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

computational models were programmed realizing (i) holistic (ii) strictly decomposed, and
(iii) hybrid representations of number magnitude. When evaluating the descriptive adequacy
of the data produced by each of these models it was found that the data by the strictly
decomposed model fitted the empirical data best. In particular, Nuerk and colleagues (2001;
see also Nuerk & Willmes, 2005) initially assumed a representation of overall number
magnitude to accompany the separate representations of tens and units as in most regression
analysis a measure coding the overall distance between the to-be-compared numbers was
observed to be the most important predictor of task performance. However, assuming such an
additional holistic representation, because a measure of overall distance between probe and
standard was included as a reliable predictor in a regression analysis, was proved unnecessary
by the current data. A measure of overall distance (i.e., difference between the logarithms)
was found to be the most important predictor of item RT even for the data produced by the
strictly decomposed model. Thereby, indicating that overall a strictly decomposed model of
two-digit number representation accounted best for the empirical data. Please note that the
superiority of the strictly decomposed model was evident even apart from the fact that the
hybrid model is the least parsimonious model and should thus only be considered when
controlling for the higher number of free parameters. Nevertheless, the computational data
clearly argue for the human representation of two-digit number magnitude to comply with the
power levels of the Arabic number system, thereby, retaining its place-value structure.
In summary, the results of the present thesis were meaningful in addressing the
question whether and if so in what way the place-value structure of the Arabic number system
is reflected in the human representation of two-digit numbers. Empirical evidence suggested
that decomposed processing of tens and units is not driven by an external presentational
format. Instead, the present data indicate that the internal representation of number magnitude
is decomposed as well (cf. Study 1). Furthermore, this important initial finding was
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