On the Cognitive Link between Space and Number: A Meta-Analysis of the SNARC Effect

Abstract An association of numbers and space (SNARC effect) has been examined in an ever growing literature. In the present quantitative meta-analysis, 46 studies with a total of 106 experiments and 2,206 participants were examined. Deeper number magnitude processing determined by task, stimulus and participants characteristics was associated with a stronger SNARC effect. In magnitude classification tasks the SNARC effect assumed consistently a categorical shape. Furthermore, the SNARC effect was found to increase with age from childhood to elderly age. No specific difference in the size of the SNARC effect was observed due to the explicit use of imagery strategies that could not be explained by increased reaction times. In general, these results corroborate the predictions by the dual-route model of the SNARC effect regarding the activation of number magnitude representation and suggest that automaticity may play a role in the development of the association of numbers and space across the lifespan. Key words: SNARC, mental number line, aging, imagery, meta-analysis In 1993, Dehaene, Bossini, and Giraux showed that small numbers (e.g., 0 or 1) were associated with faster left hand responses, and larger numbers (e.g., 8 or 9) with faster right hand responses (Figure 1A). This result held for single- (Experiment 1) as well as two-digit numbers (Experiment 2) and was not affected by whether participants were left-hand dominant (Experiment 5), or crossed their hands on the response buttons (Experiment 6). The effect did, however, depend on the relative magnitude of numbers in the stimulus set (Experiment 3) and was reduced in participants with right-to-left reading habits (Experiment 7). A similar spatial association was absent for letters (Experiment 4) but present when participants categorized number words (Experiments 8 and 9). Dehaene et al. (1993) concluded that numbers are systematically associated with space, and that this association reflects the orientation of a "mental number line". Specifically, the authors proposed that ". the representation of number magnitude is automatically accessed during parity judgment of Arabic digits. This representation may be linked to a mental number line [. ], because it bears a natural and seemingly irrepressible correspondence with the natural left - right coordinates of external space. " (p. 394). Recently, Proctor and Cho (2006) proposed an alternative explanation for the SNARC effect based on polarity correspondence that contests the necessity of assuming the existence of a mental number line. The polarity correspondence account is a general theory of compatibility effects and does not require a spatially oriented mental number line to explain the SNARC effect. Proctor and Cho (2006) argue that the polarity assigned to each stimulus and response depends on the relative saliency of their dimensions. Instead of perceptual or conceptual similarity, the polarity categorization suffices to produce the mapping of stimuli onto responses. This account is based on the activation of positive or negative polarities for different dimensions and is applicable not only to the SNARC effect but also to non-numerical experimental set-ups. When the same polarity ("+" or "-") is assigned to different dimensions of the experimental set-up (e.g., stimuli and responses), they become associated. When applied to the domain of numerical processing, both "right" and "large" have polarity "+" while both "left" and "small" have polarity "-". When the polarities of stimulus and response overlap, a link is established regardless of perceptual, spatial or conceptual overlap, improving performance. Although the polarity correspondence account offers a parsimonious explanation for the SNARC effect in speeded binary classification tasks, some new evidence from cognitive neuropsychology lends support to the existence and relevance of a mental number line for the formation of spatial numerical associations (Zorzi et al. …