# Assessment of Heavy Metal Distributions in Sand Beaches in the Maltese Islands
## 3 Results and Discussion
### Chemical Analysis
#### 3.1.3 Multivariate Statistical Analysis  
Principal component analysis (PCA) has been used to reduce the number of variations without losing important data to understand relationships between the concentrations obtained for the different heavy metals contained in sand collected from various beaches reviewed in this study. An eigenvalue of 2.2893 with 38.200% and a cumulative percentage of 38.200% for PC1 was obtained, and an eigenvalue of 1.4521 with 24.2% and a cumulative percentage of 62.4% for PC2 was achieved. Upon applying factor analysis, two factors were retained by the number of factor criterion using the Maximum Likelihood/Varimax rotations, where a variance of 1.878 with 31.295% and a cumulative percentage of 31.295% was obtained for Factor 1, and a variance of 0.933 with 15.554% and a cumulative percentage of 46.849% was achieved for Factor 2, as documented in Table 9 below. Strong effects can be identified for the elements with the higher loadings under PC1 for which only Pb content seems to have less of an effect from such influences. Effects on Pb concentrations were highlighted as dominant under PC2, which matches results issued by the rotated factor loadings under F1 and F2 in Table 9. This could possibly indicate that Cu, Fe, Mn, Sr, and Zn have a prevalent lithogenic origin, while Pb content could be affected more by anthropogenic sources. Upon observation of factor loadings, it can be noted that Cu and Zn may also be attributed to having anthropogenic relation, and thus such elemental concentrations in the sand could originate from mixed sources--natural and human-induced. A biplot (Figure 2a), a principal component loadings plot (Figure 2b), and a 3-D scatterplot (Figure 2c) are shown in Figure 2. This shows that the data obtained could be grouped into four main clusters, depicted by the differently coloured data points. Most concentrations of the elements studied obtained from the different locations can be grouped but some outliers can be easily identified. In-depth analysis of such outlier data points showed that these results were obtained from samples collected close to areas of higher human activity, namely food tills, restaurants or kiosks, and renting tills for beach leisure and water sport activities. At these sampling points, higher levels of Pb and Cu were also noted. This result matches that obtained in the FA applied, from which it could be concluded that Pb and Cu could be partly attributed to anthropogenic origin. This requires further scientific analysis to outline the real effects of such human activities on local beaches \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **PC1** & **PC2** & **F1** & **F2** \\ \hline
**Cu** & 0.605 & _0.468_ & _0.359_ & 0.676 \\
**Fe** & 0.780 & \(-\)0.099 & 0.752 & _0.230_ \\
**Mn** & 0.879 & \(-\)_0.265_ & 0.910 & 0.120 \\
**Pb** & _0.226_ & 0.822 & \(-\)0.132 & 0.842 \\
**Sr** & \(-\)0.678 & _0.487_ & \(-\)0.819 & 0.164 \\
**Zn** & 0.600 & _0.286_ & _0.429_ & 0.507 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: PCA initial factor loadings matrix and rotated factor loadings matrix. and their long-term effects on beach life, both in terms of pollution and health hazards to natural resources and human life. The clusters which resulted from the biplot and PCA scatterplot were further scrutinised by applying cluster analysis. CA was used to group similar concentrations obtained across sampling points across all bays analysed, as illustrated in Figure 3.  
Four main groups have been identified, matching results gained through conducting the PCA and FA. From the heat map included, the first cluster shows that a large number of samples had similar concentrations of Fe, Mn, and Sr, while it can be noted that an outlier for Mn and a couple for Zn were present at samples collected from St. George's Bay. The second cluster was mapped on fewer number of samples and presented all the samples that had higher Sr content.