On measuring psychometric functions

Abstract

Psychometric functions of simulated observers were obtained using the conventional constant‐stimulus method and an adaptive up–down method through a post‐hoc analysis of the track. The form of the psychometric functions was assumed to be Pc=Ψ(d’/21/2), where Ψ is the cumulative Gaussian probability function. The detectability d’, is related to the signal level x by d’=axk, where a and k are the two parameters to be estimated. Among the factors considered in the simulation were step size and number of trials. For small number of trials (n≤120), and particularly when the step size was also small, the slope values (k) estimated using the adaptive method were systematically greater than the true slopes. Such biases were smaller with the constant‐stimulus method. When the number of trials was reasonably large (n≥300), the constant‐stimulus method showed no clear advantage over the adaptive method. The only a priori information required in the adaptive method is the starting stimulus level, whereas the constant‐stimulus method requires pilot measurements in order to set all the stimulus levels properly. Thus the adaptive method is reasonably efficient for measuring psychometric functions. [Work supported by NIH.]