Perceiving the “smallest” or “largest” multi-digit number: A novel numeric-scale end effect

Abstract

Little is known about the perception of multi-digit number magnitude, and what causes us to categorize these numbers as “small/large” or “smallest/largest.” The present study examined end effects in multi-digit numbers and whether such effects are impacted by numerical syntax. Across four experiments, participants performed three types of numerical comparisons: same-scale comparisons between an end-value and a non-end-value (e.g., 100 vs. 200), different-scale comparisons between an end-value and a non-end-value (e.g., 1,000 vs. 200), and same-scale comparisons of non-end-values (e.g., 300 vs. 200). The type of the end-value (i.e., lower/upper) and overall numerical range used in each experiment varied. The results revealed: (1) a novel syntactic end effect, characterized by a relatively small end effect for comparisons between non-end-values and end-values from an adjacent scale, and a larger, consistently sized end effect for all comparisons between non-end-values and end-values from non-adjacent scales (a gap of 2 scales), (2) no end effect for same-scale comparisons of multi-digit numbers, and (3) a replication of the lower end effect for comparisons between the lower end-value of 1 and other single digits (i.e., non-end-values). These results reveal differential processing of numbers from adjacent versus non-adjacent scales. We rule out a psychophysical explanation for our findings and instead provide a syntactical explanation which is based on the perceptual dominance of the scale component and the way it is manifested in the counting process. We conclude that numerical syntax plays a crucial role in evaluating multi-digit number magnitude.