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

The authors used a magnitude comparison task with standard numbers 55 and 65. In an
external representation condition, the standard was presented together with a probe whereas in
the internal representation condition, the probe was presented alone and had to be compared
to an internal standard presented 3 seconds before. For the external standard condition, Zhang
and Wang observed reliable influences of the unit digits’ magnitude on task performance in
the external condition: (i) discontinuity effects (i.e. the RT difference between 69 and 70
differed significantly from the difference between 68 and 69) at decade boundaries or (ii)
even a reversed distance effect (i.e. at the boundary of 30s and 40s RTs to probes 36 through
39 were on average slower than those to probes 41 through 44 even though overall distance is
larger for the former probes). Quite to the contrary, the authors reported mixed results when
the standard was internal. While they observed unit-based effects in a two-way (decades ×
units) ANOVA, they completely failed to find any discontinuity or reversed distance effects.
Thus, Zhang and Wang concluded that the influence of the unit digit in number comparison is
determined by the representational format. Only when both numbers (i.e. standard and probe)
are represented externally, decomposed processing of tens and units is assumed.
However, we do not think that these null unit-effects warrant conclusions that
decomposed representations have to rely on external representations of numbers. We have
pointed out previously why null unit-effects could be observed (Nuerk & Willmes, 2005). As
this claim has guided the design of the current study a brief sketch will be given on how such
null unit effects come about.
How to observe unit-based null effects in two-digit number comparison
1. Use of small unit distances in the stimulus set
We observed repeatedly that the compatibility effect is more pronounced when unit
distances are large and possibly not even present when unit distances are small (Nuerk et al.,
2001; 2005; Nuerk, Kaufmann, Zoppoth, & Willmes, 2004). When using a standard with the
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