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

Abstract

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.

Analyzing the misperception of exponential growth in graphs.

“…Second, we analyzed the effect of noise in the dataset. Previous studies of linear scatterplots (Ciccione & Dehaene, 2021) showed that, with increasing levels of noise, participants' extrapolations depart more from the statistical ideal. In the case of exponentials, it is not known whether the underestimation bias is already present for noiseless functions or if it only arises when extracting an exponential trend from noise.…”

“…Using a terminology borrowed from machine learning literature (Geman et al, 1992), participants could be inaccurate in two ways: bias versus variance (Ciccione & Dehaene, 2021). Bias refers to the average error: a positive bias means that participants overestimate their extrapolation, whereas a negative bias means that they underestimate it.…”

“…Scatterplots are widely used to visually convey the evolution of a measure such as global temperature, salary, or mortality over time (Friendly & Denis, 2005). They allow humans to efficiently grasp a functional relationship at a glance, without serially processing the data in numerical form, and to predict values beyond the available range (Ciccione & Dehaene, 2021).…”

“…Psychophysical research indicates that human adults can extract the trend underlying a graph and that their extrapolation abilities partially extend to noisy representations of linear and non-linear functions (Ciccione & Dehaene, 2021;Schulz et al, 2017).…”

“…Third, we measured the costs and benefits of plotting the data on a log scale. When the y axis is logarithmic, exponential growth looks linear, and such linear trends can be perceived without much bias (Ciccione & Dehaene, 2021). Thus, we hypothesized that the advantage of extrapolating from a visually linear trend could eliminate the exponential growth bias altogether.…”