## 4 Initial Analyses and Findings  
### Validity and Suitability of Soil Properties  
Almost every multivariate statistical analysis requires a data set that is specifically prepared before the analysis. The reliability of the data is almost always a certain measure. However, factor analysis is also sensitive to some other aspects of the data set. Extreme outliers within the data should be discarded. The overall sample size, meaning the soil count, should be adequate, a normal distribution is desired, and linearity should be achieved.  
The first part of the suitability check of the soil properties is to distinguish the extreme outliers in the data set. The factor analysis is prone to fail if extreme outliers are included. Substantially lower or higher values within the data can affect the correlations and distort the factor analysis [56]. Since there is no singular way of measuring outliers, a few methods have been used to distinguish them. Histogram charts and scatter plots of each soil property have been checked since these charts can be used for visual interpretation. The box and whisker diagram is another valid way to spot extreme outliers. After careful examination, extreme outliers were especially found within the liquid limits and calcium carbonate contents. All outliers that may distort the analysis were discarded before proceeding to the next step.  
The next option to validate the soil properties is a reliability analysis. Reliability is a measure of consistency among the data. For this purpose, a reliability coefficient namely Cronbach's alpha can be used. In this study, Cronbach's alpha was computed as 0.65 within liquid and plastic limits, clay content, calcium carbonate and montmorillonite content. A Cronbach's alpha higher than 0.60 is regarded as sufficient in exploratory research [57; 58]. Considering this outcome, the reliability of the soil properties is found to be valid and appropriate for this study.  
The amount of data is another important consideration before initiating the analysis. However, there is no certain fact on the minimum amount [59]. Therefore, many studies have been made considering this topic, and many opinions have been yielded. According to [PERSON] and [PERSON] [60], if there are several high-loading variables in the solution, such as above 0.80, then a data amount of 150 is sufficient (Appendix A). [PERSON] and [PERSON] [61] and [PERSON] [53] noted that if there are four or more variables with factor loadings above 0.60, then any data size would be adequate. [PERSON] et al. [62] suggested a minimum of 100 cases without any other consideration. [PERSON] [63] and [PERSON] et al. [58] have a much more unconservative approach, recommending a minimum sample size of five times the variable size and an optimum amount of ten times the variable size. All things considered, the sample size in this study can be marked as sufficient for the analysis.  
Normal distribution among variables is generally an ignored aspect of factor analysis. Since the main aim of the factor analysis is to describe the relationship between variables, the normality does not affect the results drastically [64]. However, normal distribution among variables is recommended to enhance the solution. Therefore, the normal distribution of the five-soil property was checked individually. The highly regarded methods of checking the normality are using histogram charts, Q-Q pilots and a more direct measure based on skewness and kurtosis. After these checks, the normal distribution of the variables was detected to fail. Linearity of the data was also checked by scatter pilots and measuring the deviation from linearity. Whenever the normality and linearity of the soil properties failed, data transformation was carried out to enhance the analysis.