Polarity Correspondence in Comparative Number Magnitude Judgments

Article excerpt

When asked which of two digits is greater, participants respond more quickly if physical size corresponds to number magnitude, such as in 3 7, than when the two attributes contradict each other, such as in 3 7. This size congruence effect in comparative number judgments is a well-documented phenomenon. We extended existing findings by showing that this effect does not depend on physical size of the number alone but can be observed with number symmetry. In addition, we observed that symmetric numbers are judged as being smaller than asymmetric numbers, which renders an interpretation of the number symmetry congruence effect in terms of physical size implausible. We refer to the polarity correspondence principle (Proctor & Cho, 2006) to explain the present findings.

When participants in an experiment are presented with two different digits and have to decide which is greater, they are influenced by differences in the physical size of the digits: They respond more quickly if physical size and numerical magnitude coincide (e.g., 7 3) than when they are incongruent, as in the pair 7 3 (Besner & Coltheart, 1979; Henik & Tzelgov, 1982).

Additional evidence from fMRI data (Pinel, Piazza, Le Bihan, & Dehaene, 2004) and event-related potentials (Schwarz & Heinze, 1998) supports the notion that numerical judgments are related to size processing. Moreover, Cohen Kadosh and Henik (2006; Rubinsten & Henik, 2005) showed that not only physical size, but also figure- ground contrast affected comparative number judgments: Participants responded more quickly if the brighter of two digits shown on a dark background coincided with the greater numerical value. They explained their findings with the existence of an amodal representation of physical size and numerical magnitude (see Walsh, 2003). Indeed, higher figure-ground contrast may result in the subjective perception of bigger physical size (Weale, 1975).

This size congruence effect in comparative number judgments can be explained in terms of an automatic interference mechanism (Pansky & Algom, 1999). If the irrelevant attribute draws attention from the relevant attribute, interference occurs. The more salient the irrelevant attribute is, the higher the interference effect on performance of the relevant attribute becomes (Fitousi & Algom, 2006; Pansky & Algom, 1999; see Schwarz & Ischebeck, 2003, for a similar account). The only irrelevant attribute that has been tested to date is physical size, including luminance, which may result in subjective differences in physical size. Therefore, the question arises as to whether there are other irrelevant attributes that bias comparative number judgments.

In order to provide an answer to this question, we refer to the concept of polarity correspondence to explain response time (RT) differences in speeded binary classification tasks (Proctor & Cho, 2006): Research has revealed that processing is faster if the polarity of two dimensions is the same. Let us look at the so-called spatial-numerical association of response codes (SNARC) effect as an example. Dehaene, Bossini, and Giraux (1993) found that parity judgments (odd/even) were faster when participants had to respond to relatively small numbers with the left hand and to relatively large numbers with the right hand, which suggests that people represent number magnitude spatially, with lower values represented on the left and higher values on the right. When Ito and Hatta (2004) replicated the study by Dehaene et al. with a vertical arrangement of the response keys, they observed a SNARC effect: Participants answered more quickly to digits of greater numerical magnitude when they had to press the upper key, rather than the lower key. Proctor and Cho explained this finding by invoking their polarity correspondence principle: Both the stimulus attribute greater and the response attribute upper (or smaller and lower) have the same polarity. …