## 4 Results and Discussion
### Statistical Features  
The radiological parameters obtained from the measured activity concentrations of \({}^{40}\)K, \({}^{226}\)Ra and \({}^{232}\)Th were subjected to Pearson's correlation analysis, with the aim to deduce the interdependency and identify any existing relationships between the radiological indices and the concentrations of the radionuclides. This will help in making valid assessments concerning the nature and distribution of these radionuclides in the study area. The results of the Pearson's correlation coefficients are presented in Table 4. Among the negative correlations, the most interesting are those between \({}^{40}\)K and \({}^{226}\)Ra (\(-0.287\)) and between \({}^{40}\)K and \({}^{232}\)Th (\(-0.305\)), while a perfect positive correlation is found between absorbed dose rate and effective dose outdoors (1.00), and between Ra\({}_{\text{eq}}\) and absorbed dose rate (1.00) and effective dose outdoors (1.00). The correlations of the three radionuclides are positive and in agreement with all the radiological parameters considered in this study at \(p<0.01\), except for correlations between \({}^{226}\)Ra and H\({}_{\text{in}}\) (0.739) and between \({}^{232}\)Th and H\({}_{\text{in}}\) (0.719), obtained at \(p<0.05\). Moreover, \({}^{226}\)Ra and \({}^{232}\)Th are negatively correlated with the annual effective dose equivalent indoors (\(-0.378\) and \(-0.281\), respectively). The radiological parameters are positively and significantly correlated with each other, showing direct relationships. In order to better define the relationships among the specific activities of \({}^{226}\)Ra, \({}^{232}\)Th and \({}^{40}\)K, the PCA multivariate statistical method was carried out. The geological feature of sediments is the most important variable, neglecting the others (erosive power of \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{6}{c}{**Pearson Correlation Matrix (n.)**} & \\ \hline \multirow{3}{*}{**Variables**} & \multirow{3}{*}{\({}^{226}\)Ra} & \multirow{3}{*}{\({}^{232}\)Th} & \multirow{3}{*}{\({}^{40}\)K} & \multicolumn{3}{c}{**Absorbed Dose Rate**} & \multicolumn{3}{c}{**Effective Dose**} & \multirow{3}{*}{\({\text{{Ra}}}_{\text{eq}}\)**} & \multirow{3}{*}{\({\text{{Ha}}}_{\text{in}}\)} & \multirow{3}{*}{\({\text{{Gamma}}}_{\text{n}}\)} & \multirow{3}{*}{\({\text{{AGED}}}\)} \\  & & & & & **(nGy \(\text{h}^{-1}\))** & & & & & & & \\  & & & & & **(mSv y\({}^{-1}\))** & & & & & & \\ \hline \({}^{226}\)Ra & 1 & 0.649 & \(-0.287\) & 0.468 & 0.465 & \(-0.378\) & 0.468 & 0.559 & 0.739 & 0.464 & 0.417 \\ \({}^{232}\)Th & 0.649 & 1 & \(-0.305\) & 0.546 & 0.536 & \(-0.281\) & 0.546 & 0.666 & 0.719 & 0.553 & 0.494 \\ \({}^{40}\)K & \(-0.287\) & \(-0.305\) & 1 & 0.595 & 0.603 & 0.607 & 0.596 & 0.465 & 0.301 & 0.591 & 0.647 \\ Absorbed Dose & 0.468 & 0.546 & 0.595 & 1 & 1.000 & 0.236 & 1.000 & 0.988 & 0.936 & 0.999 & 0.998 \\ Rate (nGy/h) & & & & & & & & & & & \\ Effective Dose & & & & & & & & & & & \\ outdoors & 0.465 & 0.536 & 0.603 & 1.000 & 1 & 0.245 & 1.000 & 0.986 & 0.933 & 0.998 & 0.998 \\ (mSv/y) & & & & & & & & & & & \\ Effective Dose & & & & & & & & & & & \\ Indoors (mSv/y) & & \(-0.378\) & \(-0.281\) & 0.607 & 0.236 & 0.245 & 1 & 0.237 & 0.148 & 0.002 & 0.223 & 0.275 \\ Ra\({}_{\text{eq}}\) (Bq/kg) & 0.468 & 0.546 & 0.596 & 1.000 & 1.000 & 0.237 & 1 & 0.988 & 0.936 & 0.999 & 0.998 \\ H\({}_{\text{res}}\) & 0.559 & 0.666 & 0.465 & 0.988 & 0.986 & 0.148 & 0.988 & 1 & 0.970 & 0.988 & 0.976 \\ H\({}_{\text{in}}\) & 0.739 & 0.719 & 0.301 & 0.936 & 0.933 & 0.002 & 0.936 & 0.970 & 1 & 0.935 & 0.912 \\ Gamma index I & 0.464 & 0.553 & 0.591 & 0.999 & 0.998 & 0.223 & 0.999 & 0.988 & 0.935 & 1 & 0.996 \\ AGDE (\(\mu\)Sv/y) & 0.417 & 0.494 & 0.647 & 0.998 & 0.998 & 0.275 & 0.998 & 0.976 & 0.912 & 0.996 & 1 \\ \hline \hline \end{tabular} Bold values refer to \(p<0.05\).  
\end{table} 
Table 4: Pearson correlation matrix among the considered variables. rivers, solid transport, selective erosion, weathering, etc.