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Ronald Rensink; The Rapid Perception of Correlation in Scatterplots. Journal of Vision 2011;11(11):1085. doi: 10.1167/11.11.1085.
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It has been shown (Rensink & Baldridge, 2010) that the perception of Pearson correlation in scatterplots can be described by two simple laws: the just noticeable difference (jnd) follows a Weber-like law, and the subjective estimate a Fechner-like law. This suggests that correlation is (or is associated with) a perceptually simple property, even though it is conveyed by a relatively complex medium.
To investigate further, the timecourse of this process was examined. Scatterplots of extent 5.0 deg were used, each containing 100 randomly-distributed points. Means were set to 0.5 of this range, and standard deviations to 0.2. An initial scatterplot was presented for 100, 400, or 1600 ms, followed by a mask of 200 ms. A second scatterplot was then presented, and remained on until the observer responded. The observer was asked to select which scatterplot was more highly correlated. Jnds were measured for base correlations of 0.3, 0.6, and 0.9. 20 observers were tested.
Results show that jnd remained Weber-like for all timescales examined. Performance for the 400 ms and 1600 ms conditions were virtually identical. Performance for the 100 ms condition was much the same as for the other two, with only a slight decrement found, indicating that the process was largely complete by that time. This pattern held for both gaussian and uniform distributions, with nearly identical performance found for both. These results suggest that the rapid estimation of statistical properties (either directly or indirectly) can occur not only for first-order quantities (Ariely, 2001) but for second-order quantities as well.
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