Numbers are associated with space, but it is unclear how flexible these associations are. In this planned study, we will investigate whether the SNARC effect (Spatial-Numerical Association of Response Codes; Dehaene et al., 1993), which describes faster responses to small/large number magnitude with the left/right hand, respectively, is fully flexible (and depends only on relative magnitude within a stimulus set), or not (and depends on absolute magnitude as well). Evidence for relative-magnitude dependency comes from studies observing that numbers 4 and 5 were associated with the right when presented in a 0 – 5 range but with the left in a 4 – 9 range (Dehaene et al., 1993; Fias et al., 1996). However, this important conclusion was drawn solely from the absence of evidence for absolute-magnitude dependency in frequentist analysis in underpowered studies. A closer inspection of those descriptive data suggests absolute magnitude might also matter.

Hence, we conducted a close replication of Dehaene et al.’s (1993) Experiment 3 and a conceptual replication considering recent advances in SNARC research, investigating absolute- and relative-magnitude dependency by comparing intercepts and SNARC slopes across ranges with Bayesian statistics. We ran each experiment online with sequential recruitment and Bayesian analyses using an optional stopping criterion (i.e., moderate Bayesian evidence of BF < 1/3 or BF > 3). We hypothesized that both absolute and relative magnitude influence spatial-numerical associations.

Results

Both experiments were run and analyzed exactly as planned in the Stage-1 Registered Report that received in-principle acceptance by PCI. The final sample sized after sequential recruitment and Bayesian analyses were 200 (after exclusions: 173) in the direct and 300 (after exclusions: 255) participants in the conceptual replication online experiments. The observation from the two original studies was corroborated by both the direct replication using the original stimulus sets (0 – 5 vs. 4 – 9) and the conceptual replication using conceptually improved stimulus sets (1 – 5 excluding 3 vs. 4 – 8 excluding 6), pointing towards relative-magnitude dependency. However, the smallest-number spatialization and the SNARC effect’s strength differed between ranges in the conceptual replication (although being similar in the direct replication), pointing towards absolute-magnitude dependency. This discrepancy between the two experiments seems to be due to confounds in the suboptimal stimulus set from the original studies by Dehaene et al. (1993) and Fias et al. (1996). Hence, as hypothesized, both absolute and relative magnitude seem to influence spatial-numerical associations, suggesting the SNARC effect operates on fixed and flexible number representations simultaneously.

PCI Registered Report and materials

SNARC Flexibility: Range (In)Dependency

References

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396. https://doi.org/10.1037/0096-3445.122.3.371

Fias, W., Brysbaert, M., Geypens, F., & D'Ydewalle, G. (1996). The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Mathematical Cognition, 2(1), 95–110. https://doi.org/10.1080/135467996387552