Summary statistics of size: fixed processing capacity for multiple ensembles but unlimited processing capacity for single ensembles

Abstract

We assessed the processing capacity of establishing statistical summary representations (SSRs) of mean size in visual displays using the simultaneous-sequential method. Four clusters of stimuli, each composed of several circles with various diameters, were presented around fixation. Observers searched for the cluster with the largest or smallest mean size. In the simultaneous condition, all four clusters were presented concurrently; in the sequential condition, the clusters appeared two at a time. We found that the processing capacity of SSRs for multiple ensembles was as extreme as a fixed-rate bottleneck process (Experiment 1). A control experiment confirmed that this was not caused by having to compare the results of multiple averaging processes (Experiment 2). In contrast to computing SSRs across ensembles, computing SSRs for a single ensemble using the same stimuli was consistent with unlimited-capacity processing (Experiment 3). Contrary to existing claims, summary representations appear to be extracted independently for items within single ensembles but not multiple ensembles. A developing understanding of capacity limitations in perceptual processing is discussed.

Figure 1.

Trial events for the (A) simultaneous, (B) sequential, and (C) repeated conditions in Experiment 1. Observers saw four clusters of differently sized circles (one target, three distractors) and reported whether the mean size of the target cluster was relatively smaller or larger than the mean of the distractor clusters. In this example, the target cluster is smaller and presented in the lower right.

Figure 2.

Mean correct responses (%) as a function of display collapsed across observers in Experiment 1. We found equal performance between the sequential and repeated conditions, and a reliable difference in the simultaneous condition. These results suggest that summary statistic representations engage fixed-capacity processes when multiple clusters require averaging. Error bars are within-subject 95% confidence intervals (Cousineau, 2005; Morey, 2008).

Figure 3.

Trial events for the (A) simultaneous, (B) sequential, and (C) repeated conditions in Experiment 2. The size of all circles in a given cluster reflected that cluster’s mean. Computing the mean for each cluster was no longer required to perform the task since the circles were of equal size. The target cluster is smaller and presented in the lower right in this example.

Figure 4.

Mean correct responses (%) as a function of display collapsed across observers in Experiment 2. Evidence consistent with unlimited capacity was obtained when the task no longer required that subjects compute the average of each cluster. Error bars are within-subject 95% confidence intervals (Cousineau, 2005; Morey, 2008).

Figure 5.

Trial events for the (A) simultaneous, (B) sequential, and (C) repeated conditions in Experiment 3. The four clusters presented in Experiment 1 were presented on an equally spaced grid to produce the perception of a single cluster with 16 items. During practice trials (not pictured), a probe circle appeared on the response screen and subjects reported whether the mean size of the single cluster was larger or smaller than the size of the probe circle. In the real experiment (pictured), presentation of the probe circle was removed because it remained the same size on every trial. In this example, the correct response is “smaller.”

Figure 6.

Mean correct responses (%) as a function of display collapsed across observers in Experiment 3. Evidence consistent with unlimited capacity was obtained when summary statistics were computed for a single cluster. Error bars are within-subject 95% confidence intervals (Cousineau, 2005; Morey, 2008).