The SNARC (Spatial-Numerical Association of Response Codes; Dehaene et al., 1993) effect denotes faster responses to small numbers with the left and to large numbers with the right. It can be investigated in setups where participants have to respond as fast and as accurately as possible numerical stimuli presented on a computer screen. Typically, their task is to make judgments on a binary feature of the number stimuli while responding with the left or with the right. For instance, the SNARC effect can be observed in magnitude classification tasks, where Arabic digits between 1 and 9 excluding 5 have to be classified as smaller or larger than 5. However, this association between number magnitude and space can also be observed when number magnitude is completely irrelevant to the task, for example in parity judgment tasks, where Arabic digits between 1 and 9 excluding 5 have to be classified as odd or even. What is even more, the SNARC effect has been found in tasks where only superficial features of numerical stimuli such as judgments on their orientation or even on superimposed shapes have to be made.

The SNARC effect has been demonstrated not only in numerous tasks, but also in numerous setups (bimanual, unimanual, bipedal, oculomotor, pointing; Fischer & Shaki, 2014, for a review). Despite a large body of research, several crucial findings on the SNARC effect, namely their (1) automaticity, (2) task (in)dependency and (3) context (in)dependency remain yet unclear or have not been replicated with sufficient statistical power so far.

The SNARC effect (in parity judgment tasks) is typically quantified with the repeated-measures regression approach proposed by Fias et al. (1996). For this, the differences in average reaction times between the two hands (dRT = RT(right) – RT(left)) are calculated for each number and for each participant separately. Subsequently, dRTs are regressed on the magnitude of the number for each participant separately, resulting in one slope per participant. The slopes are then tested against zero or against each other in different conditions in a t-test. A negative slope reflects the number of milliseconds that the right- increases over the left-hand advantage per number magnitude unit, which is the typical SNARC effect.

Aims of the e-SNARC project

(1) Despite high theoretical importance, automaticity of the SNARC effect is a controversy rather than an assumption. The SNARC effect in the parity judgment task, which can be considered as the standard paradigm to investigate it, reflects high automaticity, because number magnitude and its mental mapping onto space are irrelevant for judging whether numbers are odd or even. Nevertheless, in the parity judgment task, the number needs to be semantically processed. On the contrary, in orientation judgment tasks or in color judgment tasks, where participants have to decide whether numbers are presented upright vs. tilted or in red vs. green, the number does not need to be semantically processed. It is under debate whether processing of number magnitude and its mental mapping onto space are triggered even in these paradigms. Fias et al. (2001) and Lammertyn et al. (2002) found the SNARC effect in several orientation judgment tasks, but not in color judgment tasks. Subsequent results investigating automaticity of the SNARC effect were mixed, but there was a huge variation in the used paradigms and most of these studies were statistically underpowered. Therefore, we want to further investigate the automaticity of SNAs within this project.

(2) Moreover, the task (in)dependence of the SNARC effect remains unclear. There seems to be a systematic difference between the SNARC effect in magnitude classification tasks and in parity judgment tasks (e.g., Gevers, Verguts, et al., 2006; Weis et al., 2018). More precisely, the SNARC effect in the parity judgment task seems to be continuous, (i.e., the larger the number, the relatively faster the right compared to the left response). In contrast to this, the SNARC effect in the magnitude classification task (i.e., decisions on whether the stimuli numbers between 1 and 9 excluding 5 are smaller or larger than 5) is instead categorical (i.e., numbers between 1 and 4 are responded to faster with the left, but numbers between 6 and 9 are responded to faster with the left). However, in the magnitude classification task, there is no SNARC effect within the smaller (1 to 4) and larger (6 to 9) numbers, such that the association of 1 with the left is not any stronger than to 4 and that the association of 9 with the right is not any stronger than to 6 (Gevers, Verguts, et al., 2006; Nuerk et al., 2005). However, all studies reporting these patterns again had relatively low power, and we thus wish to replicate this difference in the shape of the SNARC effect with high statistical power.

(3) Last, context (in)dependence is a debatable aspect of the spatial mapping of numerical magnitude. Many researchers assume that the SNARC effect is based on relative rather than absolute magnitude. This means that there is no fixed association of left and right with absolute magnitudes like 1 on the left and 9 on the right, but the spatial association is flexibly adapted to task demands, experiment settings and stimuli sets. Importantly, the studies by Dehaene et al. (1993, Experiment 3) and Fias et al. (1996, Experiment 1) are often cited in this context, but both studies were underpowered and conclusions were often erroneously drawn from the absence of evidence for a difference between the two number ranges from 0 to 5 and from 4 to 9. In therefore remains unclear whether absolute magnitude (also) plays a role for the SNARC effect.

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

Fias, W., Lauwereyns, J., & Lammertyn, J. (2001). Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. Cognitive Brain Research, 12(3), 415–423. https://doi.org/10.1016/S0926-6410(01)00078-7

Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition - From single digits to arithmetic. Quarterly Journal of Experimental Psychology (2006), 67(8), 1461–1483. https://doi.org/10.1080/17470218.2014.927515

Gevers, W., Verguts, T., Reynvoet, B., Caessens, B., & Fias, W. (2006). Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance, 32(1), 32–44. https://doi.org/10.1037/0096-1523.32.1.32

Lammertyn, J., Fias, W., & Lauwereyns, J. (2002). Semantic influences on feature-based attention due to overlap of neural circuits. Cortex, 38(5), 878–882. https://doi.org/10.1016/S0010-9452(08)70061-3

Nuerk, H.-C., Bauer, F., Krummenacher, J., Heller, D., & Willmes, K. (2005). The power of the mental number line: How the magnitude of unattended numbers affects performance in an Eriksen task. Psychology Science, 47(1), 34–50. https://psycnet.apa.org/record/2005-11470-005

Weis, T., Nuerk, H.-C., & Lachmann, T. (2018). Attention allows the SNARC effect to operate on multiple number lines. Scientific Reports, 8(1), 13778. https://doi.org/10.1038/s41598-018-32174-y