## 2 Materials and Methods
The scores were recorded, and numerical data were analyzed using the software R Studio (ver. 4.1.1, R Core Team, Vienna, Austria) and the level of statistical significance was set to \(\alpha\) = 0.05 [79]. To assess the interrater reliability, Fleiss' Kappa for \(m\) Raters was used [80]. For the Fleiss' Kappa for \(m\) Raters, the _kappa_ from the _irr_ package was used [81]. For the sample size calculation, trial questionnaire research on the research team and their co-workers was performed (a total number of 20 probands) in order to determine the presumed population proportion that would consider the AI-enhanced pictures more attractive. Afterwards, Equation (1) was used [82]:\[Sample\;size=\frac{\frac{\frac{z^{2}\times P\times(1-P)}{E^{2}}}{1+\frac{z^{2} \times P\times(1-P)}{E^{2}\times N}}}{1+\frac{z^{2}\times P\times(1-P)}{E^{2} \times N}} \tag{1}\]  
where \(z\) is the z-score for the given confidence level (1.96 for 0.95 confidence level), \(P\) is the population proportion (0.9), \(E\) is the margin of error (0.05), and \(N\) is the population size (1800). After substituting into Equation (1), a sample size of 129 respondents was obtained, as demonstrated by Equation (2). \[Sample\;size=\frac{\frac{1.96^{2}\times 0.9\times(1-0.9)}{0.05^{2}}}{1+\frac{1.96 ^{2}\times 0.9\times(1-0.9)}{0.05^{2}\times 1800}}=128.43 \tag{2}\]  
Five pairs of pictures of both male and female faces with highest attractiveness score differences before and after the AI modification were imported into the graphical software Gimp (ver. 2.10.36, Free Software Foundation, Inc., Boston, MA, USA) [83]. In total, 20% of the faces with the highest attractiveness differences were deliberately chosen to try to spot the differences, and correlated given measurements and facial attractiveness. Two layers (before and after AI enhancement) were superimposed, and by manipulating translucency, the distances of the selected facial anthropometric points (Table 1) were measured in both pictures and then compared. The anthropometric points to be studied were selected by an anthropologist. Percentual change for the selected parameters and mean values were calculated and analyzed. In addition, to demonstrate the power of AI against the power of AI, [PERSON] (OpenAI, San Francisco, CA, USA) was asked to compare each pair of the pictures [84]. The results were then analyzed in several ways:  
* Which of the two faces (AI-enhanced or original) was considered more appealing? * What was the difference of the numeric attractiveness score they achieved? * What facial modifications were responsible for the biggest score differences? * Were the observed changes located in the lower facial third? \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abbreviation** & **Craniometric Points** & **Significance** \\ \hline Ch-Ch & Ch—chelition & Mouth width \\ \hline Go-Go & Go—gonion & Mandible width \\ \hline Zy-Zy & Zy—zygion & Middle face width \\ \hline Tri-Me & Tri—trichion, Me—menton & Face height \\ \hline Sl-Me & Sl—sublabiale, Me—menton & Chin height \\ \hline Sn-Me & Sn—subnasale, Me—menton & The distance from the nose to chin \\ \hline N-Me & N—nasion, Me—menton & Anterior face height \\ \hline Al-Al & Al—alare & Nose width \\ \hline Ft-Ft & Ft—frontotemporal & The distance of the most outer points of superciliary arches on the frontozygomatic suture \\ \hline Fz-Fz & Fz—frontozygomaticus & The distance of the most outer points of superciliary arches \\ \hline Ps-Pi & Ps/i—palpebrale superius/inferius & Eye height \\ \hline Et-Etct & Ext—exocanthinon & Eye width \\ \hline Li-Cph & Li—labrale inferius, & The distance between the upper and lower lip lines \\  & Cph—crista philtri & \\ \hline Prn-Me & Prn—pronasale, Me—menton & The distance between the nose tip and chin \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The facial anthropometric points selected to compare the pairs of pictures. The pair of male pictures (original and after the AI enhancement) and the attractiveness score difference for the pair is depicted in Figures 5 and 6, respectively.