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.

KEYWORDS:

• Size-congruity effect
• individual differences
• hierarchical Bayesian model
• Bayes factors

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are openly available for download from Github. Datasets 1 and 3 can be downloaded from https://github.com/tomfaulkenberry/physNumComparisonTask, and Dataset 2 can be downloaded from https://github.com/Kbow27/Thesis.

Notes

1 Throughout the manuscript, we are assuming a population of people who are familiar with Arabic numerals and thus have a semantic association with the underlying quantities that they represent.

2 We thank Julia Haaf for suggesting this argument.

Additional information

Funding

This work was supported by a Faculty-Student Research Grant from Tarleton State University awarded to TJF.