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

Abstract

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.

Undergraduate Stem and Non-Stem Students’ Interpretation of Mean in an Infographic

“…The lack of a deep understanding of the mean is a pervasive problem. Previous studies have shown that undergraduates are prone to mistakes when interpreting the mean given in a visual form through histograms, stem-and-leaf plots, and bar graphs (Cooper & Shore, 2008;Cui & Liu, 2021;Watson & Moritz, 2000). Similar to Kaplar (2022), superficiality and reasoning based on personal beliefs rather than analyzing the presented data were observed in this study as well.…”

“…A well-designed course can have positive effects on overcoming misconceptions (DelMas et al, 2007;Gauvrit & Morsanyi, 2014;Gigerenzer et al, 2007;Masel et al, 2015). The use of real-life data, context, and examples as well as simulations and animations help students to overcome misunderstandings of basic statistical concepts (Cui & Liu, 2021;Jamie, 2002;Kaplar, 2022;Neumann et al, 2011;Wang et al, 2011). The infographics engaged students well, so they have a strong educational potential and should be included in statistics courses.…”

Graphicacy across age, education, and culture: a new tool to assess intuitive graphics skills

“…This finding suggests that participants treated the scatterplots as an ensemble, without serially processing each item: in fact, if that was the case, we should have observed an increment in response times proportional to the number of points in the dataset. Fast intuitive statistical judgments on graphs with Gaussian noise thus seem to operate similarly to ensemble perception, the human ability to rapidly extract the “average” of visually displayed items, without focusing on each particular element in the set (Cui & Liu, 2021; Whitney & Yamanashi Leib, 2018; but see, in the presence of outliers in the graph: Ciccione et al, 2022).…”

Outlier detection and rejection in scatterplots: Do outliers influence intuitive statistical judgments?

“…In the case of scatterplots, the average item location is useless when assessing a trend, which arises from the relations between data points. Future research should try to disentangle the commonalities and differences between graph and ensemble perception (for a review: Cui & Liu, 2021). At the very least, our studies prove that the two processes are not fully overlapping.…”