Estimating parameters for psychometric functions using the four-point sampling method.

Although a psychometric function describing a subject's responses to some physical stimuli is of considerable value, characterizing such functions is time consuming and, hence, is not carried out routinely in psychophysical experiments. A principal reason for the lack of efficiency in characterizing a psychometric function is the use of sampling methods that either converge on a single point on the psychometric function, such as the PEST method, or which distribute observations uniformly over a wide range, such as the constant stimuli method. As an alternative, a multimodal four-point sampling method has been proposed [C. F. Lam, J. H. Mills, and J. R. Dubno, J. Acoust. Soc. Am. 99, 3689-3693 (1996)]. A psychometric function is then fitted to the four points (each with several trials) to estimate the threshold and slope parameters of the psychometric function. Adaptive methods, such as the up-down methods [H. Levitt, J. Acoust. Soc. Am. 49, 467-477 (1971)], can be used to provide good initial estimates of the threshold and spread parameters of a psychometric function described by a logistic function. In ongoing studies of age-related changes in auditory masking and discrimination, this new four-point sampling method has been applied to determine psychometric functions for absolute thresholds as a function of duration, thresholds in simultaneous and forward masking, frequency discrimination, and intensity discrimination in both young and aged human subjects. Results indicate that a reduction in data collection time of about 50% with no increase in variance can be achieved. This increase in efficiency applies to simple detection tasks by normal hearing subjects as well as to complex discrimination tasks by older subjects with hearing loss.