Psychophysics

Psychophysics is a subdiscipline of psychology dealing with the relationship between physical stimuli and their subjective correlates, or percepts.

History
Many of the classical techniques and theory of psychophysics were formulated in 1860 when Gustav Theodor Fechner published Elemente der Psychophysik. He coined the term "psychophysics", and 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 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.

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 topics in the psychophysical classification scheme: absolute thresholds, discrimination thresholds, and scaling.

The most common use of psychophysics is in producing scales of human experience of various aspects of physical stimuli. Take for an example the physical stimulus of frequency of sound. Frequency of a sound is measured in hertz, cycles per second. But human experience of the frequencies of sound is not the same as the frequencies. For one thing, there is a frequency below which no sounds can be heard, no matter how intense they are (around 20 Hz depending on the individual) and there is a frequency above which no sounds can be heard, no matter how intense they are (around 20,000 Hz, again depending on the individual). For another, doubling the frequency of a sound (e.g., from 100 Hz to 200 Hz) does not lead to a doubling of experience. The perceptual experience of the frequency of sound is called pitch, and it is measured by psychophysicists in mels.

More analytical approaches allow the use of psychophysical methods to study neurophysiological properties and sensory processing mechanisms. This is of particular importance in human research, where other (more invasive) methods are not used due to ethical reasons.

Areas of investigation include sensory thresholds, methods of measurement of sensitivity, and signal detection theory.

Thresholds
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, however stimuli at values close to threshold will often be detectable some proportion of the time. Due to this, 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 and difference.

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.

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 difference 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.

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.

Discrimination
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 difference in stimuli that the subject notices some proportion p of the time (50% is usually used for p).

The methods of limits, constant stimuli and adjustment can be used in difference detection by asking the subject to detect a difference between stimuli rather than detect a single stimulus.

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.

Classic Methods of experimentation
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.

Method of limits
Wilhelm Wundt invented the method of limits. The subject reports whether he or she detects the stimulus. 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.

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 method 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.

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.

Method of adjustment
This is also called the method of average error, 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.

Method of propellors
The "method of propellors" involves simultaneous comparisons of three stimuli, of which one at a time is taken as a target and the observer judges the size of the difference between the target and each of the other two stimuli. For example, an observer might be asked to compare chocolate, vanilla, and strawberry ice cream. Beginning with chocolate as the target, he or she would judge the size of the difference between chocolate and vanilla, then the size of the difference between chocolate and strawberry, and report which difference was larger. Carrying out this procedure with a number of stimuli permits a rank-ordering of complex stimuli by an observer who would have said the task was impossible if asked to create a simple order. This technique is most effective for complex stimuli rather than simple size or brightness judgments.

Staircase procedure
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).

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 modelled and some practical recommendations suggested by Garcia-Perez.