## 5 Results and Data Analysis
### RQ2.2: Maintainability Measurement in Versions of a Software System  
To assess the relationship between Index variants in the context of comparing the maintainability of versions of the same software system, a correlation analysis was conducted for each case study. First, in Table 11, the results of the normality tests are reported. Even when a parametric correlation coefficient may have been appropriate to use (e.g., in the case of assessing the relationship between \(MI_{orig. }\) and \(MI_{orig. (CM)}\) for _CS2_), we opted to assess all relationships using Kendall's \(\tau\)-b Correlation Coefficient to ensure consistency in comparing and analyzing the correlations across all pairs. The results of the correlation analysis for each case study are presented in Table 12. The correlation coefficients are positive, but tend to be weaker than those reported in RQ2.1, particularly for _CS1_ and _CS2_. In the case of _CS1_ and _CS2_, the correlation ranges from moderate to very strong, while in the case of _CS3_, the correlation is very strong across all pairs. Despite the pattern being less noticeable, the correlations between two Index variants with the comment part and between two Index variants without the comment part tend to be stronger in comparison to the correlation between two Index variants, one from each of the two groups. The case of _CS1_ shows how three-metric Index variants can also be, in some cases, closely related to their four-metric alternative. For instance, the correlation between \(MI_{orig. }\) and its version with the comment part, i.e., \(MI_{orig. (CM)}\), is very strong (\(\tau\) = 0.919), while it is only considered strong between \(MI_{orig. }\) and \(MI_{LOC}\) (\(\tau\) = 0.805), as well as between \(MI_{orig. }\) and \(MI_{IH}\) (\(\tau\) = 0.729). The results of the correlation analysis were further analyzed through multidimensional scaling to gain a deeper understanding of the relationships between the Index variants. The resulting visualizations for each case study are presented in Figure 8. There is still a tendency for Index variants with comment parts to be close to each other in the vector space, as well as a tendency for Index variants without comment parts to be close to each other. However, the pattern is not as pronounced as in the previous analysis for RQ2.1. Herein, in some case studies, certain Index variants with the comment part are closer to certain Index variants without the comment part and vice versa. For example, in the case of _CS1_, \(MI_{orig. }\) appears closer to \(MI_{orig. (CM)}\) rather than to \(MI_{LOC}\) and \(MI_{IH}\). Figure 7: Correlation heat map and dendrogram of hierarchical agglomerative clustering. The consistency of the long-term trends in maintainability for each case study was analyzed using Mann-Kendall Trend Tests, and the results are presented in Table 13. The results suggest that the long-term monotonic trends in maintainability are all statistically significant and point in the same direction; the maintainability trends are negative, indicating that maintainability is consistently decreasing over time. Nonetheless, the choice of Index variant affects the magnitude of the trend, with different variants yielding different results. In the case of \(CS2\), it can be observed that the magnitude of the trends is generally slightly higher when maintainability is assessed using Index variants with comment parts (\(\beta=-0.051\), \(\beta=-0.054\), and \(\beta=-0.056\) for \(M_{orig. (CM)}\), \(M_{Impr. (CM)}\), and \(M_{I|H(CM)}\), respectively) compared to when maintainability is assessed using Index variants without comment parts (\(\beta=-0.010\), \(\beta=-0.011\), \(\beta=-0.014\), and \(\beta=-0.015\) for \(M_{orig}\), \(M_{Impr. }\)