Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill

Abstract

The SNARC (spatial–numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsignificant. Possible reasons for this nonsignificance could be that in previous studies (a) very small samples were used, (b) there were too few repetitions producing too little power and, consequently, reliabilities that were too small to reach conventional significance levels for the descriptive skill differences in the SNARC, and (c) general mathematical ability was assessed by the field of study of students, while individual arithmetic skills were not examined. Therefore we used a much bigger sample, a lot more repetitions, and direct assessment of arithmetic skills to explore relations between the SNARC effect and arithmetic skills. Nevertheless, a difference in SNARC effect between arithmetically skilled and nonskilled participants was not obtained. Bayesian analysis showed positive evidence of a true null effect, not just a power problem. Hence we conclude that the idea that arithmetically skilled and nonskilled participants generally differ in the SNARC effect is not warranted by our data.

Keywords:

• Spatial–numerical association of response codes
• Numerical cognition
• Number and space

We wish to thank Marc Brysbaert and two reviewers for numerous helpful comments on a previous version of the manuscript. In particular, we are grateful to Marc Brysbaert for putting our attention to Masson's Bayesian analysis methods, which improved the manuscript a lot and made our null results “positive evidence” for a true null SNARC slope difference between skilled and unskilled participants. We also thank Dorota Z˙elechowska and Dominika Czajak for their help in data collection and Franziska Burger for checking and correcting English spelling, expression, and grammar. H.-C. Nuerk's research on spatial–numerical cognition was supported by the German Research Foundation (DFG) by means of a project within the Research Group (Forschergruppe) Analyse und Förderung effektiver Lehr-Lern-Prozesse (FOR 738/2/TP02).

Notes

¹ Note that previous studies used only 20 participants (Dehaene et al., 1993; Fischer & Rottman, 2005).

² Note that previous studies used only 9 or 10 repetitions per block.

³ Since those questionnaires were not relevant for the aim of the study reported here, and mostly null correlations were found, they are not reported in the main body of the paper. All results are presented in Appendix B.

⁴ We wish to thank the action editor Marc Brysbaert for proposing this analysis in response to power concerns raised by the reviewers.