Psychophysics is all about quantifying and measuring perception and sensation. Perception and sensation refer to the way we interpret in incoming sensory information from the periphery, e.g. eyes for vision, ears for sound. They are what arises in the mind and thus a domain of cognitive psychology. The pioneer of psychophysics is G. Fechner, to whom this study originated. His interest was to find the relationship between a physical stimulus (an external entity that comes into contact with the body) and psychological perception (the mind) that arises from that stimulus.
The simplest method of psychophysics is the method of limits. Logically, there should be a minimum quantity, the weakest stimulus that can be detected. This quantity is called threshold or limen in Latin. In the method of limits, a trial begins with a set of stimuli in a specific order. The presentation can be in ascending or descending series. The experimenter then, little by little, increases the magnitude or intensity of the stimulus. Refer to the figure below, e.g. we can start with S1 presentation, up to S15. The participant answers “Yes” each time the stimulus is perceivable or “No” otherwise, each of which is recorded by the experimenter. Following this, the trial continues with the same presentation.
Another variant of this method is the staircase method where the stimulus is first provided with strong intensity and it is gradually reduced until the person makes mistake (descending order). The intensity is adjusted upward (ascending) until the person does not make mistake or detect it correctly. Soon after, again the stimulus intensity is reduced. Such a procedure is performed again and again. In general, staircase designs use a fixed-step size e.g. 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. One difficulty is determining the optimal step size.
A total opposite to the method of limits is the method of adjustment where the participant himself actively adjusts the stimulus magnitude until it is barely detectable.
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| Fig-1: Simple illustration of the method of limits. See how the psychometric function is produced in the right panel, with the threshold of detection defined as the intensity where the subject detects 50% of the time. |
One main drawback of the method mentioned is that the participant is able to guess the intensity of the next stimulus in the queue. An improved and more popular version is the method of constant stimuli, in which the stimulus presentation in each trial is random so that the participant is unable to guess what the upcoming trial is, that is, the stimulus is constantly changing. For example trial-1 has S4, S2, S9, S6, S10, S11, and so on. In analyzing the data, we first produce a percentage of "Yes" responses over the whole trials for each different stimulus intensity and plot them in a graph. As seen in the figure, the graph is not an abrupt change but a gradual one, a profile known as the psychometric function. The reason for this is two things: the sensory system is noisy and that the criterion of the decision may change. Note that a criterion is in the mind of the participant whereas the threshold is the physical quantity of a stimulus. A single person can have changeable or a few criteria due to various factors. The detection threshold is defined as the stimulus magnitude in which it is perceivable 50% of the time.
To avoid a response that is biased by the criterion, another method called the method of two-alternative forced choices (2AFC) is used. There is one major difference. In the visual experiment, for example, a participant is presented with two light sources instead of one. The light can appear in either left or right source, with both intensity and location vary from one presentation to the other. The participant has to respond to either the left or right source. When unsure, he or she is forced to make a choice out of two possible scenarios, rather than simply saying “No”. In other words, the question is not whether you can detect a stimulus, but which one has the stimulus. Note that to provide fair tests, the # times the stimulus appears from the left and right source has to be the same. The experimenter also notes the correct answer, who will then compute % Correct responses. The threshold obtained from this method is relatively lower than the one from the previous methods. The resulting psychometric function is now running from 50% to 100%, because at its worst state when a person responds using the same choice each time, there is 50% chance correct. We can push the lower boundary to 0% by providing more choices to select but with the cost of a more confusing the test. In practice,two stimuli can be presented in a different time interval (temporal, e.g. being separated by 750 msec) or location (spatial, e.g. top-left and bottom-right).
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| Fig-2: Simple illustration of the two-alternative force choice between right and left source. See how the psychometric function is produced in the right panel. |
So far the discussion is on the absolute threshold. There is also another term called differential threshold, i.e. the minimum difference in intensity or magnitude between a test and a reference stimulus such that they give a detectable perceptual difference. It is also called JND or 'just noticeable difference'. A pioneer in this differential sensitivity is Weber who has the name in Weber fraction k. In a later period, a different question arose: what is the relationship between stimulus magnitude and the resulting percept (a problem of scaling)? Fechner makes a bold assumption: the JNDs are perceived as being equal changes in perception. The magnitude of sensation is proportional to how many JNDs it is above the threshold. In other words, JND is a proxy to the sensation. Related to this, Weber-Fechner law states that the apparent increment in sensation declines with increasing level of stimulus. Example: an increase of 50 gram feels negligible for a 4 kg weight compared to a 0.5 kg weight.
Other topics in psychophysics will not be presented here: ratio scaling, Steven's power law, prothetic or metathetic continuum, multidimensional scaling, and static invariances.
Modern Psychophysics
The improvement in instrumentation and experimental design brings the birth of modern psychophysics that is dominated by the Signal Detection Theory, SDT, a concept borrowed from communication system during war. The threshold or limen in classical psychophysics is not without limitation. Moving away from measuring threshold without considering decision criterion, scientists moved on the performance during the task, both when the stimulus is present and when it is not. The main assumption is that our sensory system is inherently noisy. The noise can arise from an external source or internal source. It is a background activity and is typically thought to be a random process with a normal distribution. A sensory signal following a stimulus is superimposed on this background activity. Fig-3 shows two distributions of activity in the sensory system. The graph with stimulus presentation (S + N) is shifted to the right of the graph in the noise (N) condition; that is, it has a higher mean!
The main task is for the participant to judge whether, in a given trial, the activity belongs to S + N or to N only. In fact, SDT treats an observer as a binary classifier. If the participant feels that the signal can be detected, then S + N should be selected. The separation between two distributions is called sensitivity of a sensor or detector, given as d-prime (d'). It is essentially telling us how sensitive we are in detecting the real stimulus. Look at the figure below. We can compute, as in statistics, area under the distribution curve in each category, i.e. the probability (or proportion) to occur.
How to design and analyze a behavioral study using SDT? Simply, we first divide total trials, e.g. 100, into 50 trials with stimulus signal and 50 trials with noise only. The administration of the two sets is randomized (method of constant stimuli). Total "Yes" responses in trials with stimulus is called Hits, total "No" responses is Misses. On the other hand, total "Yes" responses in trials with noise only is called False Alarms, and "No" responses is Correct Rejection. Then we compute d' = ZFA ‒ ZHit. The criterion can be quantified by taking the mean of to ZFA and ZHit. Note that sign convention should be obeyed at all time when using the Z-table. A big d' means that the detector has a high ability of separating noise-only and signal. What does it mean to have d' = 0? It shows the person has no discrimination ability, the performance is at chance level. Theoretically, d' < 0 is a matter of interpretation although the nominal of Hits minus FalseAlarms can be negative. Meaning, subjects are preferentially responding to lures or distractors than to actual memory items.
Refer to Fig. 3. Note that the vertical lines are called the criterion that represents response bias. What if, for a given stimulus magnitude, the observer changes the criterion during the task? The line C will shift either to the right or left. Moving to the right (line A) means that the participant is adopting a conservative strategy as he is trying to prevent many false alarms. Conversely, shifting to the left symbolizes a more liberal strategy (line B). The phenomenon of shifting a criterion can also be depicted by another plot called receiver operating characteristic, ROC curve. For any given participant, there will only be one ROC curve that will apply in that experiment since the stimulus intensity is fixed, and the person has inherent sensitivity (d') to that stimulus. Moving along the ROC curve, we are able to estimate the conservative/liberal criterion employed. The ROC curve is also employed in other fields, e.g. medical diagnostic to test the performance of a binary classifier (disease or no-disease).
[*] Source: Levine's Fundamentals of Sensation and Perception; 3e edition.
Refer to Fig. 3. Note that the vertical lines are called the criterion that represents response bias. What if, for a given stimulus magnitude, the observer changes the criterion during the task? The line C will shift either to the right or left. Moving to the right (line A) means that the participant is adopting a conservative strategy as he is trying to prevent many false alarms. Conversely, shifting to the left symbolizes a more liberal strategy (line B). The phenomenon of shifting a criterion can also be depicted by another plot called receiver operating characteristic, ROC curve. For any given participant, there will only be one ROC curve that will apply in that experiment since the stimulus intensity is fixed, and the person has inherent sensitivity (d') to that stimulus. Moving along the ROC curve, we are able to estimate the conservative/liberal criterion employed. The ROC curve is also employed in other fields, e.g. medical diagnostic to test the performance of a binary classifier (disease or no-disease).
[*] Source: Levine's Fundamentals of Sensation and Perception; 3e edition.
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