Graphical representations of quantitative data abound in our culture, and yet the brain mechanisms of graphicacy, by which viewers quickly extract statistical information from a data graphic, are unknown. Here, using scatterplots as stimuli, we tested two hypotheses about the brain areas underlying graphicacy. First, at the perceptual level, we hypothesized that the visual processing of scatterplots and their main trend recycles cortical regions devoted to the perception of the principal axis of objects. Second, at a higher level, we speculated that the math-responsive network active during arithmetic and mathematical truth judgments should also be involved in graphical perception. Using fMRI, we indeed found that the judgment of the trend in a scatterplot recruits a right lateral occipital area involved in detecting the orientation of objects, as well as a right anterior intraparietal region also recruited during mathematical tasks. Both behavior and brain activity were driven by the t value that indexes the statistical correlation in the data, and right intraparietal activation covaried with participants' graphicacy level. On the basis of this first approach to the neural bases of graphical perception, we suggest that, like literacy and numeracy, graphicacy relies on the recycling of brain areas previously attuned to a similar problem, here the perception of object orientation.

Graphical representations of data are pervasive in modern communication and are often used to convey socio-economic, scientific, and medical information. Despite their popularity, it is still unknown whether they can enhance the long-term retention of their content. We conducted a delayed-recall task with psychology undergraduates (N = 92), in which participants read about the evolution of a socio-economic phenomenon, with five to six datapoints presented as graphics, text, or table; recall was operationalized as correct reporting of the trend in the data, 2 h after the information was presented. We found that graphics facilitated the delayed recall of such trends. No advantage was found on immediate recall of trends or specific datapoints in another sample of participants (N = 80). Thus, even for equal initial encoding of data, and even for very concise materials, graphics facilitate long-term retention. Overall, the study reveals the potential of graphics as effective tools for enhancing memory retention and therefore highlights their valuable role in educational settings.

In a visual intruder task, regular quadrilaterals such as squares and rectangles are easier to process than matched shapes devoid of parallelism, symmetry or right-angles. This geometric regularity effect was found in various human groups, including preschoolers and uneducated adults, but not in non-human primates. It was proposed to reflect a fundamental ability to combine discrete geometric features into structured representations of geometric shapes using an abstract amodal language-of-thought (LoT) that also supports the acquisition of symbolic drawing and formal mathematics. Here, we tested a prediction of this hypothesis: blind participants should have the same intuitions of geometric regularity as sighted ones. To evaluate this prediction, congenitally blind and sighted (but blindfolded) adults underwent a tactile version of the visual quadrilateral intruder task. Among six tactile shapes, five of which were identical up to small size and rotation changes, participants were asked to identify a deviant shape defined by a fixed displacement of a single vertex, and to rate their confidence in their response. Both variables revealed a geometric regularity effect in both groups, and also correlated with previous results in the visual domain. Furthermore, a symbolic LoT model was a better predictor of tactile performance than a visual CNN model in blind participants. Thus, the geometric regularity effect develops in the absence of vision.

Recent studies showed that humans, regardless of age, education, and culture, can extract the linear trend of a noisy scatterplot. Although this capacity looks sophisticated, it may simply reflect the extraction of the principal trend of the graph, as if the cloud of dots was processed as an oriented object. To test this idea, we trained Guinea baboons to associate arbitrary shapes with the increasing or decreasing trends of noiseless and noisy scatterplots, while varying the number of points, the noise level, and the regression slope. Many baboons successfully learned this conditional match-to-sample task, and their accuracy varied as a sigmoid function of the t-value of the regression, the same statistical index upon which humans also base their answers. The perceptual component of human graphics abilities seems thus to be based on the recycling of a phylogenetically older competence of the primate visual system for extracting the principal axes of visual displays.

Previous research showed that people enumerate objects faster and more accurately when they form clusters, a phenomenon called "groupitizing". While mainly studied visually, its dependence on vision is unclear. Congenitally blind (CB) individuals provide a critical test: if vision is essential, CB people should lack groupitizing; if not, they may apply it across modalities, potentially outperforming sighted participants. We compared CB and sighted adults on an auditory groupitizing task, based on the estimation of 5-12 pure tones presented either randomly or grouped by temporal proximity. Both groups showed lower errors and higher precision for grouped sequences, confirming that groupitizing can emerge without visual experience. Importantly, for larger numerosities, sighted individuals' grouping benefit decreased, whereas CB participants maintained robust advantages across all set sizes. These findings suggest that groupitizing relies on amodal perceptual mechanisms and that congenital blindness may enhance auditory enumeration strategies.

How sophisticated is young children’s comprehension of geometric lines and curves, and how can we probe it? Here, we assess an early, proto-mathematical understanding of curves by asking preschoolers (N=39) and first graders (N=42) to draw the prolongation of various mathematical patterns, ranging from linear to non-linear functions such as quadratics and exponentials, periodic functions, and more complex composite patterns. Our findings reveal that even at this early age, children’s drawings indicate an accurate differentiation of several functions, including linear and non-linear ones, and an understanding of linearity and curvature. Furthermore, both age groups displayed intuitions of compositionality by distinguishing, for example, sinusoid functions with an increasing amplitude from those with a decreasing or a constant one. All children had difficulties with more complex patterns, such as those involving changes in both amplitude and frequency, as in stair-like patterns. Our results highlight children’s early understanding of proto-mathematical concepts and the potential of drawing as a powerful tool to assess them in a concrete context.

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.

Recent studies showed that humans, regardless of age, education, and culture, can extract the linear trend of a noisy graph. Here, we examined whether such skills for intuitive statistics are confined to humans or may also exist in non-human primates. We trained Guinea baboons ( Papio papio ) to associate arbitrary geometrical shapes with the increasing or decreasing trends of noiseless and noisy scatterplots, while varying the number of points, the noise level, and the regression slope. Many baboons successfully learned this conditional match-to-sample task for both noiseless and noisy plots. Crucially, for successful baboons, accuracy varied as a sigmoid function of the t-value of the regression, the same statistical index upon which humans also base their answers, even after controlling for other variables. These results are compatible with the hypothesis that the human perception of data graphics is based on the pre-emption and recycling of a phylogenetically older competence of the primate visual system for extracting the principal axes of visual displays. ### Competing Interest Statement The authors have declared no competing interest.

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.

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.

ABSTRACT 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, thus became a fundamental cultural skill. Here, we introduce a new measure of graphicacy that assesses the 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 graphicacy even in unschooled participants living in remote Namibian villages (N=87) and 6-year-old 1 st -graders who never read a graph (N=27). However, the sigmoid slope (the “graphicacy index”) varies across participants, increases with education, and tightly correlates with statistical knowledge, showing that experience contributes to refining graphical intuitions. Our tool is publicly available online and allows to quickly evaluate intuitive graphics skills. STATEMENT OF RELEVANCE The rising cost of gas, the number of Covid deaths, the evolution of temperatures during the summer months: we often face graphs depicting these phenomena. The scientific literature has shown that human adults can intuit, within milliseconds, the statistical trend of these graphs. However, we do not know if these intuitions generalized to unschooled people and, most importantly, how to measure their variations in the population. In this study we show that intuitive graphics skills are present even in 6-year-old children who never saw a graph and in the Himba of Namibia, an indigenous people with no access to formal schooling. Furthermore, we developed a quantitative assessment of such intuitive graphics skills (which we called the “graphicacy index”), that everyone can easily obtain for free, through a short (10 minutes) online test: https://neurospin-data.cea.fr/exp/lorenzo-ciccione/graphicacy-index/ . In summary, our study provides the first attempt to formally quantify human intuitions of statistical graphs.

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 non-trivial 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, according to which humans detect outliers by computing a z-score that estimates how far a given datapoint is from the distribution of distances to the regression line. Detection is not rejection, however, and our results suggest that humans can remain biased by outliers that they have detected.

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.

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 3x3). 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 implicitly involves mental arithmetic.