Editing Psychophysics (section)

==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.<ref name=Snodgrass/><ref name=GescheiderChap1/> Software for psychophysical experimentation is overviewed by Strasburger.<ref name="software_overview">Strasburger H (1995–2020). Software for visual psychophysics: an overview. [http://www.visionscience.com/documents/strasburger/strasburger.html VisionScience.com]</ref>

===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.<ref name=GescheiderChap3>{{cite book |author=Gescheider G |year=1997 |title=Psychophysics: the fundamentals | edition=3rd |publisher=Lawrence Erlbaum Associates | chapter=Chapter 3: The Classical Psychophysical Methods |isbn=978-0-8058-2281-6 }}</ref>

====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.<ref name=GescheiderChap3/>

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 [[Psychophysics#Staircase procedures|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.<ref name=GescheiderChap3/>

====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 they are able to detect the stimulus.<ref name=GescheiderChap3/> 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.<ref name=LamingLaming1992>{{Cite journal
| doi = 10.1007/BF01358261
| issn = 0340-0727
| volume = 54
| issue = 4
| pages = 233–239
| last = Laming
| first = Donald
|author2=Janet Laming
 | title = F. Hegelmaier: On memory for the length of a line
| journal = Psychological Research
| year = 1992
| pmid = 1494608
| s2cid = 6965887
}}</ref>  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====
In the method of adjustment, the subject is asked to control the level of the stimulus and to alter it until it is just barely detectable against the background noise, or is the same as the level of another stimulus. The adjustment is repeated many times. This is also called the ''method of average error''.<ref name=GescheiderChap3 />
In this method, the observers themselves control the magnitude of the variable stimulus, beginning with a level that is distinctly greater or lesser than a standard one and vary it until they are satisfied by the subjective equality of the 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, the mean is calculated giving the average error which can be taken as a 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 most of the data are 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. Data points can also be spread in a slightly wider range, if the psychometric function's slope is also of interest. Adaptive methods can thus be optimized for estimating the threshold only, or both 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 generally more robust against lapses in attention.<ref name="Treutwein">{{cite journal|last1=Treutwein|first1=Bernhard|title=Adaptive psychophysical procedures|journal=Vision Research|date=September 1995|volume=35|issue=17|pages=2503–2522|doi=10.1016/0042-6989(95)00016-X|pmid=8594817|s2cid=10550300|doi-access=free}}</ref> Practical examples are found here.<ref name="software_overview" />

====Staircase procedures====
{{Main|Up-and-Down Designs}}

[[File:Staircase Transformed Up Down English.png|thumb|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.<ref name="Treutwein" /> 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.<ref name=GarciaPerez>{{cite journal |title=Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties |author=Garcia-Perez, MA |journal=Vision Res |year=1998 |volume=38 |pages=1861–81 |doi=10.1016/S0042-6989(97)00340-4 |pmid=9797963 |issue=12|s2cid=18832392 |doi-access=free }}</ref>

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 (ML) 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.<ref name="Treutwein" /> 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,<ref>{{cite journal|last1=Watson|first1=Andrew B.|last2=Pelli|first2=Denis G.|title=Quest: A Bayesian adaptive psychometric method|journal=Perception & Psychophysics|date=March 1983|volume=33|issue=2|pages=113–120|doi=10.3758/BF03202828|pmid=6844102|doi-access=free}}</ref> ML-PEST,<ref>{{cite journal|last1=Harvey|first1=Lewis O.|title=Efficient estimation of sensory thresholds|journal=Behavior Research Methods, Instruments, & Computers|date=November 1986|volume=18|issue=6|pages=623–632|doi=10.3758/BF03201438|doi-access=free}}</ref> and Kontsevich & Tyler's method.<ref>{{cite journal|last1=Kontsevich|first1=Leonid L.|last2=Tyler|first2=Christopher W.|title=Bayesian adaptive estimation of psychometric slope and threshold|journal=Vision Research|date=August 1999|volume=39|issue=16|pages=2729–2737|doi=10.1016/S0042-6989(98)00285-5|pmid=10492833|s2cid=8464834|doi-access=free}}</ref>

====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 [[Stevens' power law|power law]] with stable, replicable exponent. Although contexts can change the law & 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 [[Rensis Likert|Likert]] as items in attitude scales.<ref name=Stevens>{{cite journal|last1=Stevens|first1=S. S.|title=On the psychophysical law|journal=Psychological Review|date=1957|volume=64|issue=3|pages=153–181|doi=10.1037/h0046162|pmid=13441853}}</ref>