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

contrasted. In the current study it was observed that the model fit of the two-linear model was
reliably better than that of the logarithmic model for Italian-speaking children (see also
Moeller et al., 2009a for a more detailed description of identical results for the Germanspeaking
sample).
(b) Alternatively, one may also be interested in the results of separate analyses for one-
and two-digit numbers as described above on an individual bases.
(c) It is also possible to compute the optimal break-point of the two-linear model for
each individual participant and then evaluate the distribution of these break-points. Only if the
optimal break-points of the vast majority of participants fall close to the hypothetisized breakpoint
the two-linear model should be considered. Again, this was given in the present data set:
the majority of Italian-speaking participants had an optimal break-point around 10 (see also
Moeller et al., 2009a for similar results concerning the German-speaking participants).
However, as already pointed out in the introduction even in a situation where the data
undoubtedly follow a two-linear function, a logarithmic model would provide a very good
model fit and vice versa. Therefore, we evaluated this issue by comparing the distributions of
individual breakpoints of the empirical data and 100 simulated participants produced by a
100% logarithmic model. Figure A, Panel I depicts the distribution of breakpoints as observed
for the simulated data whereas the individual breakpoints empirically found for both Germanas
well as Italian-speaking children are to be found in Figure A, Panels II and III, respectively.
As can be observed from these figures the pattern differs considerably: For the simulated data
the vast majority of breakpoints was found to be located between 13 and 17 with the median
at 14.37 and the mean being very close at 15.39. Contrarily the majority of breakpoints for the
empirical data was found to be located between 8 and 12 (median at 9.8 and 11.8 for Italianand
German-speaking children, respectively; Means: 21.2 and 25.3, respectively) and thus
118