Academic journal article Canadian Journal of Experimental Psychology

Exploring the Mental Number Line Via the Size Congruity Effect

Academic journal article Canadian Journal of Experimental Psychology

Exploring the Mental Number Line Via the Size Congruity Effect

Article excerpt

To address the ongoing debate about the origins of the size effect (faster comparison time for smaller than larger numbers, given a fixed intrapair distance), an indication of automatic number processing was searched for. Participants performed a quantity comparison task in which they had to decide which of two sketched cups contained more liquid, while ignoring the number superimposed on each cup. In the congruent condition, the larger number appeared on the cup containing more liquid, while in the incongruent condition the larger number appeared on the cup containing less liquid. The size effect was found in a numerical comparison task, while in the quantity comparison task the size congruity effect decreased as the magnitude of the irrelevant numbers increased. Together, these results suggest that the size effect reflects a basic feature of the mental number line.

Keywords: size effect, mental number line, size congruity effect, automaticity

The size effect consists of faster latencies for comparisons of small numbers than large numbers, given a fixed intrapair distance (e.g., Ganor-Stern & Tzelgov, 2008; Moyer & Landauer, 1967). Dominant models in the field view this effect as one of the indicators for a condensed mental number line (MNL; Restie, 1970) representation, on which large numbers are less discriminable than small numbers are (e.g., linear, Gallistel & Gelman, 1992; logarithmic, Dehaene, 1992; or analog magnitude representation, Zorzi & Butterworth, 1999).

Alternatively, Verguts and colleagues (Verguts, Fias, & Stevens, 2005; Verguts & Van Opstal, 2005, 2008) claimed that the size effect reflects the characteristics of the task intentionally performed rather than a basic feature of the MNL. They relied on the fact that no indications of the size effect were found in a variety of tasks (such as naming, parity judgements, and same/different judgements) apart from in numerical comparisons. Verguts et al. (2005) formulated a model according to which the MNL is a linear place coding representation with a fixed variability. The model simulations replicated the size effect found in the numerical comparison task but not in other tasks. Accordingly, the size effect was viewed as a consequence of nonlinear mappings from the MNL to the comparison output units that derive from the lower frequency of larger numbers.

Intentional processing of numbers (i.e., when numbers are processed as part of the task requirements) is highly affected by task demands, such that the resulting representation reflects the specific characteristics of the task at hand (e.g., Fischer & Rottmann, 2005; Shaki & Petrusic, 2005; Tzelgov, Ganor-Stern, & MaymonSchreiber, 2009). Along these lines and following the minimal approach to automatic processing (Bargh, 1989, 1992; Tzelgov, 1997) - processing which runs without monitoring - automaticity can be used as a tool for revealing the stored mental representations. Accordingly, markers of automatic processing of numerical information can be used to uncover whether the size effect reflects a basic feature of the MNL (e.g., Cohen Kadosh, Tzelgov, & Henik, 2008a, 2008b; Tzelgov & Ganor-Stem, 2005; Tzelgov et al., 2009).

A frequently used marker of automatic processing in the numerical domain is the size congruity effect (e.g., Henik & Tzelgov, 1982). When participants perform physical size comparisons of number pairs that differ in their physical sizes and numerical values, responses are faster in the congruent (e.g., 3, 5) than in the incongruent condition (e.g., 3, 5; i.e., faster responses when the number that is physically larger is also numerically larger than when it is numerically smaller, respectively). The size congruity effect refers to the reaction time (RT) difference between the two conditions. It has been shown that the effect increases with increased intrapair distance (e.g., Henik & Tzelgov, 1982; Schwarz & Ischebeck, 2003), suggesting that the MNL was accessed. …

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