Investigating vertical spatial-arithmetic associations

Spatial-arithmetic associations (SAA) suggest that arithmetic operations induce spatial attentional shifts.While horizontal SAA is well established, vertical SAA remains inconsistent, particularly across behavioral and eye-movement measures.This study examined vertical SAA using reaction time (RT) and eye-tracking across three pre-registered experiments.In Experiment 1 (N = 27), no vertical SAA was observed in RT or mean fixation, but exploratory cluster-based permutation analysis revealed transient upward vs. downward attentional divergence after operator presentation.Experiment 2 (N = 197, online) increased temporal sensitivity by presenting targets at four arithmetic stages; although significant main effects of target position, operation, and timing emerged, no interaction supported vertical SAA in RT.Experiment 3 (N = 27) introduced explicit spatial-motor mapping ( / responses).Again, RT showed no interaction, but fixation position differed significantly by operation: addition biased gaze upward relative to subtraction.Exploratory analysis confirmed this effect was localized to the final computation stage.Overall, results indicate that vertical SAA is weak and transient, detectable primarily via eye-movement rather than RT, and modulated by task structure and spatial-motor correspondence.These findings support the view that vertical numerical attention shifts exist but require sensitive oculomotor measures to be observed.