Drawn correlations consistent with underestimation of perceived correlations from scatterplots

Previous research assessing people’s sense of correlation used scatterplots as stimuli and asked participants to estimate the correlation of said scatterplots. This method has consistently shown that people tend to underestimate the correlation of a scatterplot (e.g., guessing the correlation is 0.25 when the actual correlation is 0.5). However, it is unclear whether this underestimation is perceptual or reflective of having a poor internal representation of different correlations. We investigated this question by flipping the task: instead of estimating the correlation from a scatterplot, participants drew a scatterplot based on a given correlation. They drew 20 points onto a tablet to represent the correlation coefficients: 0, 0.25, 0.5, 0.75, and 1 in counterbalanced order. We then calculated the drawn correlations based on x, y coordinates. While the drawn correlations of 0, 0.75 and 1 were quite accurate, the drawn correlations of 0.25 and 0.5 were significantly higher than the requested correlations. The drawn correlations of 0.25 and 0.5 were consistent with the estimated correlations of 0.25 and 0.5 in the literature where participants viewed scatterplots and estimated correlations. Taken together, this suggests that people’s underestimation of correlations of < 0.5 stems from not having a good sense of what correlations 0 – 0.5 look like.