Offline and online automatic number comparison

Other researchers already obtained size congruity effects with single digits (e.g., Algom, Dekel, & Pansky, 1996; Schwarz & Ischebeck, 2000; Tzelgov et al., 1992), but in their experiments, trials on which numerical size was irrelevant were always mixed with trials on which it was relevant (either blocked or not). On the relevant trials, participants were instructed to compare the numerical size of the presented digit with the numerical size of a fixed standard. Because of this, one could argue that participants continued engaging in a numerical comparison with the standard on the irrelevant trials, despite the instruction to respond on the basis of physical size.

The interaction test between response (small/large) and number (4/5) is equivalent to a contrast that assigns a weight of +1 to the two “response = small, number = 4” conditions and the two “response = large, number = 5” conditions, and a weight of -1 to the other four conditions. Alternatively, the eight conditions can be rearranged in a congruity (congruent/incongruent) × distance (small/large) × response (small/large) format. The interaction between congruity and distance is equivalent to a contrast that assigns a weight of +1 to the two “congruity = incongruent, distance = small” conditions and to the two “congruity = congruent, distance = large” conditions, and a weight of −1 to the other four conditions. The weight assignments are equivalent for the two situations, and therefore the response × number and congruity × distance interactions are equivalent.