Bayesian modelling of the latent structure of individual differences in the numerical size-congruity effect

ABSTRACT When people choose the physically larger of two numerals, they are often slower when relative physical size is incongruent with numerical magnitude. This size-congruity effect not only informs our understanding of mental representations of number, but also serves as an index for numerical ability in individuals. In this paper, we apply methods of Haaf and Rouder (2017) to examine the size-congruity effect through the lens of individual differences. We develop and compare hierarchical Bayesian mixed models with varying levels of constraint on the individual size-congruity effects. In three data sets, the winning model was one in which the size-congruity effect was constrained to be positive. This indicates that, at least in the context of a physical comparison task with Arabic numerals, everyone exhibits a positive size-congruity effect. We discuss these results in the context of measurement fidelity and theory-building in numerical cognition.