## 5 Results and Data Analysis  
### RQ1: Maintainability Measurement in a Software System  
For each software system under study, values of the Index variants are visually presented in Figure 2. We can observe that, for each subject software, the single-valued maintainability evaluations by various Index variants were not the same. Nevertheless, certain general patterns in the Index values can be identified. The values of the Index variants that do not consider measuring code documentation, i.e., Index variants without the comment part, are on the left side of the plot, whereas the Index variants that take code comments into account in their computations are on the right side. Thus, the values of the former tend to be lower than the latter. Although this was to some extent expected given how the equations of Index variants with the comment part are formulated, an interesting observation is that the gap between the two groups of Index variants appears to be somewhat consistent for all software systems. Furthermore, we can observe that the gap tends to be slightly smaller when there is little code documentation, i.e., when the percentage of comment lines is low (e.g., in the case of _S19_, _S44_, _S45_), and the gap tends to be larger when the percentage of comment lines is higher (e.g., in the case of _S30_, _S31_). A closer examination of the individuals of the two groups reveals there is more variation in the specific Index variant values. The two lowest values are reported by \(MI_{impr. }\) and \(MI_{LOC}\). In a large majority of subject software (88.9%), \(MI_{LOC}\) has the lowest value, while in 11.1% of software, the lowest value is reported by \(MI_{impr.}\). For the second-lowest value, the situation is reversed. Next, the third- and the fourth-lowest values are reported by either \(MI_{IH}\) or \(MI_{orig.}\). In 60% of software systems, the third-lowest value is reported by \(MI_{IH}\) and in 40% by \(MI_{orig.}\). The situation is reversed with the fourth-lowest value. The next value in the rankings, i.e., the third-highest value, is, in all cases, \(MI_{impr.(CM)}\). \(MI_{IH(CM)}\) and \(MI_{orig. (CM)}\) report the two highest values. The highest value is reported by \(MI_{orig. (CM)}\) in 60% of subject software and \(MI_{IH(CM)}\) in 40%. For the second-highest values, 60% are reported by \(MI_{IH(CM)}\) and 40% by \(MI_{orig.(CM)}\). In Table 9, descriptive statistics about the Index variant values are provided, supporting the previously stated observations. In general, \(MI_{impr. }\) and \(MI_{LOC}\) suggest lower maintainability for the same software system than \(MI_{IH}\) or \(MI_{orig. }\), as the values of \(MI_{IH}\) and \(MI_{orig. }\) tend to be higher than those of \(MI_{impr. }\) and \(MI_{LOC}\). Additionally, \(MI_{IH(CM)}\) and \(MI_{orig. (CM)}\) suggest higher maintainability in comparison to \(MI_{impr. (CM)}\), since the value of \(MI_{impr. (CM)}\) tends to be lower than that of \(MI_{IH(CM)}\) and \(MI_{orig.(CM)}\). The boxplots in Figure 3 illustrate the pairwise differences between the values of different Index variants. The figure gives a general idea of the direction of the differences, i.e., whether they are generally positive, negative, or inconclusive. This helps show which Index variant has higher values between the two variants. For example, a consistent positive difference is observed between \(M\textsubscript{orig. }(CM)\) and \(M\textsubscript{orig. }\), while the results between \(M\textsubscript{orig. }\) and \(M\textsubscript{orig. }\) are shown in Figure 4.