GitHub: Matlab code and Python package
Introduction
An important aim of psychophysics is to quantify the relationship between stimulus parameters and an observer's subjective appreciation of what's going on. Signal detection theory approaches this problem by attributing perceptual sensitivity to thresholds that act at multiple levels in a system. In this context, a threshold could, for example, be how loud a sound needs to be to determine its location to a certain degree of accuracy, or how long a light needs to be on to determine its direction of movement. Above threshold, and the task is possible to a certain degree of accuracy. Below threshold and it's not possible to discriminate as accurately.
Experimentally, thresholds are often measured in two-alternative forced choice (2AFC) tasks or in go-no go paradigms (GNG). In 2AFC tasks a subject is asked to indicate one of two choices in response to a stimulus. For example, indicate white if a colour appears white, or black if it appears black in response to a shade of grey. Alternatively, GNG tasks require a subject to not respond ("no go") until a stimuli meets a certain criteria, then respond ("go").
In both of these types of task, a subjects performance can be measured as a function of the stimulus parameters - either as % correct, or similar, in 2AFC or d' in GNG, where d' is a function of hits, misses, and false alarms. Regardless of the exact metric used, the subjects performance can be described by two main parameters; bias (the "point of subject equality", PSE) and discrimination sensitivity (as in ability to discriminate between two conditions, such as white and black).
For example, imagine a subject performing a 2AFC task where they're presented with a shade of grey and they have to press one button to categorise the colour as white, or another button to categorise the colour as black. Intuitively, they're more likely to classify a grey stimulus as black the closer it is to black, and less likely the colour it is to white. So plotting their responses as a proportion of black responses (y) against the stimuli presented (x). We could use this sort of task to see how other factors, like the colour of a background, could affect perception of the shade of grey.
