These experiments explored the empirical relations among growth of detection as a function of SPL, amplitude discrimination performance, and temporal integration. To a first order of approximation the results were as follows: ROC curves in quiet were linear on normal‐normal coordinates, the slope of the psychometric function did not vary as a function of duration, the slope of the psychometric function was inversely proportional to the size of the difference limen, and amount of temporal integration was inversely related to the slope of the psychometric function. Some theoretical considerations relating to this last finding will be discussed.