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

Modelling two-digit number comparison – analysis and results
Simulated reaction times produced by either of the models were analyzed according to
the constraints of the studies of Nuerk et al. (2001) for comparisons to a variable standard
(i.e., singling out the larger of two numbers) and Moeller, Nuerk, and Willmes (2009b) for
comparisons to a fixed memorized standard and will be reported in turn. As the simulated RTs
only ranged between 0 and 50 corresponding RTs on the millisecond scale were estimated by
a linear regression approach. The slope and the intercept of the regression equation were
computed by predicting the actual empirical RTs by the simulated RTs for the comparison to
a variable standard (cf. Nuerk et al., 2001) and a fixed standard (Moeller et al., 2009b). All
analyses reported subsequently will be conducted over item RTs. In the case of the empirical
data this means the mean RT per item over all participants. However, in the case of the model
data this reflects RTs per item averaged over 10 simulation rounds (cf. Verguts et al., 2005 for
a similar proceeding). Analyses of both the model data concerning comparisons with a
variable external standard and comparisons to a fixed standard involved a categorical
AN(C)OVA as well as a multiple stepwise regression analysis (see Nuerk et al., 2001 for a
similar procedure) 2 .
The univariate ANOVA for comparisons to a variable standard incorporated the fixed
factors data origin (empirical vs. modelled), unit-decade compatibility (compatible vs.
incompatible number pairs), decade distance (small: 1 - 3 vs. large: 4 - 8), and unit distance
(small: 1 - 3 vs. large: 4 - 8). The corresponding regression analysis included the predictors (i)
overall absolute distance, (ii) logarithm of the absolute distance, (iii) distance of the
logarithmic magnitudes, (iv) absolute problem size, (v) logarithmic problem size, (vi) unit
distance (e.g., ranging from –8 for 49_61 to +8 for 51_69), (vii) absolute unit distance, and
(viii) compatibility (see Nuerk et al., 2001; Moeller et al., 2009a for similar proceedings).
2 Please note that results were identical when using the activation difference between the two output nodes
instead of simulated RT as the dependent variable suggesting the present approach of simulating RTs to be
valid.
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