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

Nevertheless, the results pattern was not so similar for the decomposed and the hybrid
model when comparisons to a fixed standard were evaluated. Although both models did not
differ reliably regarding descriptive adequacy, the compatibility effect was only found for the
data produced by the strictly decomposed model. For the hybrid model data the compatibility
effect was found in the expected direction, however, missed statistical significance. In line
with this, the continuous predictor unit distance was a reliable predictor of item RT only in the
regression analysis for the data produced by the strictly decomposed model. As for the
comparisons to a fixed standard unit distance was limited to a maximum of ±6 and this
maximal unit distance was present in only a small number of items, this may once again argue
for the importance of large unit distances when looking for unit-based effects (see Moeller et
al., 2009b) for a more detailed discussion (see also below for a discussion on possibly
different origin of the compatibility effect within the strictly decomposed and the hybrid
model). Taken together, this inconsistency in the replication of the compatibility effect
between the decomposed and the hybrid model may be a first indicator of the superiority of
the strictly decomposed model. Such an interpretation is corroborated by a general principle
of model selection as well as another result of the current simulations.
On the one hand, taking into account that the hybrid model is the less parsimonious
one and following Occam’s razor the current computational data again suggest that multi-digit
number magnitude is represented in a decomposed fashion retaining the place-value structure
of the Arabic number system (see Myung & Pitt, 1997 for a discussion on model selection
criteria). On the other hand, this interpretation can be further specified when considering the
results of the regression analyses. Basically, the incorporation of a holistic representation of
overall number magnitude in the hybrid model (Nuerk & Willmes, 2005) resulted from
repeated findings that apart from predictors indicating decomposed processing of tens and
units a measure of overall distance between the to-be-compared numbers (i.e., absolute
distance, logarithmic distance, distance between the logarithms of the two numbers) was the
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