Correlations are estimated with bias in a 2-class scatterplot

The current study examined in a multi-class scatterplot, containing multiple bivariate datasets represented by colors, whether humans can visually separate datasets based on color differences and accurately estimate the correlation of each dataset. Previous studies investigating the discrimination threshold for correlations have reported an increase in JND with scatterplots having two overlapping colors, (Elliott & Rensink, 2015 VSS; Elliott, 2021). These studies predict that magnitude of correlations might also be estimated differently in 1-class and 2-class scatterplots. The current study investigated observers’ efficiency in filtering out the irrelevant subset in estimation of target correlation in 2-class scatterplots by psychophysical experiments. In each trial, two scatterplots, one 2-class and one 1-class, were presented. Observers compared a correlation of 1-class scatterplot (Comparison) with a correlation of one sub-dataset (Target) in a 2-class scatterplot with the same color as the 1-class, and judged the stronger correlation. The correlation coefficient of Target was constant (r = 0.6), and that of the other sub-dataset (Distractor) in a 2-class was set to 4 levels (r = 0.0, 0.3, 0.6, 0.9). Using psychometric functions, we estimated the point of subjective equality (PSE) for the Target’s correlation strength. The result showed that PSE for the correlation strength of Target was biased toward that of Distractor, suggesting that it is difficult to filter out irrelevant data points in a 2-class scatterplot. Furthermore, we investigated the robustness of the bias. Manipulation of the stimulus duration (short or unlimited), and of the color and luminance difference between two datasets did not modulate the magnitude of biases at all, suggesting that the estimation of the correlation is biased robustly in a 2-class scatterplot.