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Jessica Ip, Nicholas Chin, Ronald Rensink; Correlation perception in scatterplots is invariant to dot size. Journal of Vision 2021;21(9):2171. doi: https://doi.org/10.1167/jov.21.9.2171.
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© ARVO (1962-2015); The Authors (2016-present)
To determine the extent to which the perception of Pearson correlation r in a scatterplot depends on its appearance, we examined the effect of dot size on discrimination and magnitude estimation. Scatterplots were formed of 48 solid black dots on a white background, with axes 6.5 cm by 6.5 cm, and distribution standard deviations 1.3 cm. Observers (N=18) were tested via a within-observer design involving five conditions: dot diameters of 1 mm, 3 mm, 5 mm, 8 mm, and a mix of these sizes. Viewing distance was 67 cm. The methodology was that of Rensink and Baldridge (2010). In the discrimination task, observers were asked to select the plot with the higher perceived correlation; the just noticeable difference (JND) was measured at three base correlations (0.3, 0.6, 0.9). In the magnitude estimation task, observers adjusted a test plot until its perceived correlation was midway between those of two reference plots. The discrimination task was sandwiched between two sets of estimation tasks. All conditions were counterbalanced by base correlations and dot size, using a Latin square. The resulting JNDs were slightly higher than those reported by Rensink and Baldridge (2010) and Rensink (2017), but were still strongly linear functions of correlation (R^2=0.97); the Fechner assumption of equal perceived difference for each JND was also supported. Importantly, neither discrimination nor estimation were significantly affected by dot size. This further supports the proposal (Rensink, 2017) that perceived correlation in scatterplots is based not on the physical appearance of the scatterplot, but on a more abstract quantity, such as the shape of the probability density function derived from the locations of the dots in the image.
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