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

child separately to obtain estimation accuracy. To compare overall estimation accuracy
between Italian and Austrian children an univariate ANCOVA with the factor language and
the covariate T-value of CFT1 was computed.
In a second step, R² adjusted by the number of free parameters of the respective model
(i.e., 2 in the case of the logarithmic model vs. 3 in the case of the two-linear model with fixed
breakpoint) as a measure of goodness of fit independent of influences of model proximity
(e.g., Kyllonen, Lohman, & Woltz, 1984) was computed for a linear and a logarithmic fitting
function for each child individually (see also Appendix A for further discussion and analyses
addressing the issue of possible model overfitting). Analogous to Moeller et al. (2009a), for
the scale 0-100 adjusted R² for a segmented two-linear regression with the fixed break point at
10 was computed for each child individually. Mean adjusted R² values for the different fitting
models (simple linear, logarithmic, and two-linear) for the Italian-speaking children were
compared by paired samples t-tests. All pair wise comparisons were Bonferroni-Holm
corrected (Holm, 1979) to account for alpha accumulation in multiple comparisons.
Additionally, R² values were arcsine transformed prior to the analyses as they cannot be
assumed to be normally distributed.
Finally, in a last step estimation performance for items with a small interdigit distance
(i.e., 2; to-be-estimated numbers: 35, 53, 64, and 75) were contrasted to items with a large
interdigit distance (i.e., 3-6; to-be-estimated numbers: 27, 47, 82, 95) to evaluate the origin of
possible language differences. Please note that these two sets of items did not differ in
problem size as reflected by the mean magnitude of the four numbers each [PS; t(3) = 0.35, p
= .75; mean PS for small interdigit distance: 56.75; large interdigit distance: 62.75]. To
substantiate the interpretation of the latter analysis it was evaluated whether the under-
/overestimation possibly provoked when confusing tens and units of these numbers was more
pronounced in German- as compared to Italian-speaking children. As both German- and
Italian-speaking children underestimated above mentioned two-digit numbers (i.e., 27, 35, 47,
97