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

most important predictor in a multiple regression analysis (e.g., Nuerk et al., 2001; 2002;
2004a; Moeller et al., 2009b; Wood et al., 2006). However, the current data indicated that a
holistic representation (as in the purely holistic or the hybrid model) is not a mandatory
prerequisite for an important influence of overall distance measures in the regression analyses.
Instead, it was observed that even for the data produced by the strictly decomposed model a
measure coding overall distance (i.e., distance between the logarithms of the to-be-compared
numbers) was identified to be the most important predictor of item RT. Thus, this means that
the inclusion of such a predictor is not a direct indicator for the existence of a holistic
representation of number magnitude as it was also found for data produced by a model
without any integrated representation of two-digit number magnitude.
In summary, the present results indicated that the distance effect could be accounted
for by each of the three models, whereas the compatibility effect required decomposed
representations of tens and units as suggested by Nuerk et al. (2001; see also Nuerk &
Willmes, 2005 for a review). Additionally, the reliable influence of an overall distance
measure in the regression analyses was not a necessary consequence of a holistic
representation. Thus, the current data provide first computational evidence for the assumption
of two-digit number magnitude representation to be organized in compliance with the placevalue
structure of the Arabic number system, thereby representing each power of ten (i.e.,
units, tens, etc.) separately. Under consideration of model parsimony the empirical data were
accounted for best by a strictly decomposed model realizing separate representations of tens
and units.
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