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

proportions in earlier studies. Therefore, it might be an interesting question whether these
changes also affect the goodness of logarithmic fitting.
In Figure 2, the results of fitting this logarithmic predictor can be found. Generally, the
logarithmic fitting of overall distance is still good for the present design. However, it is
influenced by the standard used. For the standard 53 fitting is better for numbers larger than
53 (see Figure 2, Panel A), whereas for the standard 57 fitting is better for numbers smaller
than 57 (see Figure 2, Panel B). The reasons for this asymmetry might be twofold: (i) In the
conditions showing better fits, there were more (i.e. 6) relatively slower within-decade
numbers. Thus, the larger within-decade distance effect might have determined the
logarithmic slope close to the standard. Contrarily, there were only few (i.e. 2) within-decade
numbers in the conditions showing worse fits, which may not be favourable to lead to a
pronounced within-decade distance effect. Additionally, these 2 within-decade numbers were
repeated quite often which may have affected their RT to a certain extent 3 . (ii) The
logarithmic fit was worse in the conditions with more incompatible trials. Considering the
standard 53, there are 6 compatible trials per decade for probes larger than the standard (e.g.
53_67) but only 2 incompatible ones (e.g. 53_71) whereas this pattern is reversed for probes
smaller than the standard (e.g. compatible: 53_41; incompatible: 53_37). For the standard 57
the compatible-incompatible pattern is reversed. The worse fit in these conditions may
indicate that enhanced decomposed processing of tens and, in particular, units is required here
to overcome unit-decade incompatibility. In turn, such an increase in decomposed processing
may reduce the influence of the holistic representation as reflected in a worse fit.
3 Note that the compatibility effect in this study was based on between-decade stimuli which were all presented
equally often only once per block.
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