*3.2. Hemispheric Brain Asymmetry*

No differences in the raw EEG power were found between the groups (see Figure A3). Non-parametrical permutation tests based on F statistics indicated that brain alpha asymmetry

scores differed between the three groups in the frontal (F = 3.45 (*<sup>n</sup>* <sup>=</sup> 49), *p* = 0.03) but not in the parietal (F = 2.33 (*<sup>n</sup>* <sup>=</sup> 49), *p* = 0.09) or the occipital ROI (F = 2.52 (*<sup>n</sup>* <sup>=</sup> 49), *p* = 0.08; (Figure 2)). Post-hoc contrasts indicated that the FAOB group showed lower left alpha brain asymmetry scores (i.e., lower left alpha compared with the right alpha), differently from the NFAOB group, in the frontal and occipital ROI (frontal (*t* = 2.36 (*<sup>n</sup>* <sup>=</sup> 33), *p* = 0.02), parietal (t = 1.68 (*<sup>n</sup>* <sup>=</sup> 33), *p* = 0.11), and occipital (F = 2.54 (*<sup>n</sup>* <sup>=</sup> 33), *p* = 0.01)), but neither of the overweight and obese groups statistically differed from the H-C group. Since the alpha power is a brain frequency inversely related to local brain activity [81], the lower alpha brain asymmetry means greater left, compared with the right, hemispheric dominance in the FAOB group compared with the NFAOB group. Note that nonparametrical tests do not use F or *t* tables; hence, the sample size is detailed rather than the degrees of freedom. Considering previous research [82], we tested for all the participants together the correlation between left alpha brain asymmetry and gender, which was not significant (*r* = 0.19 *p* = 0.15). Therefore, we did not use gender as a covariate in our electrophysiological analyses.

**Figure 2.** Group differences in brain alpha asymmetry. (**a**) Topographic plots of the mean group left alpha asymmetry power (upper row) and the group contrasts (lower row), for the FAOB, NFAOB, and H-C groups. Note that the maps are based on subtraction of alpha power between symmetric electrode pairs and are thus left/right mirrored. (**b**) Mean and SEM of left alpha asymmetry power for each group in the frontal, parietal and occipital ROI. Electrodes included in each ROI are marked in dark blue in 2a. \**p* ≤ 0.05; \*\**p* ≤ 0.01. FAOB: overweight and obese with food addiction. NFAOB: overweight and obese without food addiction. H-C: healthy controls. SEM: standard error of mean. ROI: region of interest.
