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

solution to an addition problem we restricted analyses to those items involving a correct
solution probe 1 .
Classification performance in terms of response latencies and error rates was evaluated
by a two-way ANOVA (analysis of variance) incorporating the factors problem size (small vs.
large) and carry (required vs. not required). To approximate normal distribution error rates
were arcsine transformed prior to the analysis.
For the analysis of the eye fixation behaviour only problems with a large problem size
were recruited. In the group of problems with a small problem size there were several
problems involving a single-digit summand (e.g. 9 + 14 = 23). As in these trials the number of
decade digits may vary, focussing on the problems with a large problem size ensured that the
subsequent evaluation of the distribution of fixations over tens and units was not confounded
by the fact that sometimes there were no decade digits to look at. For the subsequent
evaluation of eye fixation behaviour in terms of total reading times on either the decade or
unit digit of the first summand, the second summand, and the result areas of interest were
defined: Each digit was centred in an area of interest 75 pixels wide and 180 pixels high.
Whenever a fixation fell within one of these interest areas it was considered as a fixation on
the corresponding decade or unit digit. Subsequently, the total reading time for each interest
area was computed and submitted to a 2 × 3 × 2 ANOVA (analysis of variance) with the
factors carry (required vs. not required), problem element (first summand vs. second
summand vs. result) and digit identity (decade vs. unit digit). Whenever necessary, post-hoc
comparisons were conducted using the Games-Howell test at a significance level of p < .05 to
account for differing variances. Additionally, in the cases the sphericity assumption of the
ANOVA was violated the Greenhouse-Geisser coefficient (GG) is given to allow for an
1 Please note that we are well aware that analyzing the data of the incorrectly solved problems may be
informative on possible strategy differences between processing these and correctly solved problems and thus,
may further substantiate the observations by Menon et al. (2002). However, for the sake of brevity and lucidity
the current study focused on evaluating processes underlying the carry effect in correctly solved addition
problems.
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