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Increasing the target-field luminance aids detection for a simultaneously presented black target disc and a black masking annulus. At an intermediate interval separating the onset of the target from the mask, increasing the target-field luminance reduces target detection. This decrease in performance occurs with both temporal and spatial forced choice tasks. With a spatial forced choice, an observer's performance can fall below chance. We associate below-chance performance with a brightness reversal of the black target disc, such that the target disc appears brighter than its surround. The occurrence of brightness reversals follows from our model of the Broca-Sulzer effect, and nonmonotone masking functions result from a generalization of luminance summation.Keywords Visual backward masking . U-shaped functions . Broca-Sulzer effect . Brightness reversal . Metacontrast maskingThe detection of a briefly flashed target, such as a black disc, is sometimes suppressed by the onset of a second stimulus, the masking stimulus. When the target is followed by a surrounding figure, such as a black annulus, the interplay of target and mask is called backward masking. Under conditions of backward masking, both target detection and letter identification can decrease as the delay between the onset of the stimulus and the onset of the mask increases. The resulting nonmonotone performance curves are addressed by most accounts of visual masking . Under some conditions, however, target detection is worse than chance. No current explanation of masking accounts for below-chance performance.Our account of below-chance performance rests on three propositions: (i) A spatial two-alternative forced choice (2AFC) task can produce nonmonotone performance curves. For pronounced nonmonotone curves, detection can be worse than chance. (ii) These nonmonotone backward-masking curves represent a change in an observer's sensitivity for certain delays between target and mask onset, even for targets that fall on the fovea. A dark target, followed by an appropriate masking stimulus, sometimes appears to be brighter than its background, a phenomenon we have called a brightness reversal . Pronounced brightness reversals occur with black-on-white figures and can lead to below-chance target detection. (iii) Our conjecture is that brightness reversals result from the same combination of excitation, inhibition, and luminance summation that produces the Broca-Sulzer effect (Berman & Stewart, 1978a, 1978b, 1979Marks, 1974). These brightness reversals result in below-chance performance with a spatial 2AFC.

A procedure is described which allows the selection of a simple random sample of size n from a list of N items, where N is unknown. and only 2n independent. uniform deviates are required.

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