Despite several processing limitations that have been identified in the visual system, research shows that statistical information about a set of objects could be perceived as accurately as the information about a single object. It has been suggested that extraction of summary statistics represents a different mode of visual processing, which employs a parallel mechanism free of capacity limitations. Here, we demonstrate, using reaction time measures, that increasing the number of stimuli in the set results in faster reaction times and better accuracy for estimating the mean tendency of a set. These results provide clear evidence that extraction of summary statistics relies on a distributed attention mode that operates across the whole display at once and that this process benefits from larger samples across which the summary statistics are calculated.

*exceeds*what could be accomplished by a sampling strategy, in order to conclusively refute this explanation (Simons & Myczek, 2008).

*reduced*when the number of stimuli increases, and this reduction in reaction time is accompanied by improved (or unchanged) accuracy. This result cannot be accommodated by a focused attention mechanism deployed to individual items, with or without a sampling strategy. At the same time, we show that searching for a specific member of a set presented under identical conditions results in a steep increase in reaction time, as expected in cases of inefficient visual search (Wolfe, 1998). Taken together, these findings provide direct evidence for two different mechanisms: one involved in identifying specific items in a visual display, which operates serially, and a different one involved in extracting summary statistics from a set of items, which appears to operate automatically and in parallel across the entire visual display.

*π*(diameter/2)

^{2}), a power factor of 0.5 would have to be applied to an equidistant distribution of diameter values in order to get an equidistant distribution of areas. Chong and Treisman (2003) attempted to determine whether subjects based their estimates on the diameter or the area and concluded that the metric that seemed to be used was somewhere in between what would be predicted by averaging the diameters or the areas. It was unclear if this was due to a mixture of subjects that used one or the other strategy or if each subject used a mix of both metrics. Chong and Treisman therefore adjusted the size of their circle stimuli by a power of 0.76. This specific exponent value accords well with Teghtsoonian's (1965) finding that the apparent size of circles grows somewhat more slowly than the actual area of the stimuli, in a manner that was best fit by an exponential factor of 0.76. Therefore, in the present experiment, we followed Chong and Treisman and adjusted the diameters of our distribution of circles by a factor of 0.76.

^{0.76}. These translate to a diameter range of 38 to 129 pixels or 1.27° to 4.36° on the screen. The addition of 110 to the size, before the power function was applied, ensured that even the smallest circles were visible on the screen. Step 25 was used as the target, yielding a target size of 2.93° of visual angle (Figure 2).

*C*× the standard deviation or greater than the mean plus

*C*× the standard deviation, the outlier value was excluded permanently, and the process was repeated until no observation was rejected. The criterion,

*C,*was 3.0 or greater and was adjusted as a function of sample size, as explained in Van Selst and Jolicoeur (1994). The retained RTs were analyzed with a 2 (exposure duration: 94 ms or until response) × 6 (set size: 2, 4, 6, 8, 10, 12) repeated-measures ANOVA. RT was significantly different across set size,

*F*(5,95) = 14.31, MSE = 4388,

*p*< 0.0001 (see Figure 3). There was also a main effect of exposure duration,

*F*(1,19) = 55.46, MSE = 4388,

*p*< 0.0001, with RTs being on average 142 ms longer in the long than in the short exposure condition. However, the modulation by set size was not different for the short and the long exposure,

*F*< 1. The slope of the regression line relating RT and set size (collapsed across brief and long exposure) indicated a reduction of 9.5 ms per item, which was significantly different from zero,

*t*(19) = −4.6,

*p*< 0.0002.

*F*(5,95) = 13.65, MSE = 0.004,

*p*< 0.0001. This modulation was not different across brief and long exposure,

*F*(5,95) = 2.01, MSE = 0.0023,

*p*> 0.08, although there was overall better accuracy (by 1.5%) for long exposure compared to short exposure,

*F*(1,19) = 10.7, MSE = 0.0014,

*p*< 0.004. The slightly lower accuracy for the brief exposure resulted in the staircase adjusting the average set size to be slightly more distant from the target (i.e., easier discrimination) in this condition compared to the long exposure condition,

*F*(1,19) = 4.75, MSE = 1.03158,

*p*< 0.042. The slope of the regression line relating accuracy and set size (collapsed across brief and long exposure) showed an increase in accuracy of 0.6% per item, which was significantly different from zero,

*t*(19) = 4.3,

*p*< 0.0004.

*F*(4,92) = 0.4, MSE = 0.0359,

*p*> 0.8, but modulated RT in this task,

*F*(4,92) = 8.5, MSE = 7295,

*p*< 0.0001. As shown in Figure 4a, RT generally decreased as set size increased. The regression analysis relating the number of stimuli and RT revealed an average slope of −14.9 ms/item, which was significantly different from zero,

*t*(23) = −3.96,

*p*< 0.001, replicating the findings of Experiment 1.

*F*(4,92) = 97.4, MSE = 43,441.24,

*p*< 0.0001, and lead to a search slope of 132 ms/item, which is significantly different from zero,

*t*(23) = 10.91,

*p*< 0.0001. Accuracy was also modulated by set size,

*F*(4,92) = 29.3, MSE = 0.00252,

*p*< 0.0001. The regression analysis relating the number of stimuli and the accuracy level revealed an average slope of −1.7%/item; this was significantly different from a slope of zero,

*t*(23) = −10.84,

*p*< 0.0001. As expected, this task showed the steep search slope that is typically associated with serial processing of the stimuli (Treisman & Gelade, 1980). The long time required to perform the search task is in accordance with the difficulty observers experience when identifying individual members of a set (Ariely, 2001; Haberman & Whitney, 2007, 2009a) and stands in marked contrast to the rapid estimation of the mean of the set. The results of this experiment clearly show that stimuli that require slow serial search for individual identification are processed rapidly and with the hallmarks of a parallel mechanism when forming a summary statistical representation.