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

found that only the influence of logarithmic overall distance [constant = 1060.03; B = -
126.03; b = - .72, t = 25.29, p < .001] and problem size [B = -2.25; b = - .58, t = 20.53, p <
.001] was significant. Item RTs increased as logarithmic overall distance and problem size
decreased. Contrarily, the influence of unit distance [B = 0.26; b = .02, t = 0.72, p = .47] as
well as absolute unit distance [B = 1.24; b = .05, t = 1.67, p = .10] was not reliable. Again,
these results indicated item RTs as produced by the holistic model not to be determined by
unit-decade compatibility, but rather by measures of overall distance and problem size.
Decomposed model
ANOVA
Corroborating our expectations predicting the empirical RTs by the modelled RT data
showed a reliable R 2 of .50 [r = .71; F(1, 238) = 241.13.99, p < .001] indicating a shared
variance of 50%. More particularly, analyzing the RT data produced by the strictly
decomposed model revealed a reliable main effect of compatibility [F(1, 232) = 23.68, p <
.001] with response latencies following a compatible number pair being significantly shorter
than latencies following a incompatible pair (735 ms vs. 753 ms, respectively). Moreover, this
main effect was moderated by the interaction of compatibility and unit distance in the
expected direction [F(1, 232) = 6.28, p < .05, see Figure 2, Panel C]: the compatibility effect
was reliably more pronounced for number pairs with a large unit distance as compared to
pairs with a small unit distance (28 ms vs. 9 ms, respectively). Thereby, these results clearly
corroborate the notion of decomposed processing of tens and units. Finally, the main effect of
decade distance indicated that number pairs with a large decade distance were responded to
faster than number pairs with a small decade distance [699 ms vs. 789 ms, respectively; F(1,
232) = 573.17, p < .001]. No further main effect or interaction was statistically reliable [all F
< 1.35, all p > .25].
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