The influence of the place-value structure of the Arabic number ...

2004). So, increasing the maximum unit distance from 4 (e.g. Zhang & Wang, 2005) to 6
contributed to the observation of the compatibility effect, but it still seems to be the largest
possible unit distances (i.e. 7 and 8) that particularly enhance the compatibility effect. Nuerk
and Willmes (2005) had hypothesized that such limited unit distance may account for the lack
of unit-based effects in comparisons to a standard involving the unit digit 5. However, the
current study is the first in which this hypothesis was directly tested.
However, even when these results are hard to reconcile with the notion of two-digit
numbers to be exclusively represented as integrated entities, this does not preclude holistic
processing of two-digit numbers entirely. Decomposed representations of the magnitudes of
tens and units as indicated by the compatibility effect may exist in addition to an
(approximate) holistic representation of their integrated magnitude (see also Liu, Wang,
Corbly, Zhang, & Joseph, 2006 for neuro-imaging data corroborating this notion). Such a
view has been expressed explicitly in the hybrid model of two-digit number representation
(Nuerk & Willmes, 2005). The authors suggest that these three magnitude representations are
activated in parallel and influence each other. In particular, an excitatory influence facilitating
the correct response is assumed for the case of compatible separate comparisons of tens and
units (e.g. 42_57, 4 < 5 and 2 < 7). In contrast, when separately comparing tens and units
yields incompatible decision biases (e.g. 47_62, 4 < 6 but 7 > 2) the correct response is
inhibited. The regression analysis in this study corroborates earlier analyses in that both
predictors related to holistic processing (i.e. distance between the logarithms of standard and
probe) and of decomposed processing (i.e. unit-distance) were entered into the model.
However, it must be noted that as for the Nuerk et al. (2001) data (see Verguts & De Moor,
2005, for a reanalysis) the regression model does not get much worse if decade distance is
forced to be a predictor in the regression analysis (adjusted R 2 = .486 compared to .488 in the
original analysis). So, although we personally favour a hybrid processing model, a fully
decomposed model cannot be rejected on the basis of these data.
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