The effect of the numerical value in the physical size comparison task

Abstract

In the fields of the numerical Stroop-like tasks, it has been known that the conceptual magnitude of numbers influences the size comparison process (Henik & Tzelgov, 1982

Tzelgov, Meyer, & Henik, 1992). When the physical size of a larger number is bigger than that of a smaller number, it is a congruent condition. In contrast, the physical size of a larger number is smaller than that of a smaller number, it is an incongruent condition. Two distinguished information of numbers, the numerical value and the physical size, interact during the number comparison task, which triggers the different performance of reaction time and accuracy between the congruent and the incongruent conditions. Researchers have been mainly focused on response time and accuracy to verify the size coincidence effect. Accordingly, it is still unidentified whether the effect reflects the perceptual results during the comparison process, or simply the cognitive bias in the response stage. The purpose of this paper is to identify the effect of numerical value when people compare the physical size of numbers. The main hypothesis was that a number with a bigger value looks physically larger than a number with a smaller value. We measured the perceived size of Arabic numbers depending on the conceptual magnitude by applying the Ebbinghaus paradigm which is known to enhance the size contrast induced by the conceptual meaning of the displayed stimuli. Each stimulus consisted of a central number and six surrounding numbers. Participants were asked to respond to whether or not the target number looked smaller or larger than the inducers. As Dixon (2008) suggested the Generalized Linear Mixed Model to the repeated measures design with binary responses, we test the results with the GLMM model putting a random effect on each subject variation. Furthermore, the points of subjective equality (PSE) were calculated from binary responses on the perceptual decision as being smaller or larger. The analysis showed that participants were more likely to perceive the physical size of the target number as being smaller when surrounded by numerically larger inducers, vice versa. In study 1, we tested this perceptual effect by the influence of magnitude with two sets of font size conditions. Furthermore, we found the similar pattern on both the upright and inverted number conditions by rotating the number stimuli in study 2. In study 3, the expected result was partially observed in the range of 3 to 7 of the inducers. These results indicate that the conceptual magnitude of numbers influences the perceived size of numbers during the number comparison process.