often used). To test this threshold, several different methods are used. The subject may be asked to adjust one stimulus until it is perceived as the same as the other, may be asked to describe the magnitude of the difference between two stimuli, or may be asked to detect a stimulus against a background.
In discrimination experiments, the experimenter seeks to determine at what point the difference between two stimuli, such as two weights or two sounds, is detectable. The subject is presented with one stimulus, for example a weight, and is asked to say whether another weight is heavier or lighter (in some experiments, the subject may also say the two weights are the same). At the point of subjective equality (PSE), the subject perceives the two weights to be the same. The just noticeable difference (JND), or difference limen (DL), is the magnitude of the difference in stimuli that the subject notices some proportion p of the time (50% is usually used for p).
Absolute and difference thresholds are sometimes considered similar because there is always background noise interfering with our ability to detect stimuli, however study of difference thresholds still occurs, for example in pitch discrimination tasks.[10][5]
Experimentation
In psychophysics, experiments seek to determine whether the subject can detect a stimulus, identify it, differentiate between it and another stimulus, and describe the magnitude or nature of this difference.[5][6]
Classical psychophysical methods
Psychophysical experiments have traditionally used three methods for testing subjects' perception in stimulus detection and difference detection experiments: the method of limits, the method of constant stimuli, and the method of adjustment.[11]
Method of limits
In ascending method of limits, some property of the stimulus starts out at a level so low that the stimulus could not be detected, then this level is gradually increased until the participant reports that they are aware of it. For example, if the experiment is testing the minimum amplitude of sound that can be detected, the sound begins too quietly to be perceived, and is made gradually louder. In the descending method of limits, this is reversed. In each case, the threshold is considered to be the level of the stimulus property at which the stimuli is just detected.[11]
In experiments, the ascending and descending methods are used alternately and the thresholds are averaged. A possible disadvantage of these methods is that the subject may become accustomed to reporting that they perceive a stimulus and may continue reporting the same way even beyond the threshold (the error of habituation). Conversely, the subject may also anticipate that the stimulus is about to become detectable or undetectable and may make a premature judgment (the error of expectation).
To avoid these potential pitfalls, Georg von Bekesy introduced the staircase procedure in 1960 in his study of auditory perception. In this method, the sound starts out audible and gets quieter after each of the subject's responses, until the subject does not report hearing it. At that point, the sound is made louder at each step, until the subject reports hearing it, at which point it is made quieter in steps again. This way the experimenter is able to "zero in" on the threshold.[11]
Method of constant stimuli
Instead of being presented in ascending or descending order, in the method of constant stimuli the levels of a certain property of the stimulus are not related from one trial to the next, but presented randomly. This prevents the subject from being able to predict the level of the next stimulus, and therefore reduces errors of habituation and expectation. The subject again reports whether he or she is able to detect the stimulus.[11] Friedrich Hagelmaier described the method of constant stimuli in a 1952 paper.
Method of adjustment
The method of adjustment asks the subject to control the level of the stimulus, instructs them to alter it until it is just barely detectable against the background noise, or is the same as the level of another stimulus. This is repeated many times. This is also called the method of average error.[11]
Adaptive psychophysical methods
Often, the classic methods of experimentation are argued to be inefficient. This is because, in advance of testing, the psychometric threshold is usually unknown and a lot of data has to be collected at points on the psychometric function that provide little information about its shape (the tails). Adaptive staircase procedures can be used such that the points sampled are clustered around the psychometric threshold. However, the cost of this efficiency is that you do not get the same amount of information regarding the shape of the psychometric function as you can through classical methods. Despite this, it is still possible to estimate the threshold and slope by fitting psychometric functions to the obtained data, although estimates of psychometric slope are likely to be more variable than those from the method of constant stimuli (for a reasonable sampling of the psychometric function).[11]
Staircase procedures
Staircases usually begin with a high intensity stimulus, that is easy to detect. The intensity is then reduced until the observer makes a mistake, at which point the staircase 'reverses' and intensity is increased until the observer responds correctly, triggering another reversal. The values for these 'reversals' are then averaged. There are many different types of staircase, utilising many different decision and termination rules. Step-size, up/down rules and the spread of the underlying psychometric function dictate where on the psychometric function they converge. Threshold values obtained from staircases can fluctuate wildly, so care must be taken in their design. Many different staircase algorithms have been modeled and some practical recommendations suggested by Garcia-Perez.[12]
Magnitude estimation
In the prototypical case, people are asked to assign numbers in proportion to the magnitude of the stimulus. This psychometric function of the geometric means of their numbers is often a power law with stable, replicable exponent. Although contexts can change the law and exponent, that change too is stable and replicable. Instead of numbers, other sensory or cognitive dimensions can be used to match a stimulus and the methodd then becomes "magnitude production" or "cross-modiality matching". The exponents of those dimensions found in numerical magnitude estimation predict the exponents found in magnitude production. Magnitude estimation generally finds lower exponents for the psychophysical function than Likert scaling, because of the restricted range of the categorical Likert scales.[13].
Notes
- ^ Gescheider G (1997). Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates. p. ix.
- ^ Bruce V, Green P R, Georgeson M A (1996). Visual perception (3rd ed.). Psychology Press.
- ^ Gescheider G (1997). "Chapter 5: The Theory of Signal Detection". Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates.
- ^ Gustav Theodor Fechner (1860). Elemente der Psychophysik (Elements of Psychophysics).
- ^ a b c Snodgrass JG. 1975. Psychophysics. In: Experimental Sensory Psychology. B Scharf. (Ed.) pp. 17-67.
- ^ a b c Gescheider G (1997). "Chapter 1: Psychophysical Measurement of Thresholds: Differential Sensitivity". Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates.
- ^ Omar Khaleefa (1999). "Who Is the Founder of Psychophysics and Experimental Psychology?". American Journal of Islamic Social Sciences 16 (2).
- ^ Aaen-Stockdale, C.R. (2008). "Ibn al-Haytham and psychophysics". Perception 37 (4): 636–638. doi:.
- ^ Gescheider G (1997). "Chapter 2: Psychophysical Measurement of Thresholds: Absolute Sensitivity". Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates.
- ^ Gescheider G (1997). "Chapter 4: Classical Psychophysical Theory". Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates.
- ^ a b c d e f Gescheider G (1997). "Chapter 3: The Classical Psychophysical Methods". Psychophysics: the fundamentals (3rd ed.). Lawrence Erlbaum Associates.
- ^ Garcia-Perez, MA (1998). "Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties". Vision Res 38: 1861. doi:.
- ^ , S. S. (1957).. On the psychophysical law. Psychological Review 64(3):. pp. 153–181. PMID 13441853.
References
- Steingrimsson, R.; Luce, R. D. (2006), "Empirical evaluation of a model of global psychophysical judgments: III. A form for the psychophysical function and intensity filtering", Journal of Mathematical Psychology 50: 15–29, doi:
- Stevens, S. S. (1957). On the psychophysical law. Psychological Review 64(3):153–181. PMID 13441853.
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| Translations: Psychophysics |
Dansk (Danish)
n. - psykofysik
Nederlands (Dutch)
psychonatuurkunde
Français (French)
n. - psychophysique
Deutsch (German)
n. - Psychophysik
Ελληνική (Greek)
n. pl. - ψυχοφυσική
Italiano (Italian)
psicofisica
Português (Portuguese)
n. pl. - psicofísica (f)
Español (Spanish)
n. - psicofísica
Svenska (Swedish)
n. pl. - psykofysik
中文（简体）(Chinese (Simplified))
精神物理学
中文（繁體）(Chinese (Traditional))
n. pl. - 精神物理學
n. - 精神物理學
العربيه (Arabic)
(الجمع) علم العلاقات النفسانيه الطبيعيه, علم طبيعه النفس
עברית (Hebrew)
n. - חקר הקשרים בין המוח לגוף, פסיכופיסיקה
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Mentioned in
- William James McGill (American educator & psychologist)
- Henri Pieron
- Wolfgang Ehrenberg (parapsychology)
- Gustav Theodor Fechner
- Stanley Smith Stevens
- just-noticeable differences
- Hall (family name)
- Georg von Békésy (Hungarian–American physicist)
- Charles Samuel Myers
- James Ward
