for Estimating Empirical Thresholds
Detection theory provides tools for exploring the relation between stimuli and their psychological magnitudes. In the examples discussed so far, stimulus parameters have been chosen for their inherent interest, and the dependent variable has been d′, ln(α), or some other measure of performance.
Often it is natural to turn this experimental question around and try to find the stimulus difference that leads to a preselected level of performance. Such a stimulus difference we have called the empirical threshold or simply the threshold. For example, an experimenter may seek a physical difference just large enough so that an observer in 2AFC obtains a d′ of 1.0 or 1.5, or (equivalently, for an unbiased observer) so that p(c) equals .76 or .86. Empirical thresholds are unrelated to those of threshold theory (discussed in chap. 4); indeed, they can be measured in either detection theory (d′) or threshold theory [p(c)] terms. The double meaning of threshold, although unfortunate, is unavoidable and need cause no confusion.1
Measuring a threshold requires access to a set of stimuli that range, on some physical variable, from too small to too large for the desired level of performance. A field in which threshold measurement has been widely used is audiology, which assesses sensitivity as an aid to the diagnosis of hearing problems. Audiologists estimate thresholds by straightforward manipulation of tone intensity using a Békésy Audiometer (von Békésy, 1947). The intensity of the tone being detected is either continuously increased or continuously decreased, and the observer is told to press a switch whenever the stimulus is audible. The switch is connected to an automatic attenuator in such a way that holding down the switch decreases the intensity and letting it____________________