*2.6. Statistics*

All statistical inference tests were performed using two-tailed tests requiring an a-priory alpha level of 5%. Participants' demographic and clinical data were analyzed using descriptive statistics and a 1-way ANOVA, with the group as a between-subject factor. In the food Stroop task, to capture the maximal emotional and motivational attention elicited by the food cues [63], we focused on the differential effect of HCF and NF images on participants' performance in the task. Therefore, the Stroop bias score (incongruent-congruent) was computed and analyzed using a 2-way mixed model ANOVA (STATISTICA 13; TIBCO Soft Inc., Seattle, WA, USA) design, with image type (HCF and NF) as a within-subjects factor and the group (FAOB, NFAOB, and H-C) as a between-subjects factor. Post-hoc significance tests were Bonferroni corrected. When analyzing the Stroop bias, we controlled for PANAS as well as for VAS-hunger, based on previous addiction Stroop studies [28,40,44], demonstrating the necessity of controlling for variations between participants in hunger and transitory mood states.

All EEG data were analyzed using nonparametric permutation tests (Monte Carlo method), implemented via the FieldTrip toolbox. This method samples the data repeatedly and randomly (10,000 iterations) to evaluate the characteristics of the sample's distribution under the null hypothesis, obviating the need for prior assumptions concerning its normality.

Brain asymmetry power scores were first averaged for three regions of interest (ROI), including frontal (F5, F3, FC5, and FC3), parietal (CP5 and CP3), and occipital (PO5, PO3, and PO7) electrodes. This method was determined based on previous brain asymmetry research in healthy individuals [76] and in the eating behavior domain [77], depicting these ROI and pointing to their validity in studying brain asymmetry. Next, group differences were tested using permutation tests following the ANOVA logic, i.e., pair-wise post-hoc contrasts were tested only if differences between the three groups were first found significant in one of the ROI [73].

ERP components related to the processing of the food images during the food Stroop task were defined prior to the statistical analysis and regardless of group affiliation, using Global Mean Field Power analysis (see Figure A2) and in line with earlier literature [65,78]. We focused our investigation on the Late Positive Potential (LPP) component for two reasons: 1. It reflects the emotional processing of arousing affective pictures [79,80]. 2. It was the only component to show an association with the attention bias induced by the food cues (Figure 5). Note that if not interrupted by another stimulus (i.e., the next trial), the LPP may last a few seconds [79,80]. In contrast, in the current paradigm, this ERP is decreased in preparation for the Stroop word; thus, we subdivided this component into LPPa (300–450 ms) and LPPb (450–495 ms), to better align with differential motivational processes. Three regions of interest (ROI) were defined to capture the anterior and posterior parts of the LPP: frontal (electrodes: F1, Fz, F2, FC1, FCz, FC2), right posterior (P2, P4, P6, P8, PO4, PO6, PO8, O2), and left posterior (P1, P3, P5, P7, PO3, PO5, PO7, O1). Next, mean amplitude differences between HCF and NF were computed for the LPPa and LPPb and subjected to permutation tests as described above.
