## 5 Materials and Methods
### Data Processing  
In order to determine the most suitable set of elements for investigating the variance of the whole repertory of ceramic fragments, the relative standard deviations (RSD) were calculated (Table 1). If the whole repertory of samples is considered, most of the elements showed an RSD\(\%\) ranging between 16 and 93%, with the exception of As and Pb, which were characterized by higher values (167% and 269%, respectively). From a more in-depth investigation of the single repertories from the reference sites, the reasons for the high RSD values for As and Pb were found to have resulted from their being mainly correlated to the _sparse-glazed_ ware samples from Donoratico, suggesting that an external factor was responsible for the observed Pb fluctuations. The _sparse-glazed_ ware s consisted of single-fired lead-glazed ceramics, where a suspension of PbO (alone or mixed with SiO\({}_{2}\)) was applied to leather-hard bodies to obtain a transparent coating [81]. Depending on the firing conditions, a more or less extended diffusion of lead within the ceramic body could occur and the detection of \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & \\ \hline
**Element** & **K** & **Ca** & **Ti** & **Cr** & **Mn** & **Fe** & **Ni** & **Cu** & **Zn** & **As** & **Zr** & **Pb** & **Rb** & **Sr** \\ \hline Mean (ppm) & 26,868 & 26,662 & 4197 & 221 & 639 & 34,949 & 75 & 29 & 76 & 40 & 209 & 1781 & 186 & 163 \\ Population STD & 4240 & 28,373 & 815 & 141 & 356 & 10,049 & 42 & 13 & 20 & 67 & 59 & 4790 & 58 & 104 \\ RSD \% & 16 & 93 & 19 & 64 & 56 & 29 & 56 & 46 & 26 & 167 & 28 & 269 & 31 & 64 \\ \hline \multicolumn{11}{c}{Castellina} \\ \hline
**Element** & **K** & **Ca** & **Ti** & **Cr** & **Mn** & **Fe** & **Ni** & **Cu** & **Zn** & **As** & **Zr** & **Pb** & **Rb** & **Sr** \\ \hline Mean (ppm) & 28,360 & 29,768 & 4139 & 171 & 567 & 31,807 & 60 & 25 & 72 & 34 & 228 & 482 & 214 & 192 \\ Population STD & 4284 & 28,531 & 743 & 101 & 311 & 9820 & 31 & 10 & 19 & 30 & 63 & 2107 & 52 & 96 \\ RSD \% & 15 & 89 & 18 & 59 & 55 & 31 & 52 & 40 & 26 & 87 & 27 & 437 & 24 & 50 \\ \hline \multicolumn{11}{c}{Donoratico} \\ \hline
**Element** & **K** & **Ca** & **Ti** & **Cr** & **Mn** & **Fe** & **Ni** & **Cu** & **Zn** & **As** & **Zr** & **Pb** & **Rb** & **Sr** \\ \hline Mean (ppm) & 24,651 & 5588 & 4982 & 440 & 695 & 43,026 & 139 & 30 & 78 & 51 & 210 & 3916 & 128 & 69 \\ Population STD & 2089 & 1380 & 320 & 107 & 414 & 7874 & 23 & 10 & 15 & 110 & 33 & 5522 & 10 & 10 \\ RSD \% & 8 & 25 & 6 & 24 & 59 & 18 & 16 & 34 & 20 & 216 & 15 & 141 & 8 & 14 \\ \hline \multicolumn{11}{c}{Monterotondo Maritimo} \\ \hline
**Element** & **K** & **Ca** & **Ti** & **Cr** & **Mn** & **Fe** & **Ni** & **Cu** & **Zn** & **As** & **Zr** & **Pb** & **Rb** & **Sr** \\ \hline Mean (ppm) & 27,318 & 39,202 & 4339 & 178 & 924 & 39,742 & 70 & 35 & 90 & 30 & 147 & 24 & 146 & 171 \\ Population STD & 4529 & 20,773 & 687 & 23 & 336 & 5801 & 28 & 11 & 13 & 23 & 29 & 6 & 50 & 97 \\ RSD \% & 17 & 53 & 16 & 13 & 36 & 14 & 40 & 30 & 15 & 75 & 20 & 24 & 34 & 57 \\ \hline \multicolumn{11}{c}{Rococastrada} \\ \hline
**Element** & **K** & **Ca** & **Ti** & **Cr** & **Mn** & **Fe** & **Ni** & **Cu** & **Zn** & **As** & **Zr** & **Pb** & **Rb** & **Sr** \\ \hline Mean (ppm) & 22,435 & 8285 & 3120 & 152 & 510 & 29,533 & 41 & 26 & 67 & 35 & 159 & 39 & 201 & 82 \\ Population STD & 2728 & 2643 & 538 & 47 & 339 & 7915 & 13 & 8 & 17 & 44 & 43 & 10 & 47 & 38 \\ RSD \% & 12 & 32 & 17 & 31 & 66 & 27 & 32 & 31 & 25 & 127 & 27 & 27 & 24 & 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The RSDs that are representative of each element, calculated from all assays taken from the powdered samples. RSD values of the whole repertory, as well as from the assemblages from the reference sites of Castellina, Donoratico, Monterotondo Maritimo and Roccastrada, are reported. high levels of lead in some of the glazed samples was considered to be a consequence of the incomplete removal of the external layers during sampling procedures.