The psychophysics of absolute threshold and signal duration: a probabilistic approach

The absolute threshold for a tone depends on its duration; longer tones have lower thresholds. This effect has traditionally been explained in terms of "temporal integration" involving the summation of energy or perceptual information over time. An alternative probabilistic explanation of the process is formulated in terms of simple equations that predict not only the time ∕ duration dependence but also the shape of the psychometric function at absolute threshold. It also predicts a tight relationship between these two functions. Measurements made using listeners with either normal or impaired hearing show that the probabilistic equations adequately fit observed threshold-duration functions and psychometric functions. The mathematical formulation implies that absolute threshold can be construed as a two-valued function: (a) gain and (b) sensory threshold, and both parameters can be estimated from threshold-duration data. Sensorineural hearing impairment is sometimes associated with a smaller threshold ∕ duration effect and sometimes with steeper psychometric functions. The equations explain why these two effects are expected to be linked. The probabilistic approach has the potential to discriminate between hearing deficits involving gain reduction and those resulting from a raised sensory threshold.