The nature of correlation perception in
scatterplots
Ronald A. Rensink
University of British Columbia
Psychonomic
Bulletin & Review, 24: 776-797. [pdf] [web]
For
scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two
simple laws: a linear one for discrimination, and a logarithmic one for
perceived magnitude (Rensink & Baldridge, 2010).
The underlying perceptual mechanisms, however, remain poorly understood. To
cast light on these, four different distributions of datapoints
were examined. The first had 100 points with equal variance in both dimensions.
Consistent with earlier results, just noticeable difference (JND) was a linear
function of the distance away from r = 1, and the magnitude of perceived
correlation a logarithmic function of this quantity. In addition, these laws
were linked, with the intercept of the JND line being the inverse of the bias
in perceived magnitude. Three other conditions were also examined: a dot cloud
with 25 points, a horizontal compression of the cloud, and a cloud with a
uniform distribution of dots. Performance was found to be similar in all
conditions. The generality and form of these laws suggest that what underlies
correlation perception is not a geometric structure such as the shape of the
dot cloud, but the shape of the probability distribution of the dots, likely
inferred via a form of ensemble coding. It is suggested that this reflects the
ability of observers to perceive the information entropy in an image, with this
quantity used as a proxy for Pearson correlation.