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

Table 5: Predictors included in the final regression model for the decomposed data
Predictor B b t sign.
Change in
R 2
Raw
correlation
Partial
correlation
Constant 491.63 - 78.30 < .001 - - -
Overall Distance -2.04 - .69 10.16 < .001 .48 - .69 - .85
Problem size .74 .50 7.42 < .001 .25 .50 .76
Unit distance - 1.14 - .29 4.33 < .001 .09 - .30 - .57
At last, the regression analysis including only the two predictors identified to
significantly predict item RT in the study by Moeller et al. (2009b) resulted in a reliable
model [adj. R 2 = .51, R = .73, F(2, 41) = 23.23, p < .001]. However, descriptive adequacy of
the model was considerably reduced as compared to the final model of the stepwise regression
analysis. Nevertheless, both variables predicted item RTs reliably. Inspection of the beta
weights revealed that item RTs increased as logarithmic overall distance [constant = 575.48;
B = -63.81; b = - .66, t = 6.20, p < .001] as well as unit distance [B = -1.12; b = - .29, t = 2.68,
p < .01] decreased. Again, the reliable negative influence of unit distance indicated item RTs
to be driven by unit-decade compatibility. In summary, these analyses consistently indicated a
good fit between the data produced by the strictly decomposed model and the empirical
results, not only regarding descriptive adequacy, but also concerning the reliable simulation of
the relevant effects (i.e., distance and compatibility effect).
Hybrid model
ANCOVA
Overall, predicting empirical RTs by the RT estimates produced by the hybrid model
resulted in a R 2 of .43 [r = .65; F(2, 70) = 52.24, p < .01]. However, unlike previously
observed for the comparisons to a variable standard (see above) the strictly decomposed and
the hybrid model did not perform similarly for comparisons to an internal standard. No
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