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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"
[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]
Psychophysics also refers to a general class of methods that can be applied to study a
perceptual system. Modern applications rely heavily on threshold measurement,
[3] ideal observer analysis, and
signal detection theory.
[4]
Psychophysics has widespread and important practical applications. For example, in the study of
digital signal processing, psychophysics has informed the development of models and methods of
lossy compression.
These models explain why humans perceive very little loss of signal
quality when audio and video signals are formatted using lossy
compression.
History
Many of the classical techniques and theories of psychophysics were formulated in 1860 when
Gustav Theodor Fechner in Leipzig published
Elemente der Psychophysik (Elements of Psychophysics).
[5]
He coined the term "psychophysics", describing research intended to
relate physical stimuli to the contents of consciousness such as
sensations
(Empfindungen). As a physicist and philosopher,
Fechner aimed at developing a method that relates matter to the mind,
connecting the publicly observable world and a person's privately
experienced impression of it. His ideas were inspired by experimental
results on the sense of touch and light obtained in the early 1830s by
the German physiologist
Ernst Heinrich Weber in Leipzig,
[6][7]
most notably those on the minimum discernible difference in intensity
of stimuli of moderate strength (just noticeable difference; jnd) which
Weber had shown to be a constant fraction of the reference intensity,
and which Fechner referred to as Weber's law. From this, Fechner derived
his well-known logarithmic scale, now known as Fechner scale. Weber's
and Fechner's work formed one of the bases of psychology as a
science, with
Wilhelm Wundt
founding the first laboratory for psychological research in Leipzig
(Institut für experimentelle Psychologie). Fechner's work systematised
the introspectionist approach (psychology as the science of
consciousness), that had to contend with the Behaviorist approach in
which even verbal responses are as physical as the stimuli. During the
1930s, when psychological research in
Nazi Germany essentially came to a halt, both approaches eventually began to be replaced by use of
stimulus-response relationships as evidence for conscious or unconscious processing in the mind.
[8] Fechner's work was studied and extended by
Charles S. Peirce, who was aided by his student
Joseph Jastrow,
who soon became a distinguished experimental psychologist in his own
right. Peirce and Jastrow largely confirmed Fechner's empirical
findings, but not all. In particular, a classic experiment of Peirce and
Jastrow rejected Fechner's estimation of a threshold of perception of
weights, as being far too high. In their experiment, Peirce and Jastrow
in fact invented randomized experiments: They randomly assigned
volunteers to a
blinded,
repeated-measures design to evaluate their ability to discriminate weights.
[9][10][11][12]
Peirce's experiment inspired other researchers in psychology and
education, which developed a research tradition of randomized
experiments in laboratories and specialized textbooks in the 1900s.
[9][10][11][12] The Peirce–Jastrow experiments were conducted as part of Peirce's application of his
pragmaticism program to
human perception; other studies considered the perception of light, etc.
[13]
Jastrow wrote the following summary: "Mr. Peirce’s courses in logic
gave me my first real experience of intellectual muscle. Though I
promptly took to the laboratory of psychology when that was established
by
Stanley Hall,
it was Peirce who gave me my first training in the handling of a
psychological problem, and at the same time stimulated my self-esteem by
entrusting me, then fairly innocent of any laboratory habits, with a
real bit of research. He borrowed the apparatus for me, which I took to
my room, installed at my window, and with which, when conditions of
illumination were right, I took the observations. The results were
published over our joint names in the
Proceedings of the National Academy of Sciences.
The demonstration that traces of sensory effect too slight to make any
registry in consciousness could none the less influence judgment, may
itself have been a persistent motive that induced me years later to
undertake a book on
The Subconscious." This work clearly distinguishes observable cognitive performance from the expression of consciousness.
Modern approaches to sensory perception, such as research on vision,
hearing, or touch, measure what the perceiver's judgment extracts from
the stimulus, often putting aside the question what sensations are being
experienced. One leading method is based on
signal detection theory, developed for cases of very weak stimuli. However, the subjectivist approach persists among those in the tradition of
Stanley Smith Stevens (1906–1973). Stevens revived the idea of a
power law suggested by 19th century researchers, in contrast with Fechner's log-linear function (cf.
Stevens' power law). He also advocated the assignment of numbers in ratio to the strengths
of stimuli, called magnitude estimation. Stevens added techniques such
as magnitude production and cross-modality matching. He opposed the
assignment of stimulus strengths to points on a line that are labeled in
order of strength. Nevertheless, that sort of response has remained
popular in applied psychophysics. Such multiple-category layouts are
often misnamed
Likert scaling
after the question items used by Likert to create multi-item
psychometric scales, e.g., seven phrases from "strongly agree" through
"strongly disagree".
Omar Khaleefa
[14] has 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.
[15]
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 a stimulus (absolute
threshold
[16]) or the presence of a difference between two stimuli (difference threshold
[7]).
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 occasions;
therefore, a threshold is considered to be the point at which a
stimulus, or change in a stimulus, is detected some proportion
p of occasions.
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).
[17]
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. Several different methods are used for measuring absolute thresholds (as with discrimination thresholds; see below).
Discrimination
A difference threshold (or
just-noticeable difference,
JND) is the magnitude of the smallest difference between two stimuli of
differing intensities that the participant is able to detect some
proportion of the time (the percentage depending on the kind of task).
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 (method of adjustment), may be asked to describe the
direction and magnitude of the difference between two stimuli, or may be
asked to decide whether intensities in a pair of stimuli are the same
or not (forced choice). The just-noticeable difference (JND) is not a
fixed quantity; rather, it depends on how intense the stimuli being
measured are and the particular sense being measured.
[18] Weber's Law states that the just-noticeable difference of a stimulus is a constant proportion despite variation in intensity.
[19]
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,
[20] 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 in the comparison task). In addition, a
two-alternative forced choice
(2-afc) paradigm can be used to assess the point at which performance
reduces to chance on a discrimination between two alternatives (
p will then typically be 75% since
p=50% corresponds to chance in the 2-afc task).
Absolute and difference thresholds are sometimes considered similar
in principle because there is always background noise interfering with
our ability to detect stimuli.
[6][21]
Experimentation
In
psychophysics, experiments seek to determine whether the subject can
detect a stimulus, identify it, differentiate between it and another
stimulus, or describe the magnitude or nature of this difference.
[6][7] Software for psychophysical experimentation is overviewed by Strasburger.
[22]
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.
[23]
Method of limits
In
the 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 are just
detected.
[23]
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 anticipation).
To avoid these potential pitfalls,
Georg von Békésy 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.
[23]
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.
For 'absolute thresholds' again the subject reports whether he or she is
able to detect the stimulus.
[23]
For 'difference thresholds' there has to be a constant comparison
stimulus with each of the varied levels. Friedrich Hegelmaier described
the method of constant stimuli in an 1852 paper.
[24] This method allows for full sampling of the
psychometric function, but can result in a lot of trials when several conditions are interleaved.
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.
[23]
In this method the observer himself controls the magnitude of the
variable stimulus beginning with a variable that is distinctly greater
or lesser than a standard one and he varies it until he is satisfied by
the subjectivity of two. The difference between the variable stimuli and
the standard one is recorded after each adjustment and the error is
tabulated for a considerable series. At the end mean is calculated
giving the average error which can be taken as the measure of
sensitivity.
Adaptive psychophysical methods
The
classic methods of experimentation are often argued to be inefficient.
This is because, in advance of testing, the psychometric threshold is
usually unknown and much data is collected at points on the
psychometric function
that provide little information about the parameter of interest,
usually the threshold. Adaptive staircase procedures (or the classical
method of adjustment) can be used such that the points sampled are
clustered around the psychometric threshold. However, the cost of this
efficiency is that there is less information regarding the psychometric
function's shape. Adaptive methods can be optimized for estimating the
threshold only, or threshold
and slope. Adaptive methods are
classified into staircase procedures (see below) and Bayesian or
maximum-likelihood methods. Staircase methods rely on the previous
response only and are easier to implement. Bayesian methods take the
whole set of previous stimulus-response pairs into account and are
believed to be more robust against lapses in attention.
[25]
Staircase procedures
Diagram showing a specific staircase procedure: Transformed Up/Down
Method (1 up/ 2 down rule). Until the first reversal (which is
neglected) the simple up/down rule and a larger step size is used.
Staircases usually begin with a high intensity stimulus, which 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 the last of these 'reversals' are then
averaged. There are many different types of staircase procedures, using
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.
[25]
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.
[26]
One of the more common staircase designs (with fixed-step sizes) is
the 1-up-N-down staircase. If the participant makes the correct response
N times in a row, the stimulus intensity is reduced by one step size.
If the participant makes an incorrect response the stimulus intensity is
increased by the one size. A threshold is estimated from the mean
midpoint of all runs. This estimate approaches, asymptotically, the
correct threshold.
Bayesian and maximum-likelihood procedures
Bayesian
and maximum-likelihood adaptive procedures behave, from the observer's
perspective, similar to the staircase procedures. The choice of the next
intensity level works differently, however: After each observer
response, from the set of this and all previous stimulus/response pairs
the likelihood is calculated of where the threshold lies. The point of
maximum likelihood is then chosen as the best estimate for the
threshold, and the next stimulus is presented at that level (since a
decision at that level will add the most information). In a Bayesian
procedure, a prior likelihood is further included in the calculation.
[25]
Compared to staircase procedures, Bayesian and ML procedures are more
time-consuming to implement but are considered to be more robust.
Well-known procedures of this kind are Quest,
[27] ML-PEST,
[28] and Kontsevich & Tyler’s method.
[29]
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 method then becomes "magnitude production" or
"cross-modality 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 multiple-category responses, because of
the restricted range of the categorical anchors, such as those used by
Likert as items in attitude scales.
