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

3. The hybrid model
The hybrid model (e.g., Nuerk, Weger, & Willmes, 2001; Nuerk & Willmes, 2005)
suggests that both, decomposed as well as holistic representations of number magnitude get
activated in a comparison task. Magnitude comparison is assumed to operate in parallel on
both representations, but depending on task requirements either one may be of more
relevance (e.g., the holistic representation for approximation). As the hybrid model is
assumed to incorporate characteristics of both of its constituting models the distance as well
as the problem size effect are accounted for accordingly.
Because each of the three models can account for the distance as well as the problem
size effect, another distinguishing feature is required. Nuerk and colleagues presented
evidence suggesting “decade breaks in the mental number line” (Nuerk et al., 2001, p. B25):
the unit-decade compatibility effect. In the next paragraph a distinction between the three
approaches based on the compatibility effect will be discussed, and open questions will be put
forward afterwards.
The Compatibility effect
The decade-unit-compatibility effect (Nuerk et al., 2001; Nuerk, Weger, & Willmes,
2002; 2004a; 2005; Moeller, Fischer, Nuerk, & Willmes, 2009a; Pixner, Moeller, Zuber, &
Nuerk, 2009; Wood, Nuerk, & Willmes, 2006) describes the finding that it takes participants
significantly longer to single out the larger number of e.g. the pair 38_53 than the pair 42_57.
This is supposed to be the case because in the first example separate comparisons of tens and
units lead to transient incompatible decision biases (i.e., 38_53 3 < 5, but 8 > 3) whereas in
the latter, compatible pair of numbers no such incompatibility occurs (i.e., 42_57 4 < 5 and
2 < 7). Because the absolute overall distance is 15 in both examples, no compatibility effect
should be observed if an exclusively analogue (holistic) magnitude representation for two-
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