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

Finally, a regression analysis only incorporating the four reliable predictors of item RT as
identified by Nuerk and colleagues (2001; i.e., logarithmic distance, problem size, unit
distance, and absolute unit distance) was conducted to evaluate in how far the predictors for
empirical item RT also hold for modelled item RT.
For the comparisons with a fixed standard an ANCOVA was conducted to account for
the influence of problem size which cannot be matched between compatible and incompatible
comparisons when controlling for overall distance at the same time. Apart from the covariate
problem size the ANCOVA discerned the factors unit-decade compatibility (compatible vs.
incompatible) and unit distance (small: 1_3 vs. large: 4_6). Furthermore, a stepwise multiple
regression analysis was run over item RTs including the following predictors: (i) overall
absolute distance, (ii) logarithm of the absolute distance, (iii) distance of the logarithmic
magnitudes, (iv) problem size, (v) logarithmic problem size, (vi) unit distance ranging from -6
for e.g., 71_57 to +6 for e.g., 53_69, (vii) absolute unit distance and (vii) compatibility 3 .
Again, in a final step a regression analysis only incorporating the four reliable predictors of
empirical item RT as identified by Moeller and colleagues (2009b; i.e., logarithmic distance
and unit distance) was conducted.
Before turning to the results of the network models, the original results for the
empirical RT data of the two original studies (i.e., Nuerk et al., 2001 and Moeller et al.,
2009b) will be summarized briefly.
3 Please note that classifying items according to these constraints would have resulted in a larger overall
distance for compatible than for incompatible number pairs, thereby confounding the distinction between
effects of overall distance and unit-decade compatibility. Thus, to balance overall distance between compatible
and incompatible comparisons selectively chosen probes were excluded from further analyses in each of the
two item croups. It is important to note that overall distance cannot be matched by excluding randomly chosen
probes (see Moeller et al., 2009b for a more detailed discussion of this point). Additionally, as it is not
possible match compatible and incompatible comparisons for both overall distance and problem size (½ *
(standard + probe)), the latter was considered as a covariate in all analyses.
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