## 3 Results and Discussion
### Statistical Features  
The sphericity (or Bartlett) test was preliminarily conducted with the aim of making multivariate treatments more reliable and statistically significant, furnishing a \(p\)-value equal to 0.04. Thus, considering that a high statistical significance of the data is ensured for \(p\)-values \(<\) 0.05, it follows that starting from reliable data, the results of the calculation algorithms will also be trustworthy [45]. Furthermore, in order to understand any possible relationship between the different variables, expressed as concentrations of the detected potentially toxic elements, the Pearson correlation matrix was calculated. The results of the Pearson's correlation coefficients are presented in Table 4.  
All positive correlations were detected, with the exception of CSb-CII (\(-\)0.08), CCd-CNi (\(-\)0.05), CCd-CCl (\(-\)0.04), CPb-CSb (\(-\)0.03). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Variables** & **CAs** & **CCd** & **CCu** & **CHg** & **CNi** & **CPb** & **CSb** & **CII** & **CZn** \\ \hline CAs & **1.00** & 0.03 & 0.61 & 0.43 & **0.76** & **0.67** & 0.19 & \(-\)0.15 & **0.80** \\ CCd & 0.03 & **1.00** & 0.15 & 0.13 & \(-\)0.05 & 0.24 & 0.16 & \(-\)0.04 & 0.04 \\ CCu & 0.61 & 0.15 & **1.00** & **0.68** & **0.68** & **0.71** & 0.18 & 0.27 & **0.72** \\ CH\({}_{\text{B}}\) & 0.43 & 0.13 & **0.68** & **1.00** & 0.44 & 0.30 & 0.55 & 0.01 & 0.45 \\ CNi & **0.76** & \(-\)0.05 & **0.68** & 0.44 & **1.00** & 0.39 & 0.28 & 0.23 & **0.97** \\ CPb & **0.67** & 0.24 & **0.71** & 0.30 & 0.39 & **1.00** & \(-\)0.03 & 0.16 & 0.48 \\ CSb & 0.19 & 0.16 & 0.18 & 0.55 & 0.28 & \(-\)0.03 & **1.00** & \(-\)0.08 & 0.22 \\ CII & \(-\)0.15 & \(-\)0.04 & 0.27 & 0.01 & 0.23 & 0.16 & \(-\)0.08 & **1.00** & 0.18 \\ CZn & **0.80** & 0.04 & **0.72** & 0.45 & **0.97** & 0.48 & 0.22 & 0.18 & **1.00** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pearson correlation matrix among the considered variables. Values in bold are different from 0 at the significance level \(\alpha\) = 0.05. As far as the PCA algorithm is concerned, ten variables (Site IDs, C\({}_{\text{As}}\), C\({}_{\text{Cd}}\), C\({}_{\text{Cu}}\), C\({}_{\text{Hg}}\), C\({}_{\text{Ni}}\), C\({}_{\text{Pb}}\), C\({}_{\text{Sb}}\), C\({}_{\text{TI}}\) and C\({}_{\text{Zn}}\)) were processed, also performing the Varimax rotation [46]. The obtained results are reported in Figure 2.  
As can be seen from a first inspection of the figure, the PCA and Pearson matrix results appear to be coherent with each other. In particular, PCA elaboration allowed us to clearly discriminate three groups of samples. The first is formed by pyroclastic products from ID 6, 8 and 10 sites (yellow area in Figure 2), and it is clearly separated from the others on the first main component (PC1). The second group contains pyroclastic products from ID 1, 4, 5, 7 and 9 sites (salmon area in Figure 2) whose variance is more justified by the PC2. The last ideal group seems to be formed by pyroclastic wastes from ID 2 and 3 sites (light-blue area in Figure 2). It is worth noting that the difference in the behavior of samples of the same type, i.e., pyroclastic wastes from previous volcanic activities, may depend on the different residence time of the pyroclastic products in the soil, and on the possible differential pollution that the pyroclastic waste samples have undergone [47]. Figure 3 shows the outcome dendrogram of the HCA. The dotted line represents the cut automatically made by the calculation algorithm, which allows us to identify the formation of three clusters (C1, C2 and C3). Figure 2: 2D plots of the first two PCs obtained through PCA elaboration after the Varimax rotation. The C1 cluster (green color in Figure 3) is made up of 60% of the samples (ID 1, 2, 3, 4, 5 and 7 sites), while 30% of the pyroclastic products fall within the C2 cluster (blue color in Figure 3) and come from the ID 6, 9 and 10 sites. The last cluster (C3) is instead formed by samples from the ID 8 site.