equation for psychometric function
P(x) = y + (1-(wavelength)-y)p(x)
The psychometric function is generally represented by a mathematical equation that models the relationship between the physical characteristics of a stimulus and the perception or response of an observer. There are several different forms that the psychometric function can take, but one commonly used equation is the logistic function or sigmoid function:
P(x) = 1 / (1 + e^(a(x – b)))
In this equation, P(x) represents the probability of the observer perceiving or responding to the stimulus at a particular intensity level x. The parameters a and b determine the shape and position of the psychometric function, respectively.
The logistic function is chosen for its S-shaped curve, which is often observed in psychophysical experiments. It has both a lower and an upper asymptote at 0 and 1, respectively, and transitions smoothly between these extremes as x increases. By fitting this equation to experimental data, researchers can estimate the threshold at which an observer is able to detect the stimulus with a defined criterion, as well as other parameters of interest such as slope and lapse rate.
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