Figure 1
Reaction times plotted as a function of the displayed numbers in the non-symbolic (left) and symbolic (right) conditions in Experiment 1. Blue line represents the regression of numerical distance on reaction time, separately for both formats and numbers larger or smaller than the reference (55). Red line represents the mean reaction time for each presented number.
Figure 2
Relation between the distance and size effect unstandardized regression coefficients, displayed on scatterplots and measured with correlation coefficients for dot comparison.
Figure 3
Histogram of participants with significant size or distance effects in Experiment 1 in two digits symbolic (Symbolic) and the dot arrays (Non-symbolic) conditions. The black rectangles (overlap) depict the number of participants showing both effects in both formats.
Table 1
The unstandardized regression coefficients, t and p values for the distance, size, distance-size interaction and ratio effects of the three experimental conditions (non-symbolic, symbolic integer, and symbolic decimal). Distance, size and their interaction effects were evaluated within the same linear mixed model. To evaluate the ratio effect, we employed an additional linear mixed-effects model. In all models, participants were treated as random intercepts to account for individual variability. Degrees of freedom of Distance, Size and their interaction for the non-symbolic, symbolic integer and symbolic decimals are respectively 2.528e+04, 1.286e+04 and 2.940e+04. Degrees of freedom of Ratio for the non-symbolic, symbolic integer and symbolic decimals are respectively 2.528e+04, 1.286e+04 and 2.941e+04.
| FORMAT | DISTANCE EFFECT | SIZE EFFECT | SIZE*DISTANCE EFFECT | RATIO EFFECT | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| coeff | t | p | coeff | t | p | coeff | t | p | coeff | t | p | |
| Non-Symbolic | –9.861e–03 | 17.257 | <.001 | 3.957e–03 | 26.313 | <.001 | 2.261e–05 | 2.007 | .045 | 5.460e–01 | 98.94 | <.001 |
| Symbolic Integers | –2.672e–02 | 11.543 | <.001 | 3.079e–03 | 5.243 | <.001 | 5.782e–04 | 2.558 | .011 | 1.941e–01 | 44.10 | <.001 |
| Symbolic Decimals | –5.123e–03 | 5.302 | <.001 | 1.663e–02 | 3.481 | <.001 | 1.158e–03 | 1.343 | .179 | 6.756e–02 | 9.408 | <.001 |
Table 2
Correlation coefficients of distance and size effect, separately for each format. Significant correlations are shown in bold print.
| CORRELATION WITH OUTLIERS | CORRELATION WITHOUT OUTLIERS | |
|---|---|---|
| Non-Symbolic | –.81 (95% CI[–.92, –.70]) | –.88 (95% CI[–.95, –.81]) |
| Symbolic Integer | –.19 (95% CI[–.49, .11]) | .01 (95% CI[–.30, .32]) |
| Symbolic Decimal | .40 (95% CI[.14, .66]) | .36 (95% CI[.09, .63]) |
| Symbolic Decimal identical DP1 | .11 (95% CI[–.19, .41]) | .11 (95% CI[–.19, .41]) |
| Symbolic Decimal non-identical DP1 | .44 (95% CI[.19, .69]) | .39 (95% CI[.13, .65]) |
Table 3
Correlation coefficients of ratio effects, between each conditions (and sub-conditions inside the Symbolic Decimal). Significant correlations are shown in bold print.
| SYMBOLIC INTEGER | SYMBOLIC DECIMAL | SYMBOLIC DECIMAL IDENTICAL DP1 | SYMBOLIC DECIMAL NON-IDENTICAL DP1 | |
|---|---|---|---|---|
| Non-Symbolic | .56 | –.19 | –.11 | –.26 |
| Symbolic Integer | –.43 | –.36 | –.50 |
Figure 4
Size (right) and distance (left) effects for non-symbolic magnitude comparison, one-digit integers, and decimals in Experiment 2.
Figure 5
Distance effect for non-symbolic (NS), symbolic integer (SI) and symbolic decimal (SD) conditions, and for symbolic decimal identical DP1 (SD-I) and symbolic decimal non-identical DP1 (SD-NI) sub-conditions in Experiment 2.
Figure 6
Histogram of participants with significant size or distance effects in Experiment 2 in the dot arrays (NS), one-digit integer (SI), two-digit decimal (SD) conditions, Symbolic decimal identical DP1 (SD-I) and Symbolic decimal non-identical DP1 (SD-NI) sub-conditions. The black rectangles (overlap) depict the number of participants showing both effects in each condition.