# Estimating Tetrachloroethene Sorption Coefficients Based on Soil Properties in Organic-Poor Soils
## 3 Results and Discussion
### Statistical Data Analysis
As the result of the AHC analysis, soil samples were grouped into three distinct classes of soils, primarily differentiated by their textural characteristics: Class 1 included fine- to coarser-grained soils with predominantly sand particles content (>50%), Class 2 comprised the finest soil types with lower sand particles content (<50%), and Class 3 consisted of high or predominantly silt (>50%) and small sand particle content (<50%) (Figure 3B). The resulting clusters showed strong agreement with the traditional sections in the soil textural triangle, validating the effectiveness of the clustering approach. These findings are consistent with prior research that highlights the relationship between particle size distribution and sorption behavior. The observed classifications enhance the accuracy of sorption models by incorporating textural differences, which influence sorption capacity. This supports the broader understanding of how soil texture impacts the interactions between contaminants and soil particles [22]. The Kruskal-Wallis test was employed to assess the statistical significance of individual soil properties in influencing sample distribution across clusters. The results with Chi-squared (Chi\({}^{2}\)) values exceeding 5.991 (degrees of freedom (df) = 2) and \(p\)-values below 0.05 indicated statistically significant differences across the three clusters. Significant differences (\(p<\alpha\)) were observed in OC, clay, silt, and sand content (Table 4). These findings corroborated the initial assumptions derived from PCA and Pearson's test. Mean values of significant soil properties for each cluster are summarized in Table S4. LDA elucidated relationships within clusters based on significant soil properties: OC, clay, silt, and sand content (%). Soils in the first class, predominantly sandy, exhibited lower organic carbon content compared to soils in the second and third classes (Table 5). Class 2, which comprised the finest particles, exhibited the highest \(K_{\text{d}}\) values, while Class 1, consisting mainly of sandy soils, showed the lowest \(K_{\text{d}}\). This trend aligns with the general principle that smaller particles tend to have higher sorption capacities due to their larger surface area and greater cation exchange capacity [54; 55; 56; 57; 58]. Figure 4 shows the correlation of initial variables with two factors. The first factor (F1) accounted for 70.72% of the variance and strongly correlated with sand and clay content; this indicates that these variables are important for distinguishing between groups. Factor 2 (F2) showed strong correlations with silt and clay content (Figure 4A). The score plot with confidence ellipses (Figure 4B) represents each observation on the factor axes, with observations classified based on highest probability of belonging. All observations fell within the 95% confidence ellipses. The confusion matrix summarized the classification of observations into three classes (14, 14, and 6 observations per class, respectively). These results indicate 100% accuracy in discrimination, demonstrating accurate sample discrimination based on four significant parameters (OC, clay, silt, and sand content). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Chi-Squared Value** & \(p\)**-Value** \\ \hline
**OC** & 8.394 & 0.015 \\
**Clay** & 23.362 & <0.001 \\
**Silt** & 19.061 & <0.001 \\
**Sand** & 24.964 & <0.001 \\
**Si** & 0.218 & 0.890 \\
**Al** & 0.976 & 0.614 \\ \(\rho_{\text{s}}\) & 0.435 & 0.813 \\ \(\rho_{\text{b}}\) & 0.500 & 0.829 \\ \(\varepsilon\) & 0.520 & 0.771 \\
**SSA** & 3.889 & 0.143 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of Kruskal–Wallis test and corresponding \(p\)-values.