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 will conduct 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. To achieve a power of .90 for detecting moderate evidence (Bayes Factor above 3 or below 1/3) for Cohen’s d = 0.15, we will conduct each experiment online with maximum 800 participants, but run sequential analyses with optional stopping at moderate evidence. We hypothesize that both absolute and relative magnitude influence spatial-numerical associations, suggesting the SNARC effect operates on flexible and absolute number representations simultaneously.

Our results are yet to come!

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