Psychometric function
Encyclopedia
A psychometric function describes the relationship between a parameter of a physical stimulus
and the responses of a person who has to decide about a certain aspect of that stimulus. Usually these sensory decisions take the form of a two-alternative forced choice (2-AFC). The psychometric function usually resembles a sigmoid function
. Two different types of psychometric plots are in common use. One plots the percentage of correct responses (or a similar value) displayed on the y-axis and the physical parameter on the x-axis. If the stimulus parameter is very far towards one end of its possible range, the person will always be able to respond correctly. Towards the other end of the range, the person never perceives the stimulus properly and therefore the probability of correct responses is at chance level. In between, there is a transition range where the subject has an above-chance rate of correct responses, but does not always respond correctly. The inflection point
of the sigmoid function or the point at which the function reaches the middle between the chance level and 100% is usually taken as sensory threshold
. The second type plots the proportion of "yes" responses on the y-axis, and therefore will have a sigmoidal shape covering the range [0, 1], rather than merely [0.5 , 1], and we move from a subject being certain that the stimulus was not of the particular type requested to certainty that it was. This second way of plotting psychometric functions is often preferable, as it is more easily amenable to principled quantitative analysis using tools such as probit
analysis (fitting of cumulative Gaussian distributions).
A common example is visual acuity
testing with an eye chart
. The person sees symbols of different sizes (the size is the relevant physical stimulus parameter) and has to decide which symbol it is. Usually, there is one line on the chart where a subject can identify some, but not all, symbols. This is equal to the transition range of the psychometric function and the sensory threshold corresponds to visual acuity. (Strictly speaking, a typical optometric measurement does not exactly yield the sensory threshold due to biases in the standard procedure.)
Stimulus (physiology)
In physiology, a stimulus is a detectable change in the internal or external environment. The ability of an organism or organ to respond to external stimuli is called sensitivity....
and the responses of a person who has to decide about a certain aspect of that stimulus. Usually these sensory decisions take the form of a two-alternative forced choice (2-AFC). The psychometric function usually resembles a sigmoid function
Sigmoid function
Many natural processes, including those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used. A sigmoid curve is produced by a mathematical...
. Two different types of psychometric plots are in common use. One plots the percentage of correct responses (or a similar value) displayed on the y-axis and the physical parameter on the x-axis. If the stimulus parameter is very far towards one end of its possible range, the person will always be able to respond correctly. Towards the other end of the range, the person never perceives the stimulus properly and therefore the probability of correct responses is at chance level. In between, there is a transition range where the subject has an above-chance rate of correct responses, but does not always respond correctly. The inflection point
Stationary point
In mathematics, particularly in calculus, a stationary point is an input to a function where the derivative is zero : where the function "stops" increasing or decreasing ....
of the sigmoid function or the point at which the function reaches the middle between the chance level and 100% is usually taken as sensory threshold
Sensory threshold
Sensory threshold is a theoretical concept used in psychophysics. A stimulus that is less intense than the sensory threshold will not elicit any sensation...
. The second type plots the proportion of "yes" responses on the y-axis, and therefore will have a sigmoidal shape covering the range [0, 1], rather than merely [0.5 , 1], and we move from a subject being certain that the stimulus was not of the particular type requested to certainty that it was. This second way of plotting psychometric functions is often preferable, as it is more easily amenable to principled quantitative analysis using tools such as probit
Probit
In probability theory and statistics, the probit function is the inverse cumulative distribution function , or quantile function associated with the standard normal distribution...
analysis (fitting of cumulative Gaussian distributions).
A common example is visual acuity
Visual acuity
Visual acuity is acuteness or clearness of vision, which is dependent on the sharpness of the retinal focus within the eye and the sensitivity of the interpretative faculty of the brain....
testing with an eye chart
Eye chart
An eye chart is a chart used to measure visual acuity. Types of eye charts include the logMAR chart, Snellen chart, Landolt C, and the Lea test.-Procedure:Charts usually display several rows of optotypes , each row in a different size...
. The person sees symbols of different sizes (the size is the relevant physical stimulus parameter) and has to decide which symbol it is. Usually, there is one line on the chart where a subject can identify some, but not all, symbols. This is equal to the transition range of the psychometric function and the sensory threshold corresponds to visual acuity. (Strictly speaking, a typical optometric measurement does not exactly yield the sensory threshold due to biases in the standard procedure.)