## 3 Results and Discussion
### Statistical Features  
First of all, before moving forward with any relevant statistical process, the suitability of the normal distribution assumption of the data was verified. For this purpose, [PERSON]'s test was run [45], giving a \(p\)-value of 0.04 [46]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Group ID**} & \(D\) & \(AEDE_{out}\) & \(AEDE_{in}\) & \(I\) \\  & **(nGy h\({}^{-1}\))** & **(mSv y\({}^{-1}\))** & **(mSv y\({}^{-1}\))** & **(mSv y\({}^{-1}\))** \\ \hline G1 & 42.3 & 0.052 & 0.208 & 0.34 \\ \hline G2 & 63.6 & 0.078 & 0.312 & 0.51 \\ \hline G3 & 30.1 & 0.037 & 0.148 & 0.24 \\ \hline G4 & 49.4 & 0.061 & 0.244 & 0.39 \\ \hline G5 & 17.3 & 0.021 & 0.084 & 0.14 \\ \hline G6 & 66.6 & 0.082 & 0.328 & 0.52 \\ \hline G7 & 47.2 & 0.058 & 0.232 & 0.38 \\ \hline G8 & 4.4 & 0.005 & 0.020 & 0.03 \\ \hline G9 & 54.6 & 0.067 & 0.268 & 0.41 \\ \hline G10 & 1.3 & 0.002 & 0.008 & 0.01 \\ \hline Average & 37.7 & 0.046 & 0.185 & 0.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Radiological hazard indices. See text for details [43]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Group ID**} & \(C_{R\alpha}\) & \(C_{Th}\) & \(C_{K}\) \\  & **(Bq kg\({}^{-1}\) d.w.)** & **(Bq kg\({}^{-1}\) d.w.)** & **(Bq kg\({}^{-1}\) d.w.)** \\ \hline G1 & \(12.1\pm 3.8\) & \(23.1\pm 6.5\) & \(546\pm 67\) \\ G2 & \(15.3\pm 4.9\) & \(23.0\pm 6.4\) & \(1022\pm 116\) \\ G3 & \(13.5\pm 4.1\) & \(5.8\pm 2.9\) & \(486\pm 56\) \\ G4 & \(8.3\pm 3.1\) & \(15.2\pm 4.8\) & \(873\pm 98\) \\ G5 & \(10.6\pm 3.3\) & \(13.3\pm 3.9\) & \(104\pm 21\) \\ G6 & \(55.9\pm 6.8\) & \(54.1\pm 6.7\) & \(196\pm 38\) \\ G7 & \(26.5\pm 4.8\) & \(48.5\pm 5.9\) & \(136\pm 25\) \\ G8 & \(3.5\pm 1.8\) & \(1.5\pm 0.9\) & \(43.7\pm 5.8\) \\ G9 & \(80.8\pm 9.8\) & \(26.4\pm 4.8\) & \(32.4\pm 5.1\) \\ G10 & \(0.75\pm 0.18\) & \(1.1\pm 0.2\) & \(7.6\pm 3.8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average specific activities \(C_{R\alpha}\), \(C_{Th}\), and \(C_{K}\), of, respectively, \({}^{226}\)Ra, \({}^{232}\)Th, and \({}^{40}\)K (Bq kg\({}^{-1}\) d.w.), evaluated for the investigated groups of pigments. Moreover, activity concentrations of the investigated radionuclides, together with the radiological indices, were tested for [PERSON]'s correlation analysis, which put forward evidence that variables are all positively correlated. Moreover, the Group IDs, \(C_{Ra}\), \(C_{Th}\), \(C_{K}\), \(D\), \(AEDE_{out}\), \(AEDE_{in}\), and \(I\) variables were elaborated via the PCA algorithm, giving significant factors reported in Table 5.  
The results of PCA analysis are reported in Figure 2, where PC1 and PC2 are put into evidence, accounting for the 95.12% of the total variance. The figure clearly shows that the variables are all positively correlated and in agreement with [PERSON]'s correlation matrix. Moreover, via analysis of the biplot, we can identify four areas that group the considered samples: the first one composed of G1, G2, and G4; the second one of G3 and G8; the third one of G5 and G10; and the last one of G6, G7, and G9. The different behavior evidenced by the PCA algorithm can be strictly dependent on the chemical composition and mineralogical nature of the investigated pigments [47; 48; 49; 50; 51]. Finally, the dendrogram reporting the HCA statistical results is shown in Figure 3.  
The automatic cut (dotted line), placed on the dendrogram at a 0.104 distance, involves the formation of five clusters. In detail, the first cluster regrouped G1, G2, and G4, whereas G3 and G8 fell into the second cluster. The third cluster was composed of G5 and G10, whereas the fourth and the fifth clusters were formed of G6 and G7 (the fourth one) and G9 (the fifth one), respectively. From HCA, samples were grouped into five clusters (C1, C2, C3, C4, and C5) (see Figure 4), in very good agreement with the results provided by PCA, from which four clearly distinguishable areas are provided. Figure 2: PCA biplot. Green circles represent areas that group the considered samples.