Variability leads to overestimation of mean summaries

Effects of outlier and familiar context in trend-line estimates in scatterplots

Lately, there has been a growing fascination with blending research on visualizing data and understanding how our basic visual perception works. Taking this path, this research delved into the connection between ensemble perception, which involves quickly and accurately grasping essential information from sets of visually similar objects, and how we process scatterplots. Across two experiments, we aimed to answer a couple of connected questions. First, we investigated whether having an outlier in a scatterplot affects how people draw trend-line estimates. Second, we explored whether what we are familiar with and the presence of outliers that match the trend affect how we draw trend-line estimates in scatterplots. In both experiments, we showed participants scatterplots for a short time, manipulating whether there were outliers or not. Then, using a computer mouse, participants drew their trend-line estimates. By comparing what they drew with possible trend-line solutions, we discovered that when there is no context, the outlier and the other points in a scatterplot are seen as equally important in drawing the trend-line estimate. But when the scatterplot depicted a familiar context and the outlier fitted the trend, people tended to give more weight to those outlier points in their drawings. This suggested that what we already believe can sway how we draw trend-line estimates even from quickly shown scatterplots.

Ensemble Coding of Crowd with Cross-Category Facial Expressions

Ensemble coding allows observers to form an average to represent a set of elements. However, it is unclear whether observers can extract an average from a cross-category set. Previous investigations on this issue using low-level stimuli yielded contradictory results. The current study addressed this issue by presenting high-level stimuli (i.e., a crowd of facial expressions) simultaneously (Experiment 1) or sequentially (Experiment 2), and asked participants to complete a member judgment task. The results showed that participants could extract average information from a group of cross-category facial expressions with a short perceptual distance. These findings demonstrate cross-category ensemble coding of high-level stimuli, contributing to the understanding of ensemble coding and providing inspiration for future research.

Perception of visual variance is mediated by subcortical mechanisms

Variance characterizes the structure of the environment. This statistical concept plays a critical role in evaluating the reliability of evidence for human decision-making. The present study examined the involvement of subcortical structures in the processing of visual variance. To this end, we used a stereoscope to sequentially present two circle arrays in a dichoptic or monocular fashion while participants compared the perceived variance of the two arrays. In Experiment 1, two arrays were presented monocularly to the same eye, dichopticly to different eyes, or binocularly to both eyes. The variance judgment was less accurate in different-eye condition than the other conditions. In Experiment 2, the first circle array was split into a large-variance and a small-variance set, with either the large-variance or small-variance set preceding the presentation of the second circle array in the same eye. The variance of the first array was judged larger when the second array was preceded by the large-variance set in the same eye, showing that the perception of variance was modulated by the visual variance processed in the same eye. Taken together, these findings provide evidence for monocular processing of visual variance, suggesting that subcortical structures capture the statistical structure of the visual world.

Nonadditive integration of visual information in ensemble processing

Statistically summarizing information from a stimulus array into an ensemble representation (e.g., the mean) improves the efficiency of visual processing. However, little is known about how the brain computes the ensemble statistics. Here, we propose that ensemble processing is realized by nonadditive integration, rather than linear averaging, of individual items. We used a linear regression model approach to extract EEG responses to three levels of information: the individual items, their local interactions, and their global interaction. The local and global interactions, representing nonadditive integration of individual items, elicited rapid and independent neural responses. Critically, only the neural representation of the global interaction predicted the precision of the ensemble perception at the behavioral level. Furthermore, spreading attention over the global pattern to enhance ensemble processing directly promoted rapid neural representation of the global interaction. Taken together, these findings advocate a global, nonadditive mechanism of ensemble processing in the brain.

Subcortical encoding of summary statistics in humans

Statistical encoding compresses redundant information from multiple items into a single summary metric (e.g., mean). Such statistical representation has been suggested to be automatic, but at which stage it is extracted is unknown. Here, we examined the involvement of the subcortex in the processing of summary statistics. We presented an array of circles dichoptically or monocularly while matching the number of perceived circles after binocular fusion. Experiments 1 and 2 showed that interocularly suppressed, invisible circles were automatically involved in the summary statistical representation, but only when they were presented to the same eye as the visible circles. This same-eye effect was further observed for consciously processed circles in Experiment 3, in which the estimated mean size of the circles was biased toward the information transmitted by monocular channels. Together, we provide converging evidence that the processing of summary statistics, an assumed high-level cognitive process, is mediated by subcortical structures.

Perceptual history biases in serial ensemble representation

Ensemble perception refers to the visual system's ability to efficiently represent groups of similar objects as a unified percept using their summary statistical information. Most studies focused on extraction of current trial averages, giving little attention to prior experience effects, although a few recent studies found that ensemble mean estimations contract toward previously presented stimuli, with most of these focusing on explicit perceptual averaging of simultaneously presented item ensembles. Yet, the time element is crucial in real dynamic environments, where we encounter ensemble items over time, aggregating information until reaching summary representations. Moreover, statistical information of objects and scenes is learned over time and often implicitly and then used for predictions that shape perception, promoting environmental stability. Therefore, we now focus on temporal aspects of ensemble statistics and test whether prior information, beyond the current trial, biases implicit perceptual decisions. We designed methods to separate current trial biases from those of previously seen trial ensembles. In each trial, six circles of different sizes were presented serially, followed by two test items. Participants were asked to choose which was present in the sequence. Participants unconsciously rely on ensemble statistics, choosing stimuli closer to the ensemble mean. To isolate the influence of earlier trials, the two test items were sometimes equidistant from the current trial mean. Results showed membership judgment biases toward current trial mean, when informative (largest effect). On equidistant trials, judgments were biased toward previously experienced stimulus statistics. Comparison of similar conditions with a shifted stimulus distribution ruled out a bias toward an earlier, presession, prototypical diameter. We conclude that ensemble perception, even for temporally experienced ensembles, is influenced not only by current trial mean but also by means of recently seen ensembles and that these influences are somewhat correlated on a participant-by-participant basis.

Variability of dot spread is overestimated

Previous research has demonstrated that individuals exhibit a tendency to overestimate the variability of both low-level features (e.g., color, orientation) and mid-level features (e.g., size) when items are presented dynamically in a sequential order, a finding we will refer to as the variability overestimation effect. Because previous research on this bias used sequential displays, an open question is whether the effect is due to a memory-related bias or a vision-related bias. To assess whether the bias would also be apparent with static, simultaneous displays, and to examine whether the bias generalizes to spatial properties, we tested participants' perception of the variability of a cluster of dots. Results showed a consistent overestimation bias: Participants judged the dots as being more spread than they actually were. The variability overestimation effect was observed when there were 10 or 20 dots but not when there were 50 dots. Taken together, the results of the current study contribute to the ensemble perception literature by providing evidence that simultaneously presented stimuli are also susceptible to the variability overestimation effect. The use of static displays further demonstrates that this bias is present in both dynamic and static contexts, suggesting an inherent bias existent in the human visual system. A potential theoretical account-boundary effect-is discussed as a potential underlying mechanism. Moreover, the present study has implications for common visual tasks carried out in real-world scenarios, such as a radiologist making judgments about distribution of calcification in breast cancer diagnoses.

Ensemble size perception: Its neural signature and the role of global interaction over individual items

To efficiently process complex visual scenes, the visual system often summarizes statistical information across individual items and represents them as an ensemble. However, due to the lack of techniques to disentangle the representation of the ensemble from that of the individual items constituting the ensemble, whether there exists a specialized neural mechanism for ensemble processing and how ensemble perception is computed in the brain remain unknown. To address these issues, we used a frequency-tagging EEG approach to track brain responses to periodically updated ensemble sizes. Neural responses tracking the ensemble size were detected in parieto-occipital electrodes, revealing a global and specialized neural mechanism of ensemble size perception. We then used the temporal response function to isolate neural responses to the individual sizes and their interactions. Notably, while the individual sizes and their local and global interactions were encoded in the EEG signals, only the global interaction contributed directly to the ensemble size perception. Finally, distributed attention to the global stimulus pattern enhanced the neural signature of the ensemble size, mainly by modulating the neural representation of the global interaction between all individual sizes. These findings advocate a specialized, global neural mechanism of ensemble size perception and suggest that global interaction between individual items contributes to ensemble perception.