Size congruity effects with two-digit numbers: Expanding the number line?

Abstract

Is 7 greater than 5? This appealingly simple question prompts a rapid and accurate answer with virtually all people. The ease with which people respond conceals the fact that complex cognitive operations are involved. To respond, people must retrieve the underlying magnitudes; note that, as mere graphic signs, 7 is neither larger nor smaller than 5. This fast (automatic?) retrieval of numerical information is particularly impressive when numerical values are irrelevant to the task at hand and can actually hurt performance. Consider a task in which pairs of digits are compared with respect to physical size. This task focuses on a nonsemantic attribute of the digits, yet the now irrelevant numerical values do, nonetheless, facilitate (in congruent pairs, such as 8-6) or impair (in incongruent pairs, such as performance. This size congruity effect (SCE) has evolved into an important marker of the potency of numerical activation (Algom, Dekel, & Pansky, 1996;Besner & Coltheart, 1979;Foltz, Poltrock, & Potts, 1984;Hatta, 1977;Henik & Tzelgov, 1982;Pansky & Algom, 1999Schwarz & Heinze, 1998;Schwarz & Ischebeck, 2003;Takahashi & Green, 1983;Tzelgov, Meyer, & Henik, 1992;Vaid, 1985;Vaid & Corina, 1989).Despite the importance of the SCE, studies probing the phenomenon have been confined to date to singledigit numbers. Application to two-digit numbers has been thwarted, due to methodological problems. This is unfortunate, because the similarity (or lack thereof ) in the processing of single-and two-digit numbers is consequential theoretically, yet relevant evidence is missing, due to the paucity of studies with two-digit numbers. Reynvoet and Brysbaert (1999) have noted that "although a lot of research on number representations has been done . . . there is still little or no direct evidence whether or not units and teens make access to a single number line. Most researchers avoid the problem by using unit numbers only" (p. 192). In this study, we bypassed the methodological problems and probed the SCE with single-and two-digit numbers within a common design. The results contribute to an understanding of two-digit number processing and bear on the general question of the uniformity of access to the number line across different orders of magnitude.Are single-and two-digit numbers governed by the same rules of processing and common mechanisms? Available evidence is equivocal. Take the well-known distance effect (Moyer & Landauer, 1967) as a handy example. The effect documents the finding that the time taken to decide which of a pair of numerals is larger numerically is inversely related to the numerical distance separating the members of the pair. The overwhelming majority of studies concerned single digits, with the effect invariably governing performance with such digits. In contrast, the results with two-digit numbers have been variable. Brysbaert (1995) recorded the typical form of the distance effect only when the two-digit numbers were confined to the same decade. Dehaene and Akhavein (1995) did not detect a distance ...

Numerical comparison of two-digit numbers: How differences at encoding can involve differences in processing

“…Therefore, the U-T presentation should facilitate the relevant decades comparison, whereas the T-U presentation should involve a greater interference of the units comparison. However, if the type of processing of two-digit numbers essentially depends on the mode of presentation (simultaneous 0parallel processing vs. sequential 0 holistic processing), as it has also been suggested recently (Ganor-Stern et al, 2009;Zhang & Wang, 2005;Zhou et al, 2008; but see Moeller et al, 2009), then a holistic comparison process should be found in our three conditions. Indeed, our three conditions corresponded to a sequential presentation, as in all of them the target numbers had to be compared to the standard 55 kept in memory.…”

“…Since Nuerk et al's (2001) study, the compatibility effect has been largely replicated: with German verbal written numerals (Nuerk, Weger, & Willmes, 2002; with Arabic numerals presented in diagonal (Nuerk, Weger, & Willmes, 2004), as well as horizontally (Ganor-Stern, Tzelgov, & Ellenbogen, 2007); with Arabic numerals in native German speakers whose number word system presents an inversion property (e.g., 22: ''zweiundzwanzig'' 0''two-and-twenty''), but also in native English (Nuerk et al, 2005) and Spanish (Macizo & Herrera, 2008) speakers whose number word system does not present an inversion property (e.g., 22: ''twenty-two'' in English, ''veintidó s'' in Spanish); and in schoolaged children (Mussolin & Noë l, 2008). Moreover, recent neuroimaging studies found neural correlates of the compatibility effect in the intraparietal cortex (Wood et al, 2008;Wood, Nuerk, & Willmes, 2006).…”

“…Second, it has been postulated that the automaticity versus the intentionality of the numerical comparison determines the type of processing involved (Ganor-Stern et al, 2007;Mussolin & Noë l, 2008). By using the size congruency effect (SiCE) 1 to study the automatic processing of twodigit numbers in adults (Ganor-Stern et al, 2007) and school-aged children (Mussolin & Noë l, 2008), it has been found that intentional processing of two-digit numbers (i.e., numerical comparison task) involved a hybrid representation (i.e., whole magnitude and components' magnitude activated) (but see Fitousi & Algom, 2006), whereas an automatic processing of two-digit numbers (i.e., physical comparison task) involved a decomposed parallel representation (i.e., components' magnitude activated).…”

“…In other words, the components' magnitude is accessed when the comparison process involves an initial processing. On the other hand, a holistic comparison process takes place (i.e., the whole targets' magnitude is accessed), once one of the target numbers has to be kept in short-term memory (i.e., serial presentation or comparison to a fixed standard) (Ganor-Stern et al, 2009;Zhang & Wang, 2005;Zhou et al, 2008; but see Moeller, Nuerk, & Willmes, 2009).…”

“…By using the size congruency effect (SiCE) 1 to study the automatic processing of twodigit numbers in adults (Ganor-Stern et al, 2007) and school-aged children (Mussolin & Noë l, 2008), it has been found that intentional processing of two-digit numbers (i.e., numerical comparison task) involved a hybrid representation (i.e., whole magnitude and components' magnitude activated) (but see Fitousi & Algom, 2006), whereas an automatic processing of two-digit numbers (i.e., physical comparison task) involved a decomposed parallel representation (i.e., components' magnitude activated). Therefore, according to Ganor-Stern et al (2007), the whole The SiCE corresponds to the difference between the congruent and the incongruent conditions in a Stroop-like numerical task, in which participants have to undertake a physical comparison task on Arabic numbers varying along both the physical and numerical dimensions. In other words, the SiCE corresponds to an interference effect that is assumed to reflect the automatic processing of the irrelevant numerical dimension.…”