## 4 Materials and Methods
### Methodology
#### 4.2.2 Statistical Analyses  
Spearman Correlation Coefficient (\(\rho\))  
The Spearman correlation determines if two continuous or ordinal variables have a monotonic connection. The variables in a monotonic connection tend to change simultaneously but not always at the same rate, which is suitable for our data. It is possible to have a perfect Spearman correlation of 1 or \(-1\) when there are no repeated data values [44]. Principal Component Analysis  
Large datasets are becoming more common across a wide range of fields. Methods for interpreting such datasets must dramatically reduce their dimensionality while keeping the majority of the information in the data. Several techniques have been created for this purpose, but PCA is one of the oldest and most commonly utilized [45]. The data set involved in this study was subjected to a PCA analysis to reduce dimensionality and arrange parameters within a lower group of factors. Cluster Analysis  
There are many clustering algorithms to choose from and no single best clustering algorithm for all cases. Instead, it is a good idea to explore a range of clustering algorithms and different configurations for each algorithm. This study used two main clustering algorithms, the hierarchical (HCA) and the TwoStep. The HCA is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types [46]. This algorithm is the primary statistical method for finding relatively homogeneous clusters of cases based on measured characteristics. It starts with each case as a separate cluster, i.e., there are as many clusters as cases, and then combines the clusters sequentially, reducing the number of clusters at each step until only one cluster is left. The clustering method uses the dissimilarities or distances between objects when forming the clusters. The SPSS program calculates 'distances' between data points in terms of the specified variables. A hierarchical tree diagram, called a dendrogram on SPSS, can be produced to show the linkage points. The clusters are linked at increasing levels of dissimilarity [13]. Using the TwoStep Cluster Analysis process, one can discover naturally occurring groupings (or clusters) within a dataset that would otherwise be undetectable using traditional statistical methods. The algorithm used by this procedure has several beneficial characteristics that distinguish it from typical clustering algorithms [46], including the following: In the statistical software package SPSS, a method known as two-step cluster analysis is utilized to analyze massive databases [47]. TwoStep cluster analysis is a technique that takes only a single pass through the data set to be effective [48]. The method is divided into two essential steps: the first is the initial grouping of data into small subclusters, followed by the treatment of these subclusters as independent observations, and the second is the subsequent treatment of these subclusters as separate observations [46; 48]. The distance criteria will determine whether the observation will be added to an existing cluster or whether a new cluster will be generated based on the observation. The hierarchical cluster approach is used to organize these new data into more manageable groups [48]. It is feasible for the algorithm of the TwoStep cluster analysis to determine the number of clusters that may be assigned or the number of clusters that can be determined by hand. The second stage is groping, in which the subclusters serve as the foundation for the analysis and are then sorted into the necessary number of clusters by the algorithm. Since the number of subclusters is less than the number of observations, it is simple to utilize the usual grouping methods to organize the data [46; 48]. The technique becomes increasingly precise as the number of subclusters increases [49]. The dataset was subjected to a two-step cluster analysis.