=psignifit()?> is a statistical software tool for vision and hearing scientists, experimental psychologists and human factors researchers. Its aim is to fit psychometric functions to psychophysical data sets using the method of maximum-likelihood, to test the quality of the fit, and to provide confidence intervals on the parameters of the fitted functions.
The psychometric function is a curve that relates an observer's ability to detect a stimulus (or to detect differences between two or more stimuli) to the intensity of the stimulus (or to the size of the difference). Its range is a probability measure - the probability with which the observer reports that the stimulus is present (in "yes-no" experiments), or the probability with which he or she can correctly identify the target stimulus in comparison with others (in "forced-choice" experiments). It is usually an increasing function of stimulus intensity, and usually a sigmoid curve such as a logistic or cumulative normal.
In most cases, there are two parameters of the psychometric function that are of interest to the experimenter. One is the stimulus intensity at which the observer achieves a certain prescribed probability of detection: this is often called a sensory "threshold", and it effectively specifies the location of the curve along the stimulus axis. The other parameter is the slope of the function, the rate at which performance increases with increasing stimulus intensity.
In any practical application, however, there are additional "nuisance" parameters that must be estimated: in forced-choice experiments, there is the "lapse rate", i.e. the rate at which the subject makes stimulus-independent errors. In yes-no experiments, there is a similar parameter which is the rate at which the subject reports that the stimulus is absent independently of intensity, and in addition there is the rate at which the subject performs the converse response, reporting that the stimulus is present irrespective of its intensity or of whether it is actually there at all. These are "nuisance" parameters because they reflect aspects of the subject's behaviour that are, at best, of secondary importance - it is the threshold and slope of the underlying psychometric function, discounting such "lapses", that the psychophysicist really wishes to measure. However, accurate estimates of these nuisance parameters are required for unbiased estimation of threshold and slope.