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

Estimated
value
100
75
Breakpoint
logarithmic fitting:
y = 16.91ln(x) - 2.27
R 2 = 0.93
50
25
0
two-linear fitting:
y one-digit = 3.73x + 2.70
y two-digit = 0.40x + 40.47
R 2 = 0.96
0 10 20 30 40 50 60 70 80 90 100
Actual value
Figure 2: Results of both logarithmic (dashed line) and two-linear (solid line) fitting
for the mean estimates across all German-speaking children
(see Moeller et al., 2009 for further details)
Similar to the Austrian children, for Italian children logarithmic fitting accounted for a
reliably larger part of overall variance than did simple linear fitting for the 0-to-100 scale
[t(96) = 3.46, p < .01] with R² log = .68 and R² lin = .63. However, comparable to the results for
the German-speaking children two-linear fitting was significantly better than the logarithmic
fitting in terms of descriptive adequacy for Italian children as well [t(96) = 11.73; p < .001].
Average adjusted R² two-lin was .82 compared to an R² lin of .68. 2
Two more observations corroborate the superior fit of the two-linear model. First, as
found for the German-speaking sample, inspection of the correlation between the slopes of the
two linear segments of the two-linear model showed that these were negatively correlated (r =
- .42; n = 97; see Moeller et al., 2009a for detailed explanations). Second, inspection of the
distribution of the individual breakpoints of the participating children revealed another
2 Please note that results were identical when excluding all teen numbers from the analyses which are
constructed differently in German and Italian number words [Italian-speaking: t(96) = 13.82, p < .001, mean of
individual R 2 for logarithmic fitting R 2 log = .69, mean R 2 two-lin = .84; German-speaking: t(127) = 5.82, p < .001,
mean R 2 log = .70, mean R 2 two-lin = .83]. This suggested that the current results were not driven by differences at
the level of teen numbers which are a special case in both languages.
100