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

data again indicated that decomposed representations of tens and units are necessary to
account for the compatibility effect, even though they did not seem to preclude the existence
of a concomitant representation of overall magnitude.
Contrasting the correlations with empirical data
Finally, to directly compare the individual correlation coefficients reflecting the
interrelation between modelled and empirical data these correlation coefficients were
transformed into Fisher’s Z-values. Contrasting the Z-values showed that the data produced
by the decomposed (Z decomposed = .89) exhibited a descriptively better fit to the empirical data
than the holistic or the hybrid model which was however not statistically reliable (Z holistic =
.78; Z hybrid = .74; difference in z-scores: Z decomposed vs. Z holistic = 1.22; Z decomposed vs. Z yhbrid =
1.59; critical difference at the .05 significance level = ±1.96). The difference between the
model fit of the holistic and the hybrid model was also not statistically reliable (difference in
Z-scores = 0.37).
In summary, the current computational results for comparisons to a variable standard
indicated that (i) all three models were able to simulate the distance effect, (ii) the
compatibility effect cannot be accounted for by a holistic representation of number
magnitude, (iii) the inclusion of a predictor reflecting a measure of overall difference such as
the difference of the logarithms of the to-be-compared numbers was not necessarily
determined by the presence of a holistic representation either and (iv) the more complex
hybrid model did not perform better than the more parsimonious strictly decomposed model.
258