# Cluster Analysis with K-Mean versus K-Medoid in Financial Performance Evaluation
## 4 Research Results  
### Descriptive Statistical Results  
As shown in the previous section (Table 2), based on the descriptive analysis (mean, minimum--maximum values, standard deviation), the statistical results clearly show that the elements are heterogeneous, with a very large range of data for all financial indicators. Thus, in the case of the Hungarian database (N = 211), as well as in the case of the Romanian database (N = 690), very high differences between minimum and maximum values are noticed for all three financial indicators (ROS, ROA and ROE).  
Therefore, before beginning the grouping process, outliers were identified. An \"outlier\" is defined by [PERSON] and [PERSON] [61] as \"one that appears to deviate markedly from other members of the sample in which it occurs\" (p. 85). According to [PERSON] [62], \"outliers deviate significantly from the expectations\".  
Extreme values were identified step by step using the BoxPlot chart, separately for each database and separately for each indicator (ROS, ROA, ROE). Many authors describe the BoxPlot diagram method as a possible (visually) method to detect outliers [61; 63; 64; 65]. The BoxPlot chart helped us visually identify values that are outside the \"normal\" \"value clouds\", values that can distort and tilt the group average.  
Based on several boxplot charts, and eliminating the outliers step by step, we have reached the following minimum and maximum values for the three financial indicators (ROS, ROA, ROE) separately for the Romanian and the Hungarian companies (see Tables 4 and 5, Figures 1 and 2). For the Hungarian companies, the minimum and maximum values are as follows: for ROS, \(-36.36\%\) and \(+32.00\%\); for ROA, \(-83.17\%\) and \(+55.85\%\); and for ROE, \(-173.88\%\) and \(+127.87\%\). The values of the financial indicators in the case of the Romanian companies are: \(-174.19\%\) and \(+63.97\%\) (for ROS); \(-370.43\%\) and \(+148.75\%\) (for ROA); and \(-487.92\%\) and \(+216.63\%\) (for ROE).  
The distribution of the mean values for ROS (Return on Sales), ROA (Return on Assets) and ROE (Return on Equity) without outliers is shown in Figures 1 and 2.  
In the end, the numbers of the remaining companies in the two databases were as follows: the Romanian database contained 640, while the Hungarian database contained 190 companies.  
The kurtosis and skewness indicators (Tables 4 and 5) also support what the previous indicators have shown: the companies are very different from the normal distribution. Examining the values of these statistical indicators, we can definitely conclude that the companies differ greatly from the normal distribution for both countries. These results confirmed our initial assumption that the differences between the individuals (companies) in the database are significant, so homogeneous grouping is required.  
The results of the correlation analysis (Table 4) highlighted that, in the case of Hungarian companies, ROS was positively correlated with both the ROA (r = 0.668) and ROE (r = 0.395). The same positive correlation (but of a lower intensity) was seen between all three indicators in the case of Romanian companies (Table 5), confirming that the level of cost management, the efficiency of assets and the efficiency of invested resources are interlinked (Figure 3).  
Figure 1: Distribution of the ROS, ROA and ROE averages (%) for Hungarian companies without outliers. Source: Authors’ own editing, based on own calculations.  
Figure 2: Distribution of the ROS, ROA and ROE averages (%) for Romanian companies without outliers. Source: Authors’ own editing, based on own calculations.