A system factorial technology analysis of the size congruity effect: Implications for numerical cognition and stochastic modeling

We applied the methodology known as the system factorial technology (SFT) to diagnose the information-processing architecture underlying the size-congruity effect (SCE) in numerical cognition. The SCE documents the interference in judging the physical size of numerals when this size disagrees with their numerical magnitude or the facilitation when the two attributes agree. Traditional theories of the SCE implicate the automatic activation of numerical magnitude and hence the mandatory interaction in processing between number and size. In contrast, in a pair of experiments we found serial minimum-time processing of number and size, an outcome which excludes the possibility of interaction. In the face of this architecture, we still recorded appreciable amounts of redundancy gains when number and size corresponded (=SCE). However, we show that this SCE does not derive from an interaction in processing. We show that, given stochastic independence, certain species of serial self-terminating models actually mandate the SCE. Other species of serial self-terminating models do not allow an SCE, an outcome that accounts for the absence of an observable SCE in a fair number of studies. Our results are inconsistent with the belief that numerical information is activated in an automatic fashion under all circumstances.