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

DISCUSSION
Internal or external decomposed representations?
The objective of the present study was straightforward: Does the assumption of a
strictly holistic internal representation of two-digit numbers hold under conditions more
favourable to detect unit-based effects? The current data indicate that the answer should be
no. When allowing for unit distances larger than 4 and employing a balanced number of
between- and within-decade trials, a reliable unit-decade compatibility effect was observed.
Such a compatibility effect in an internal condition cannot be explained by a holistic
representation, but is consistent with an independent contribution of the unit digit’s
magnitude.
In line with the hypothesis, the changes introduced in the experimental design did help
to observe unit-based effects: (i) besides the significant unit-decade compatibility effect, the
present data also showed that this effect was mainly driven by a compatibility effect for large
unit distance (i.e. 4 - 6). This not only corroborated the objections against the use of a
standard involving the unit digit 5 as raised in the introduction, but also indicates that the
compatibility effect is not a simple attentional congruity effect. It rather reflects processing of
the unit digit’s magnitude and thus points to the importance of the units in two-digit number
comparison. (ii) In accordance with the findings of Knops (2006) the current results imply
that the use of a considerable proportion of within-decade trials in which comparing the unit
digits is decisive (e.g. 53_58) seems to be necessary to prevent participants from exclusively
focusing their attention on the decade digits and therefore to reduce the possibility to obtain
unit-based effects. Finally, the significant compatibility effect is particularly relevant as it
emerges even against the impact of the congruency effect described in the introduction which
is inevitably confounded with the use of an internally represented standard.
Although reliable, the compatibility effect in the present study was smaller than that
reported in previous studies (12 ms vs. 31 ms in Nuerk et al., 2001; 29 ms in Nuerk et al.,
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