Abstract: Spatial-numerical associations (SNAs), showing that small numbers have stronger associations with left space and large numbers have stronger associations with right space, are a hot topic in the field of cognitive psychology. An important index to explore SNAs is the spatial-numerical association of response codes (SNARC) effect (i.e., faster responses to small numbers using left effectors, and the inverse for large numbers), which provides strong evidence for the existence of SNAs. Previous studies have verified the universality of the SNARC effect. This effect could be observed across a wide range of numbers, diversified materials, different sensory channels, different ways participants react, and various reaction indexes. Importantly, the SNARC effect is also flexible in direction and the processing stage at which it occurs. First, the direction of the SNARC effect is flexible. Previous studies showed that the direction of the SNARC effect could be influenced by different reading habits (e.g., left-to-right or right-to-left), varying ranges of numbers (e.g., 1~9, 0~4, and 4~9), different representations (e.g., ruler or alarm clock), serial position in working memory, and reference numbers for comparison. The mental number line, working memory account and other theories have been proposed to explain the directional flexibility of the SNARC effect. Second, the processing stage in which the SNARC effect occurs is flexible. Researchers have tried to determine the processing stage in which the SNARC effect occurs from three perspectives: the relationship between the SNARC effect and other effects occurring at different stages (e.g., the Simon effect, Stroop effect, numerical distance effect, and switch cost), changes in the SNARC effect in different response effectors (e.g., hand response and eye movement), and the event-related potentials (ERPs) components induced by the SNARC effect. Three views of the processing stage in which the SNARC effect occurs have been proposed, but the conclusions are still discordant. The first view supports that the SNARC effect occurs at the semantic representation stage, the second view supports that it occurs at the response selection stage, and some recent studies have proposed a third view that the SNARC effect occurs flexibly at both stages. This dispute may be caused by the following four reasons: (1) disparities in the comprehension of additive-factor logic, which led to indirect inference; (2) observation from a single point, which led to indirect inference; (3) different types of Simon effects were adopted as the measure index, which led to different results; and (4) different tasks were adopted, which led to different results. Combining the above reasons, a new two-stage processing (spatial representation of magnitude, spatial representation to response selection) model was proposed. This model distinguished the different processing pathways of magnitude information in the magnitude comparison task (task-relevant) and in the parity judgment task (task-irrelevant). Also, it was proposed that different interference factors acting on the two stages might be the core reason for the flexibility of the SNARC effect. This model covered and explained the flexible variation in the SNARC effect observed in most previous studies. Future research could focus on comparisons of different tasks and the adoption of various interference factors to verify the two-stage processing model and combine cognitive neuroscience technologies to further elucidate the neural mechanism underlying the flexibility of SNAs.

Key words: SNARC effect, flexibility, Spatial-Numerical Associations, two-stage processing model