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Ronald Rensink, Gideon Baldridge; The Visual Perception of Correlation in Scatterplots. Journal of Vision 2010;10(7):975. doi: 10.1167/10.7.975.
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© 2016 Association for Research in Vision and Ophthalmology.
A set of experiments investigated the precision and accuracy of the visual perception of correlation in scatterplots. These used classical psychophysical methods applied directly to these relatively complex stimuli. Scatterplots (of extent 5.0 deg) each contained 100 normally-distributed values. Means were set to 0.5 of the range of the scatterplot, and standard deviations to 0.2 of this range. 20 observers were tested. Precision was determined via an adaptive algorithm that found the just noticeable differences (jnds) in correlation, i.e., the difference between two side-by-side scatterplots that could be discriminated 75% of the time. Accuracy was determined by direct estimation: reference scatterplots were created with fixed upper and lower values, and a test scatterplot adjusted so that its correlation appeared to be midway between these two. This process was then recursively applied to yield several further estimates. Results show that jnd(r) = k (1/b − r), where r is the Pearson correlation, and k and b are parameters such that 0 <k, b <1; typical values are k = 0.2 and b = 0.9. Integration yields the subjective estimate of correlation g(r) = ln (1 − br) / ln (1 − b); this closely matches the results of the direct estimation method. As such, the perception of correlation in a scatterplot is completely specified by just two easily-measured parameters.
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