Academic journal article Memory & Cognition

A Memory-Based Account of Automatic Numerosity Processing

Academic journal article Memory & Cognition

A Memory-Based Account of Automatic Numerosity Processing

Article excerpt

We investigated the mechanisms responsible for the automatic processing of the numerosities represented by digits in the size congruity effect (Henik & Tzelgov, 1982). The algorithmic model assumes that relational comparisons of digit magnitudes (e.g., larger than {8,2}) create this effect. If so, congruity effects ought to require two digits. Memory-based models assume that associations between individual digits and the attributes "small" and "large" create this effect. If so, congruity effects ought only to require one digit. Contrary to the algorithmic model and consistent with memory-based models, congruity effects were just as large when subjects judged the relative physical sizes of small digits paired with letters as when they judged the relative physical sizes of two digits. This finding suggests that size congruity effects can be produced without comparison algorithms.

In the size congruity effect, subjects observe two digits, one of which is presented in a larger font size than the other. Subjects then judge which of the two digits is presented in the larger (or smaller) font size. Only the physical sizes of the digits are relevant for this task; the numerosities represented by the digits are irrelevant. Nevertheless, a size congruity effect is typically observed such that the time needed to identify the relative sizes of the digits is faster when the difference in the numerosities represented by the digits is congruent with the difference in font sizes (e.g., {2 8}) than when it is incongruent with the difference in font sizes (e.g., {2 s}). These size congruity effects also tend to interact with the distance between the numerosities represented by the digits such that congruity effects are larger for pairs that are far away from each other (e.g., {2 8}) than for pairs that are close together (e.g., {2 4}). These effects demonstrate that the numerosities represented by the digits interfere with size judgments even though people are trying to ignore them and pay exclusive attention to physical size. The purpose of the research reported here was to explore the mechanisms responsible for these size congruity effects.

Several views regarding the nature of the representations and processes involved in the size congruity effect have been proposed. One view-henceforth, called the algorithmic model-is that subjects map the numerosities represented by the digits to an analogue numerosity representation and then use the analogue representation to identify the digit that represents the larger (or smaller) numerosity. The result of this comparison process is thought to interfere with judgments of physical size (Dehaene & Akhavein, 1995; Schwarz & Ischebeck, 2003; Tzelgov, Yehene, Kotler, & Alon, 2000). The interaction between size congruity and distance is often cited as especially strong evidence for this view because the larger congruity effects for digit pairs whose members represent dissimilar numerosities are believed to reflect faster processing for values that are more discriminable (i.e., farther apart) on the analogue numerosity representation.

The algorithmic model assumes that processing of the numerosities represented by digits is accomplished in multiple stages. The numerosities represented by each of the to-be-compared digits, A and B, must be retrieved and mapped to the analogue numerosity representation. The values on the analogue representation must then be compared to produce a relational judgment of the form larger than [numerosity A, numerosity B] or smaller than [numerosity B, numerosity A]. This calculation is faster the greater the difference between the numerosities, purportedly because larger differences are more discriminable on the analogue numerosity representation. Finally, this relational judgment undergoes processing by which it facilitates or interferes with relational judgments of the form larger than [physical size B, physical size A] or smaller than [physical size A, physical size B]. …

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