What makes multiplication facts difficult. Problem size or neighborhood consistency?

Two current models of arithmetic fact retrieval, the network interference theory (NIT; Campbell, 1995) and the interacting neighbors (IN) model (Verguts & Fias, 2005a), predict that errors in simple multiplication should be more probable, if they include the same digit as the correct result (i.e., if they are "consistent," compared with "inconsistent" errors). In a reanalysis of error data originally reported by Campbell (1997), we provide first empirical evidence for this prediction. Furthermore, these results support the notion of different quantity representations for decades and units as proposed by Nuerk, Weger, and Willmes (2001). However, the NIT and IN-model differ in their explanations of the problem-size effect, a hallmark finding robustly observed in arithmetic fact retrieval. Only the IN-model predicts that a correct answer's neighborhood consistency can fully account for the problem-size effect, which was confirmed in our analysis.