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

Appendix C
On the interrelation of problem size and distance in the stimulus set used
As can be seen from Figure F the interrelation between the two reliable predictors of
item RT produced by the holistic model (i.e., difference between the logarithms of the two
numbers and problem size) is curvilinear rather than linear. However, the multiple linear
regression analysis is not able to account for this. Closer inspection of the figure shows that
the curvilinear relation means that up to a problem size of about 65 the difference between the
logarithms is positively correlated with problem size. Only for items with a problem size
larger than this the correlation becomes negative.
Relation difference of logarithms and problem size
0.7
0.6
Curvilinear: y = -0.0004x 2 + 0.04x - 0.70
R 2 = 0.30
Difference of logarithms
0.5
Linear: y = -0.004x + 0.52
R 2 = 0.08
0.4
0.3
0.2
0.1
0
20
-0.1
30 40 50 60 70 80 90 100
-0.2
Problem size
Figure F: Simple linear and curvilinear fitting of the interrelation of the two reliable
predictors of item RT difference between the logarithms and problem size
At the same time, inspection of Figure G reveals that item RT decreases with
increasing problem size up to exactly the same point of a problem size of about 65; thereby,
indicating a reversed problem size effect. Only for items with a problem size above 70 a
regular problem size effect of item RT increasing together with problem size can be observed.
284