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

Procedure: After ten randomly chosen practice trials the first of 2 runs with 10 blocks
each was started. Each block consisted of all 72 probe numbers for one of the two standards.
Half of the participants started with ten blocks of comparing the probe to the internal standard
53 while the other half started with the internal standard 57 1 . Trial order was randomized for
each participant separately. Viewing distance was approximately 60 cm.
In each trial, a fixation mark located at the centre of the screen was presented for 500
ms. Then the probe number appeared and remained on the screen until a response was given.
Participants had to press the up-arrow key of a standard keyboard with their right index finger
when the probe was larger than the standard and the down-arrow key with their left index
finger when the probe was smaller than the standard.
Mode of analysis: For between-decade trials the factors standard number (53 vs. 57),
unit-decade compatibility (compatible vs. incompatible, e.g. 57_43 vs. 53_37), and unit
distance (small: 1 – 3 vs. large: 4 – 6) were discerned. Please note that no
compatible/incompatible distinction is possible for probes deviating from the standard by a
multiple of ten. Therefore, these probes were not considered in the analysis. Based on this
classification, overall distance would have been larger for compatible than for incompatible
number pairs making it impossible to distinguish holistic from decomposed accounts.
Therefore, 6 selectively chosen compatible as well as incompatible probes were excluded
based on the constraint of balancing overall distance for compatible and incompatible trials.
Note that matched overall distance can only be achieved by excluding specific, not randomly
chosen probes (see Appendix A for details). However, it is impossible to match both overall
distance and problem size (½ * (standard + probe)). Therefore, the latter was incorporated in
the analyses as a covariate. As problem size can only be computed for trials but not
1 Please note that this procedure is even stricter than in Zhang and Wang’s (2005) study as it leaves much more
time to internalize standards. In Zhang and Wang, standards could be internalized for 3 seconds for one
comparison, while in our study the standard could be internalized for 720 trials being more comparable to the
procedure used by Dehaene and colleagues (1990).
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