An efficient adaptive procedure for psychophysical discrimination experiments

We present an adaptive procedure to conduct psychophysical discrimination experiments. In a discrimination experiment, an observer senses (sees, hears, feels, etc,) two stimuli (separated in space or time) and is asked to order these stimuli with respect to a particular parameter (say,s). Under the usual assumption of a locally linear internal representation of s, perturbed by additive Gaussian noise, the probability P(s(2))-of judging test stimulus s(2) ''larger'' than a reference stimulus s(1)-is an error function (a cumulative normal distribution). Such an error function, Erf[(s(2)-mu)/sigma], is parametrized by two parameters: mu and sigma. The parameter mu is the value for which P(s(2)) = 50% and is related to possible bias effects in the internal representation of the observer. The parameter sigma is root 2 times the standard deviation of the noise distribution and is generally called the discrimination threshold. In this paper, we present (1) an algorithm to estimate mu and sigma given the data generated by such an observer, (2) an analysis of the efficiency of a stimulus presentation with respect to the estimation of mu and sigma, and (3) a method that controls the specific choice of stimulus values during an experiment so that an optimal estimation of mu and sigma is obtained.