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

Contrarily, data produced by a two-linear model (again including some random noise) must
not be fitted better by a logarithmic model. To test these predictions we simulated the data of
100 participants using both a logarithmic as well as a two-linear model incorporating a
Gaussian random error term and fitted the resulting data in a logarithmic and a two-linear
regression analysis for each of these modelled data sets. Subsequently, adjusted R 2 resulting
from either regression were compared using paired t-tests. The results of the t-tests showed
that logarithmic fitting did account for reliably more variance of the data produced by a
logarithmic model than did two-linear fitting [t(99) = 1.99, p < .05; R 2 log = .94 vs. R 2 two-lin =
.93]. On the other hand, two-linear fitting resulted in a higher adjusted R 2 than did logarithmic
fitting for the data produced by a two-linear model [t(99) = 10.28, p < .001; R 2 log = .87 vs.
R 2 two-lin = .93]. Apart from the fact that all analyses were run on R 2 values adjusted for
differing numbers of free parameters this finding again argues against an overfitting of the
empirical data by the two-linear model.
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