Ensemble statistics accessed through proxies: Range heuristic and dependence on low-level properties in variability discrimination

Decoding time-resolved neural representations of orientation ensemble perception

The visual system can compute summary statistics of several visual elements at a glance. Numerous studies have shown that an ensemble of different visual features can be perceived over 50-200 ms; however, the time point at which the visual system forms an accurate ensemble representation associated with an individual's perception remains unclear. This is mainly because most previous studies have not fully addressed time-resolved neural representations that occur during ensemble perception, particularly lacking quantification of the representational strength of ensembles and their correlation with behavior. Here, we conducted orientation ensemble discrimination tasks and electroencephalogram (EEG) recordings to decode orientation representations over time while human observers discriminated an average of multiple orientations. We modeled EEG signals as a linear sum of hypothetical orientation channel responses and inverted this model to quantify the representational strength of orientation ensemble. Our analysis using this inverted encoding model revealed stronger representations of the average orientation over 400-700 ms. We also correlated the orientation representation estimated from EEG signals with the perceived average orientation reported in the ensemble discrimination task with adjustment methods. We found that the estimated orientation at approximately 600-700 ms significantly correlated with the individual differences in perceived average orientation. These results suggest that although ensembles can be quickly and roughly computed, the visual system may gradually compute an orientation ensemble over several hundred milliseconds to achieve a more accurate ensemble representation.

How do students reason about statistical sampling with computer simulations? An integrative review from a grounded cognition perspective

Interactive computer simulations are commonly used as pedagogical tools to support students' statistical reasoning. This paper examines whether and how these simulations enable their intended effects. We begin by contrasting two theoretical frameworks-dual processes and grounded cognition-in the context of people's conceptions about statistical sampling, setting the stage for the potential benefits of simulations in learning such conceptions. Then, we continue with reviewing the educational literature on statistical sampling simulations. Our review tentatively suggests benefits of the simulations for building statistical habits of mind. However, challenges seem to persist when more specific concepts and skills are investigated. With and without simulations, students have difficulty forming an aggregate view of data, interpreting sampling distributions, showing a process-based understanding of the law of large numbers, making statistical inferences, and context-independent reasoning. We propose that grounded cognition offers a framework for understanding these findings, highlighting the bidirectional relationship between perception and conception, perceptual design features, and guided perceptual routines for supporting students' meaning making from simulations. Finally, we propose testable instructional strategies for using simulations in statistics education.

The role of visual working memory in capacity-limited cross-modal ensemble coding

Ensemble coding refers to the brain's ability to rapidly extract summary statistics, such as average size and average cost, from a large set of visual stimuli. Although ensemble coding is thought to circumvent a capacity limit of visual working memory, we recently observed a VWM-like capacity limit in an ensemble task where observers extracted the average sweetness of groups of food pictures (i.e., they could only integrate information from four out of six available items), thus suggesting the involvement of VWM in this novel form of cross-modal ensemble coding. Therefore, across two experiments we investigated if this cross-modal ensemble capacity limit could be explained by individual differences in VWM processing. To test this, observers performed both an ensemble task and a VWM task, and we determined 1) how much information they integrated into their ensemble percepts, and 2) how much information they remembered from those displays. Interestingly, we found that individual differences in VWM capacity did not explain differences in performance on the ensemble coding task (i.e., high-capacity individuals did not have significantly higher "ensemble abilities" than low-capacity individuals). While our data cannot definitively state whether or not VWM is necessary to perform the ensemble task, we conclude that it is certainly not sufficient to support this cognitive process. We speculate that the capacity limit may be explained by 1) a bottleneck at the perceptual stage (i.e., a failure to process multiple visual features across multiple items, as there are no singular features that convey taste), or 2) the interaction of multiple cognitive systems (e.g., VWM, gustatory working memory, long term memory). Our results highlight the importance of examining ensemble perception across multiple sensory and cognitive domains to provide a clearer picture of the mechanisms underlying everyday behavior.

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.

Perceived variability reflects the reliability of individual items

When confronted with many visual items, people can compute their variability accurately and rapidly, which facilitates efficient information processing and optimal decision making. However, how the visual system computes variability is still unclear. To investigate this, we implemented situations whereby estimates of variability based on several possible variability measures (e.g., range, standard deviation, and weighted standard deviation) could be differentiated, and then examined which best accounted for human variability perception. In three psychophysical experiments, participants watched two arrays of items with various orientations and judged which had more variable orientations. Results showed that perceived variability was most consistent with the weighted standard deviation based on the reliability of individual items. Specifically, participants gave less consideration to deviant orientations that were likely to be outliers, and greater consideration to salient orientations that were likely to be encoded precisely. This reliability-based weighted standard deviation suggests an efficient and flexible way of representing visual variability.

Dissociating implicit and explicit ensemble representations reveals the limits of visual perception and the richness of behavior

Our senses provide us with a rich experience of a detailed visual world, yet the empirical results seem to suggest severe limitations on our ability to perceive and remember. In recent attempts to reconcile the contradiction between what is experienced and what can be reported, it has been argued that the visual world is condensed to a set of summary statistics, explaining both the rich experience and the sparse reports. Here, we show that explicit reports of summary statistics underestimate the richness of ensemble perception. Our observers searched for an odd-one-out target among heterogeneous distractors and their representation of distractor characteristics was tested explicitly or implicitly. Observers could explicitly distinguish distractor sets with different mean and variance, but not differently-shaped probability distributions. In contrast, the implicit assessment revealed that the visual system encodes the mean, the variance, and even the shape of feature distributions. Furthermore, explicit measures had common noise sources that distinguished them from implicit measures. This suggests that explicit judgments of stimulus ensembles underestimate the richness of visual representations. We conclude that feature distributions are encoded in rich detail and can guide behavior implicitly, even when the information available for explicit summary judgments is coarse and limited.

Global and local interference effects in ensemble encoding are best explained by interactions between summary representations of the mean and the range

Through ensemble encoding, the visual system compresses redundant statistical properties from multiple items into a single summary metric (e.g., average size). Numerous studies have shown that global summary information is extracted quickly, does not require access to single-item representations, and often interferes with reports of single items from the set. Yet a thorough understanding of ensemble processing would benefit from a more extensive investigation at the local level. Thus, the purpose of this study was to provide a more critical inspection of global-local processing in ensemble perception. Taking inspiration from Navon (Cognitive Psychology, 9(3), 353-383, 1977), we employed a novel paradigm that independently manipulates the degree of interference at the global (mean) or local (single item) level of the ensemble. Initial results were consistent with reciprocal interference between global and local ensemble processing. However, further testing revealed that local interference effects were better explained by interference from another summary statistic, the range of the set. Furthermore, participants were unable to disambiguate single items from the ensemble display from other items that were within the ensemble range but, critically, were not actually present in the ensemble. Thus, it appears that local item values are likely inferred based on their relationship to higher-order summary statistics such as the range and the mean. These results conflict with claims that local information is captured alongside global information in summary representations. In such studies, successful identification of set members was not compared with misidentification of items within the range, but which were nevertheless not presented within the set.

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

In the age of big data, we are constantly inventing new data visualizations to consolidate massive amounts of numerical information into smaller and more digestible visual formats. These data visualizations use various visual features to convey quantitative information, such as spatial position in scatter plots, color saturation in heat maps, and area in dot maps. These data visualizations are typically composed of ensembles, or groups of related objects, that together convey information about a data set. Ensemble perception, or one's ability to perceive summary statistics from an ensemble, such as the mean, has been used as a foundation for understanding and explaining the effectiveness of certain data visualizations. However, research in data visualization has revealed some perceptual biases and conceptual difficulties people face when trying to utilize the information in these graphs. In this tutorial review, we will provide a broad overview of research conducted in ensemble perception, discuss how principles of ensemble encoding have been applied to the research in data visualization, and showcase the barriers graphs can pose to learning statistical concepts, using histograms as a specific example. The goal of this tutorial review is to highlight possible connections between three areas of research-ensemble perception, data visualization, and statistics education-and to encourage research in the practical applications of ensemble perception in solving real-world problems in statistics education.

Task-driven and flexible mean judgment for heterogeneous luminance ensembles

Spatial averaging of luminances over a variegated region has been assumed in visual processes such as light adaptation, texture segmentation, and lightness scaling. Despite the importance of these processes, how mean brightness can be computed remains largely unknown. We investigated how accurately and precisely mean brightness can be compared for two briefly presented heterogeneous luminance arrays composed of different numbers of disks. The results demonstrated that mean brightness judgments can be made in a task-dependent and flexible fashion. Mean brightness judgments measured via the point of subjective equality (PSE) exhibited a consistent bias, suggesting that observers relied strongly on a subset of the disks (e.g., the highest- or lowest-luminance disks) in making their judgments. Moreover, the direction of the bias flexibly changed with the task requirements, even when the stimuli were completely the same. When asked to choose the brighter array, observers relied more on the highest-luminance disks. However, when asked to choose the darker array, observers relied more on the lowest-luminance disks. In contrast, when the task was the same, observers' judgments were almost immune to substantial changes in apparent contrast caused by changing the background luminance. Despite the bias in PSE, the mean brightness judgments were precise. The just-noticeable differences measured for multiple disks were similar to or even smaller than those for single disks, which suggested a benefit of averaging. These findings implicated flexible weighted averaging; that is, mean brightness can be judged efficiently by flexibly relying more on a few items that are relevant to the task.

Emotional judgments of scenes are influenced by unintentional averaging

Background

The visual system uses ensemble perception to summarize visual input across a variety of domains. This heuristic operates at multiple levels of vision, compressing information as basic as oriented lines or as complex as emotional faces. Given its pervasiveness, the ensemble unsurprisingly can influence how an individual item is perceived, and vice versa.

Methods

In the current experiments, we tested whether the perceived emotional valence of a single scene could be influenced by surrounding, simultaneously presented scenes. Observers first rated the emotional valence of a series of individual scenes. They then saw ensembles of the original images, presented in sets of four, and were cued to rate, for a second time, one of four.

Results

Results confirmed that the perceived emotional valence of the cued image was pulled toward the mean emotion of the surrounding ensemble on the majority of trials, even though the ensemble was task-irrelevant. Control experiments and analyses confirmed that the pull was driven by high-level, ensemble information.

Conclusion

We conclude that high-level ensemble information can influence how we perceive individual items in a crowd, even when working memory demands are low and the ensemble information is not directly task-relevant.

Color ensembles: Sampling and averaging spatial hue distributions

Color serves both to segment a scene into objects and background and to identify objects. Although objects and surfaces usually contain multiple colors, humans can readily extract a representative color description, for instance, that tomatoes are red and bananas yellow. The study of color discrimination and identification has a long history, yet we know little about the formation of summary representations of multicolored stimuli. Here, we characterize the human ability to integrate hue information over space for simple color stimuli varying in the amount of information, stimulus size, and spatial configuration of stimulus elements. We show that humans are efficient at integrating hue information over space beyond what has been shown before for color stimuli. Integration depends only on the amount of information in the display and not on spatial factors such as element size or spatial configuration in the range measured. Finally, we find that observers spontaneously prefer a simple averaging strategy even with skewed color distributions. These results shed light on how human observers form summary representations of color and make a link between the perception of polychromatic surfaces and the broader literature of ensemble perception.

Independent and parallel visual processing of ensemble statistics: Evidence from dual tasks

The visual system can represent multiple objects in a compressed form of ensemble summary statistics (such as object numerosity, mean, and feature variance/range). Yet the relationships between the different types of visual statistics remain relatively unclear. Here, we tested whether two summaries (mean and numerosity, or mean and range) are calculated independently from each other and in parallel. Our participants performed dual tasks requiring a report about two summaries in each trial, and single tasks requiring a report about one of the summaries. We estimated trial-by-trial correlations between the precision of reports as well as correlations across observers. Both analyses showed the absence of correlations between different types of ensemble statistics, suggesting their independence. We also found no decrement (except that related to the order of report explained by memory retrieval) in performance in dual compared to single tasks, which suggests that two statistics of one ensemble can be processed in parallel.