Can humans perform mental regression on a graph? Accuracy and bias in the perception of scatterplots.

Despite the widespread use of graphs, little is known about how fast and how accurately we can extract information from them. Through a series of four behavioral experiments, we characterized human performance in "mental regression", i.e. the perception of statistical trends from scatterplots. When presented with a noisy scatterplot, even as briefly as 100 ms, human adults could accurately judge if it was increasing or decreasing, fit a regression line, and extrapolate outside the original data range, for both linear and non-linear functions. Performance was highly consistent across those three tasks of trend judgment, line fitting and extrapolation. Participants' linear trend judgments took into account the slope, the noise, and the number of data points, and were tightly correlated with the t-test classically used to evaluate the significance of a linear regression. However, they overestimated the absolute value of the regression slope. This bias was inconsistent with ordinary least squares (OLS) regression, which minimizes the sum of square deviations, but consistent with the use of Deming regression, which treats the x and y axes symmetrically and minimizes the Euclidean distance to the fitting line. We speculate that this fast but biased perception of scatterplots may be based on a "neuronal recycling" of the human visual capacity to identify the medial axis of a shape.

The interplay between spatial and non-spatial grouping cues over approximate number perception.

Humans and animals share the cognitive ability to quickly extract approximate number information from sets. Main psychophysical models suggest that visual approximate numerosity relies on segmented units, which can be affected by Gestalt rules. Indeed, arrays containing spatial grouping cues, such as connectedness, closure, and even symmetry, are underestimated compared to ungrouped arrays with equal low-level features. Recent evidence suggests that non-spatial cues, such as color-similarity, also trigger numerosity underestimation. However, in natural vision, several grouping cues may coexist in the scene. Notably, conjunction of grouping cues (color and closure) reduces perceived numerosity following an additive rule. To test whether the conjunction-effect holds for other Gestalt cues, we investigated the effect of connectedness and symmetry over numerosity perception both in isolation and, critically, in conjunction with luminance similarity. Participants performed a comparison-task between a reference and a test stimulus varying in numerosity. In Experiment 1, test stimuli contained two isolated groupings (connectedness or luminance), a conjunction (connectedness and luminance), and a neutral condition (no groupings). Results show that point of subjective equality was higher in both isolated grouping conditions compared to the neutral condition. Furthermore, in the conjunction condition, the biases from isolated grouping cues added linearly, resulting in a numerosity underestimation equal to the sum of the isolated biases. In Experiment 2 we found that conjunction of symmetry and luminance followed the same additive rule. These findings strongly suggest that both spatial and non-spatial isolated cues affect numerosity perception. Crucially, we show that their conjunction effect extends to symmetry and connectedness.

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

According to a growing body of research, human adults are remarkably accurate at extracting intuitive statistics from graphs, such as finding the best-fitting regression line through a scatterplot. Here, we ask whether humans can also perform outlier rejection, a nontrivial statistical problem. In three experiments, we investigated human adults' capacity to evaluate the linear trend of a flashed scatterplot comprising 0-4 outlier datapoints. Experiment 1 showed that participants did not spontaneously reject outliers: when outliers were not mentioned, their presence biased the participants' trend judgments and regression line estimates. In Experiment 2, where participants were explicitly asked to exclude outliers, the outlier-induced bias was reduced but remained significant. In Experiment 3, where participants were asked to explicitly detect any outlier before adjusting their regression line, outlier detection was satisfactory, but the detected outliers continued to bias the regression responses, unless they were quite distant from the main regression line. We propose a simple model for outlier detection, based on the computation of a z-score that estimates how far a given datapoint is from the distribution of distances to the regression line, and we show that this model closely approximates human performance. Detection is not rejection, however, and our results suggest that humans can remain biased by outliers that they have detected. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Trend judgment as a perceptual building block of graphicacy and mathematics, across age, education, and culture.

Data plots are widely used in science, journalism and politics, since they efficiently allow to depict a large amount of information. Graphicacy, the ability to understand graphs, has thus become a fundamental cultural skill comparable to literacy or numeracy. Here, we introduce a measure of intuitive graphicacy that assesses the perceptual ability to detect a trend in noisy scatterplots ("does this graph go up or down?"). In 3943 educated participants, responses vary as a sigmoid function of the t-value that a statistician would compute to detect a significant trend. We find a minimum level of core intuitive graphicacy even in unschooled participants living in remote Namibian villages (N = 87) and 6-year-old 1st-graders who never read a graph (N = 27). The sigmoid slope that we propose as a proxy of intuitive graphicacy increases with education and tightly correlates with statistical and mathematical knowledge, showing that experience contributes to refining graphical intuitions. Our tool, publicly available online, allows to quickly evaluate and formally quantify a perceptual building block of graphicacy.

Analyzing the misperception of exponential growth in graphs.

Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.

Grouping Mechanisms in Numerosity Perception.

Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed "groupitizing," appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance, using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1-15 dots in various arrangements, for instance, 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2 + 3 + 4), or three identical groups of 3 items (affording multiplication 3 × 3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task involves mental arithmetic.