Academic journal article Memory & Cognition

# Size Congruity Effects with Two-Digit Numbers: Expanding the Number Line?

Academic journal article Memory & Cognition

# Size Congruity Effects with Two-Digit Numbers: Expanding the Number Line?

## Article excerpt

The size congruity effect is the interesting result that comparisons of the sizes of the physical formats in which numerals appear are affected by the numerical magnitudes of the respective numerals. We demonstrated that separating the physical and the numerical attributes in space leaves the effect unchanged. We then applied the spatially separated version to two-digit numerals and showed the effect to be comparable to that obtained with single numerals. We showed further that the effect is sensitive to the relative salience of the numeric and physical dimensions, to the extent that when the latter is the more salient dimension, a reverse effect obtains by which physical size interferes with number comparison. The results can be explained by a relative speed of processing account, but they are also compatible with an attention account that does not appeal to the notion of automaticity.

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 8-6) 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, 1999,2002; Schwarz & 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 single-digit 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. …

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