The Perception of Correlation in Scatterplots

We present a rigorous way to evaluate the visual perception of correlation in scatterplots, based on classical psychophysical methods originally developed for simple properties such as brightness. Although scatterplots are graphically complex, the quantity they convey is relatively simple. As such, it may be possible to assess the perception of correlation in a similar way. Scatterplots were each of 5.0 degrees extent, containing 100 points with a bivariate normal distribution. Means were 0.5 of the range of the points, and standard deviations 0.2 of this range. Precision was determined via an adaptive algorithm to find 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 measured by direct estimation, using reference scatterplots with fixed upper and lower values, with a test scatterplot adjusted so that its correlation appeared to be halfway between these. This process was recursively applied to yield several further estimates. Results of the discrimination tests show jnd(r) = k (1/b - r), where r is the Pearson correlation, and parameters 0 < k, b < 1. Integration yields a subjective estimate of correlation g(r) = ln(1 - br) / ln(1 - b). The values of b found via discrimination closely match those found via direct estimation. As such, it appears that the perception of correlation in a scatterplot is completely described by two related performance curves, specified by two easily-measured parameters.