The psychophysics of informal covariation assessment: perceiving relatedness against a background of dispersion

The goal of 2 studies was to develop a psychophysical model of informal covariation assessment. The results of Experiment 1 suggest that mean covariation estimates are a function of the ratio of the lengths of the major and minor principal-components axes of correlated bivariate data. In Experiment 2, multidimensional scaling showed that observers perceived (a) the lengths of the major and minor principal-components axes and (b) the slope and dispersion of correlated data. The focal stimulus for mean covariation estimates was the ratio of the major and minor principal-components axes. Moreover, dispersion constituted a background context that lowered estimates somewhat. These results suggested a model of covariation assessment in which mean estimates were mapped onto a product of power transformations of the axis ratio and dispersion of correlated data. This model accounted for 96% of the variability in mean covariation estimates.