In particular, Baldassi and Burr (2000) observed that orientation thresholds varied with set size according to the square root of the number of elements, and that this relationship persisted across the whole range of noise levels and experimental conditions. Two studies using an identification task ( Baldassi & Burr, 2000 Morgan, Ward, & Castet, 1998) have suggested that the information about a given visual feature (the target) may be diluted by adding neutral elements (distractors) through the action of a pooling mechanism. However, as postulated formerly by Green and Swets (1966) and by Shaw (1982), information might be integrated in a different way via mechanisms that pool together individual responses by what is generally referred to as the summation rule or Sum rule ( Graham, Kramer, & Yager, 1987). All of these studies used paradigms well suited to this integration rule, commonly referred to as maximum-of-outputs rule or Max rule. Similar models have also been successful in explaining the additional disruption of performance occurring in conjunction search tasks ( Eckstein, 1998). In other words, the magnitude of the observed threshold increase is consistent with a model that predicts only an increase in uncertainty with increasing set size. For this class of models, every new element contributes uncertainty.
In particular, by using threshold measures across various visual dimensions, such as contrast, length, speed, and orientation discrimination, different studies have shown that the increase in thresholds with increasing set size is well fit by the prediction of a SDT model that chooses the strongest response among independent detectors ( Palmer, 1994 Palmer, Ames, & Lindsey, 1993 Palmer, Verghese, & Pavel, 2000 Shaw, 1980 Shaw, 1982 Shiu & Pashler, 1995 Verghese & Stone, 1995 Solomon, Lavie, & Morgan, 1997). However, they may differ substantially in the specific rule they implement. Parallel models share the idea that an integration rule combines the responses to individual inputs to yield a decision variable. Although the function relating thresholds to set size had a slope consistent with both the Signed-Max and the Summation models, the shape of individual psychometric functions was in the most crucial conditions better predicted by the Signed-Max model, which chooses the largest tilt while keeping track of the direction of tilt. We then compared the data to the predictions of two models: a Summation model that integrates both signal and noise from local detectors and a Signed-Max model that first picks the maxima on both sides of vertical and then chooses the value with the highest absolute deviation from the reference. The orientation jitter was set at multiples of the estimated internal noise, which was invariant across set sizes and measurement techniques. Measurements were made at different set sizes in the presence of various levels of orientation jitter. Here we varied the target tilt and measured psychometric functions for identifying the direction of tilt from vertical. When the target is tilted in either direction from the reference orientation and the task is to identify the sign of tilt, the loss of performance with set size is much greater than predicted by the Max rule. The Max rule bases its decision on the largest response from a set of independent noisy detectors. Typically these models use a maximum-of-outputs rule (Max rule) to predict search performance. Search performance for a target tilted in a known direction among vertical distractors is well explained by signal detection theory models.
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