True or false: The effect of numerical magnitude on sense of agency

• Sense of agency (SoA) refers to the feeling that one’s own actions influence the external world. • We examined how the numerical magnitude of action outcomes influences the SoA through six experiments. • Numerical magnitude increased SoA ratings, but this was mainly due to response bias. Sense of agency (SoA) refers to the feeling that one’s actions cause environmental changes. A previous study showed that SoA is enhanced when keypress-triggered motion stimuli move faster, suggesting that SoA depends on the extent of action outcomes. We examined whether the numerical magnitude of action outcomes similarly affects SoA. Participants pressed a key, which triggered the presentation of dots (Experiments 1–2) or digit values (Experiment 3), and then rated their SoA on a 10-point scale. Results showed that SoA ratings increased with greater numerical magnitude. However, Experiments 4a and 4b, using an intentional binding paradigm, found that the interval between the keypress and dot onset was perceived as longer when more dots were presented. This contradicts Experiments 1–3 and suggests the observed SoA enhancement might stem from response bias (e.g., higher numerical magnitude of the outcomes leading to higher values in the rating/estimating phase). To test this, Experiments 5a and 5b replicated Experiment 2 with a reversed rating scale (1 = strongest, 10 = weakest) and support the response bias account. In contrast, the effect of motion speed was unaffected by rating direction, suggesting a genuine influence on SoA (Experiment 6). These findings highlight the importance of carefully distinguishing true effects from mere response biases when evaluating how outcome magnitude influences SoA.