The distance effect is the change in the performance during numerical magnitude comparison, depending on the numerical distance between the compared numbers (Moyer & Landauer, Nature, 215[5109], 1519-1520, 1967). This effect is generally accepted as evidence for the mental number line (MNL) hypothesis, which proposes that the mental representation of the numbers align in an increasing linear (or monotone) order. The majority of studies investigating the distance effect are focused on the reaction time (RT) findings, which show slower responses for closer numbers. In the present study, we examined the distance effect by applying signal detection theory (SDT) to a magnitude comparison task. We aimed to reveal whether discrimination ability and the response bias measures were affected by the location of numbers on the MNL. To accomplish this, we developed a magnitude comparison task using a go/no-go procedure in which participants performed a magnitude comparison based on a reference number (i.e., 5). Results revealed a substantial distance effect in both sensitivity and response bias measures-a better discrimination performance for far numbers, and a larger response bias for close numbers. In addition, an RT distribution analysis revealed that the distance effect seems to originate mainly from slower responses. Based on the current data, we suggest that sensitivity and response bias measures could offer comprehensive information in the understanding of number-based decisions.
Keywords: Distance effect; Go/no-go task; Magnitude comparison; Mental number line; Signal detection theory.