Numerical values modulate size perception

Abstract

The link between various codes of magnitude and their interactions has been studied extensively for many years. In the current study, we examined how the physical and numerical magnitudes of digits are mapped into a combined mental representation. In two psychophysical experiments, participants reported the physically larger digit among two digits. In the identical condition, participants compared digits of an identical value (e.g., "2" and "2"); in the different condition, participants compared digits of distinct numerical values (i.e., "2" and "5"). As anticipated, participants overestimated the physical size of a numerically larger digit and underestimated the physical size of a numerically smaller digit. Our results extend the shared-representation account of physical and numerical magnitudes.

Keywords: Magnitude interaction; Mental representations; Numerical processing; Point of subjective equality; Size-congruity effect (SiCE).

Fig. 1

Psychophysical functions of our experimental conditions pooled across participants. The legend denotes the condition. The left digit in legend labels denotes the reference digit in each condition (e.g., “5” was the reference digit in the different condition in Experiment 1). The X-axis denotes the size of the reference digit in visual angles. The Y-axis denotes the probability to respond “larger” to the reference digit. Vertical lines denote the point of subjective equality (PSE) values of each condition. See the Appendix for the raw (unmodeled) subject mean for each condition overlayed on the model curves

Fig. 2

Point of subjective equality (PSE) (Panel A) and just noticeable difference (JND) (Panel B) means of our experimental conditions pooled across participants. The legend denotes the experiment. The X-axis denotes the condition and the pair of digits that was used. The bold digit in the first and fourth values on the X-axis denotes the standard digit in these conditions (i.e., the digit whose size was held constant). The Y-axis denotes mean PSE values (Panel A) and mean JND values (Panel B) in visual angles. Error bars denote 95% CIs. The gray points denote individual values of participants. The horizontal black solid line in Panel A denotes the size of the standard digit

Fig. 3

Estimated probabilities of size of reference stimulus by condition. Note. The figure presents the estimated probabilities of each size of reference stimulus by condition. The legend denotes the condition. The left digit in the legend labels denotes the reference digit in each condition (e.g., “5” was the reference digit in the different condition in Experiment 1). The X-axis denotes the size of the reference digit in visual angles. The Y-axis denotes the probability to respond “larger” to the reference digit. White data points correspond to the 10 sizes used in the experiments, denoting estimated mean probabilities to respond “larger”. Error bars denote standard errors of estimated mean probabilities (SE)