This is an anonymized version of the pre-registration. It was created by the author(s) to use during peer-review.

A non-anonymized version (containing author names) should be made available by the authors when the work it supports is made public.

No, no data have been collected for this study yet.

To answer the question of how does the brain process numbers we investigate functional lateralization of number processing considering individual characteristics (handedness), cultural characteristics (reading direction), and stimulus characteristics (magnitude size).

Study 1: Anodal tDCS over the left IPS vs. sham decreases reaction time (RT) for number comparison in right-handers, while anodal tDCS over the right IPS vs. sham decreases RT in left-handers.

Study 2: Anodal tDCS over the left IPS vs. sham and over the right IPS vs. sham differentiates RT in number comparison between left and right readers.

Study 3: Anodal tDCS over the left IPS vs. sham decreases RT more in number comparison with small distance, while anodal tDCS over the right IPS vs. sham decreases RT more with large distance.

In the symbolic number comparison task, two numbers will be presented and participants are asked to decide which one is larger. The number pairs will consist of single-digit or two-digit numbers with small and large distances (unit-decade compatibility will be counterbalanced). The dependent variable will be reaction time (RT).

Design: Randomized, counterbalanced, single-blind design.

Stimulation conditions: anodal stimulation over the left IPS, anodal stimulation over the right IPS, and sham stimulation.

Stimulus conditions: single and two-digit numbers.

Study 1: The German sample will be categorized based on handedness: right-handers vs. left-handers.

Study 2: The right-handers will be categorized based on reading direction: left to right readers (German) vs. right to left readers (Iranian).

Study 3: Only German right-handers will be considered; the focus is on the within-subject factor distance: small vs. large.

Study 1: 3 stimulation (left IPS vs. right IPS vs. sham) x 2 handedness (left vs. right) mixed ANOVAs will be conducted separately for single-digit and two-digit number comparison. Paired t-tests for right IPS vs. sham for left-handers and left IPS vs. sham for right-handers are planned.

Study 2: 3 stimulation (left IPS vs. right IPS vs. sham) x 2 reading direction (left to right vs. right to left) mixed ANOVAs will be conducted separately for single-digit and two-digit number comparison. To compare stimulation vs. sham, paired t-tests within each group are planned.

Study 3: 3 stimulation (left IPS vs. right IPS vs. sham) x 2 distance (small vs. large) within-subject ANOVAs will be conducted separately for single-digit and two-digit number comparison. Paired t-tests for left IPS vs. sham for small distance and right IPS vs. sham for large distance are planned.

All analyses will be complemented by Bayesian ANOVAs in case of null effects.

Exclusion criteria for participants: mixed-handers, non-German or non-Farsi mother tongue and German-Farsi bilinguals, age below 18 and above 50 years old, technical problems with stimulation (e.g., stimulation less than 15 min), non-completion of the study, accuracy below 75%.

Exclusion criteria for trials: incorrectly solved trials (errors, missings), RT below 200 ms (anticipations) and above 1500 ms, RT more than 3 SD above or below the individual M (iterative trimming procedure).

No need to justify decision, but be precise about

Sample size estimation according to power analyses (G*Power, version 3.1) for the planned ANOVAs to detect effects of partial eta squared of 0.02 (power = .90; α = 0.05;):

Study 1: A minimum total sample of N = 53 German right-handers and N = 53 German left-handers

Study 2: A minimum total sample of N = 53 German right-handers and N = 53 Iranian right-handers.

Study 3: A minimum total sample of N = 54 German right-handers.

(e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)

Further analyses will compare stimulation effects between single-digit and two-digit number comparison. Additional analyses will consider stimulation effects on the distance and compatibility effects.

Study 2: Groups will be compared regarding left start vs. right start finger counting direction by a chi-squared test. In case of significance, a 3 (stimulation) x 2 (reading direction) x 2 (finger counting direction) ANOVA will be conducted or the analysis will be conducted only on one finger counting direction, if the cell size is too small.