## 4 Initial Analyses and Findings
### Applicability of the Analysis  
After the soil properties have been validated and assessed as suitable, the next step is to check the factorability of the data set. The most common way to determine the applicability is by checking the intercorrelations among the variables and performing tests for sphericity and sampling adequacy.  
Checking the correlations among the variables is a useful first step before proceeding to the analysis. This step is a basic examination of Pearson correlation coefficients between the variables. The relationship between the soil properties should be high enough so that there will be a meaningful interpretation of the underlying relations of soil properties. As a rule of thumb, [PERSON] [59] recommends searching for a coefficient of correlation of at least 0.30. [PERSON] and [PERSON] [64] and [PERSON] et al. [58] approach this factorability check in a similar fashion. They suggested that there should be a substantial number of correlations above 0.30. In this study, the interrelations between the soil properties yielded coefficients of correlation above 0.30 (Table 2). Only calcium carbonate content is found to be negatively correlated with the rest of the soil properties. The reason behind this outcome is that liquid limit, plastic limit, clay content, and montmorillonite content tend to be positively correlated. Meaning that, if one of them increases the others should also increase and vice versa. However, this outcome also suggests that an increase in calcium carbonate content should decrease the rest of the soil properties. Considering, the liquid limit, plastic limit, clay content, and montmorillonite content increase the soil plasticity, the negative correlation of the calcium carbonate content is a sign of its negative effect on the plasticity characteristics of soils.  
The factor analysis generates results based on the correlations between variables. If there is no correlation, then factor analysis cannot be performed. [PERSON]'s test of sphericity measures the overall correlation among the variables and yields only one measurement [58]. If [PERSON]'s test yields a significancy value below 0.05 then the analysis is statistically significant [63; 65]. In this study, [PERSON]'s test generated a significant value below 0.001. Therefore, the outcome of this study has statistical significance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **LL** & **PL** & **Clay Content** & **Montmorillonite** & **CaCO3** \\ \hline
**LL** & 1.000 & 0.871 & 0.639 & 0.918 & \(-\)0.419 \\
**PL** & & 1.000 & 0.477 & 0.841 & \(-\)0.416 \\
**Clay Content** & & & 1.000 & 0.602 & \(-\)0.331 \\
**Montmorillonite** & & & & 1.000 & \(-\)0.485 \\
**CaCO3** & & & & & 1.000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pearson coefficients of correlation between the soil properties.  
Another important consideration before performing the analysis is the measurement of the sampling adequacy. It is a measure of intercorrelations and factorability of the data set. The sampling adequacy, namely Kaiser-Meyer-Olkin (KMO) test, ranges from 0 to 1. If the KMO value is below 0.5, the factorability of the data set is rejected [66]. In this study, the KMO value is calculated as 0.807, which indicates the data are meritorious and factorable [66].