Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

Abstract

The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not difficult to detect a SNARC effect within a group, but it has been quite unusual to find group differences. Is the SNARC effect as it is usually estimated using regression slopes largely insensitive to group differences, and are there design parameters necessary to increase sensitivity in group comparison analyses? Using numerical simulations, we provide evidence that both sample size and the number of stimulus repetitions, as well as intra-individual variability, contribute in a substantial way to the probability of detecting an existing SNARC effect. Our results show that the adequate choice of either sample size or number of repetitions per experimental cell does not fully compensate for a poor choice of the other parameter. Moreover, repeated failures to find significant group differences in the SNARC effect can be explained by insufficient power. Fortunately, increasing the number of repetitions to about 20 and testing at least 20 participants provides in most cases sufficient sensitivity to reliably detect the SNARC effect as well as group differences. Power plots are provided, which may help to improve both the economy and sensitivity of experimental design in future SNARC experiments, or, more generally when regression slopes are estimated intra-individually.

Keywords: ANOVA; Monte Carlo simulations; Regression Analysis; SNARC effect; power analysis.

FIGURE 1

Power graph for all parameters used in the simulations (power of detecting existing SNARC effect at 0.05). Small panels represent sample sizes, big panels represent levels of intra-individual variability (SD response). X axis represents number of repetitions from 10 to 120 in steps of 10. Black lines represent powers of 0.80 and 0.95.

FIGURE 2

Observed power for detecting an existing difference between two SNARC slopes (at 0.05 level). Small panels represent sample sizes, big panels represent levels of intra-individual variability (SD response). X axis represents number of repetitions from 10 to 120 in steps of 10. Black lines represent 0.80 and 0.95 power.