One and only SNARC? Spatial-Numerical Associations are not fully flexible and depend on both relative and absolute number magnitude

Numbers are associated with space, but it is unclear how flexible these associations are. We investigated whether the SNARC effect (Spatial-Numerical Association of Response Codes; Dehaene <i>et al</i>. 1993 <i>J. Exp. Psychol</i>. <b>122</b>, 371-396. (doi:10.1037/0096-3445.122.3.371); i.e. faster responses to small/large number magnitude with the left/right hand, respectively) is fully flexible (depending only on relative magnitude within a stimulus set) or not (depending on absolute magnitude as well). Evidence for relative-magnitude dependency came from studies observing that numbers 4 and 5 were associated with the right in a 0-5 range but with the left in a 4-9 range (Dehaene <i>et al</i>. 1993; Fias <i>et al</i>. 1996 <i>Math. Cogn</i>. <b>2</b>, 95-110 (doi:10.1080/135467996387552). Within this Registered Report, we conducted two online experiments running Bayesian analyses with optional recruitment stopping at moderate evidence (BF₁₀ above 3 or below 1/3). Experiment 1 (<i>n</i> = 200) replicated relative-magnitude dependency using the original stimuli. However, Experiment 2 (<i>n</i> = 300) additionally demonstrated absolute-magnitude dependency, while considering recent advances in SNARC research using 1-5 excluding 3 and 4-8 excluding 6. In contrast to the frequently perpetuated notion of fully flexible Spatial-Numerical Associations, some fixed relation to absolute magnitude prevails. These findings have important consequences for understanding how Spatial-Numerical Associations might support numerical processing.