## 5 Results and Data Analysis
### RQ2.2: Maintainability Measurement in Versions of a Software System
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Case Study** & \(M_{orig.}\) & \(M_{orig.(CM)}\) & \(M_{Impr.}\) & \(M_{Impr.(CM)}\) & \(M_{ILOC}\) & \(M_{I|H}\) & \(M_{I|H(CM)}\) \\ \hline \(CS1\). AssertJ & W = 0.151, \(p\) = 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\ \(CS2\). Caffeine & W = 0.102, \(p\) = 0.186 & \(p\) = 0.011 & \(p\) = 0.200 & \(p\) = 0.006 & \(p\) = 0.050 & \(p\) = 0.200 & \(p\) \(<\) 0.001 \\ \(CS3\). Joda-Time & W = 0.404, \(p\) = 0.395, \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Kolmogorov–Smirnov normality test. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multicolumn{2}{l}{\(CS1\). AssertJ} & \multicolumn{1}{l}{\(M_{orig. }\)} & \multicolumn{1}{l}{\(M_{orig. (CM)}\)} & \multicolumn{1}{l}{\(M_{Impr. }\)} & \multicolumn{1}{l}{\(M_{Impr. (CM)}\)} & \multicolumn{1}{l}{\(M_{ILOC}\)} & \multicolumn{1}{l}{\(M_{I|H}\)} & \multicolumn{1}{l}{\(M_{I|H(CM)}\)} \\ \hline \(M_{Iorig. }\) & 1 & 0.919 & 0.942 & 0.870 & 0.805 & 0.729 & 0.724 \\ \(M_{Iorig. (CM)}\) & 0.919 & 1 & 0.873 & 0.943 & 0.745 & 0.663 & 0.789 \\ \(M_{Iimpr. }\) & 0.942 & 0.873 & 1 & 0.838 & 0.860 & 0.780 & 0.750 \\ \(M_{Iimpror. (CM)}\) & 0.870 & 0.943 & 0.838 & 1 & 0.716 & 0.630 & 0.813 \\ \(M_{LOC}\) & 0.805 & 0.745 & 0.860 & 0.716 & 1 & 0.887 & 0.683 \\ \(M_{I|H}\) & 0.729 & 0.663 & 0.780 & 0.630 & 0.887 & 1 & 0.667 \\ \(M_{I|H|(CM)}\) & 0.724 & 0.789 & 0.750 & 0.813 & 0.683 & 0.667 & 1 \\ \hline \multicolumn{2}{l}{\(CS2\). Caffeine} & & & & & & & \\ \hline  & \(M_{orig. }\) & \(M_{orig. (CM)}\) & \(M_{Impr. }\) & \(M_{Impr. (CM)}\) & \(M_{ILOC}\) & \(M_{I|H}\) & \(M_{I|H(CM)}\) \\ \hline \(M_{Iorig. }\) & 1 & 0.629 & 0.909 & 0.651 & 0.892 & 0.885 & 0.629 \\ \(M_{I|H}\) & 0.629 & 1 & 0.67\(M_{I}H\), and \(MI_{LOC}\), respectively). Additionally, a pattern can be noted between the magnitudes of the trends based on the maintainability assessment made by a three-metric Index variant and the one made by its four-metric alternative across all three case studies. For instance, in the case of \(CS1\), the magnitude of the trend assessed by \(M_{orig. (CM)}\) (\(\beta=-0.064\)) is higher than the one by \(M_{orig. }\) (\(\beta=-0.056\)); the magnitude of the trend assessed by \(M_{impr. (CM)}\) (\(\beta=-0.055\)) is higher than the one by \(M_{limpr. }\) (\(\beta=-0.048\)); the magnitude of the trend assessed by \(M_{IPh(CM)}\) (\(\beta=-0.033\)) is higher than the one by \(M_{IPh}\) (\(\beta=-0.025\)). To examine the short-term trends in the maintainability of each case study, the differences in maintainability from one software release to its previous version are presented separately for each Index variant under study in Figure 9. Since the differences in maintainability have a large range of values, the Y axis uses a symmetrical logarithmic scale to help the reader better observe all these changes. This scale represents small values, i.e., small differences in maintainability, on a linear scale and larger values, i.e., large differences, on a logarithmic scale. Blue highlights are placed behind the lines to emphasize changes that majorly differ from those observed in the maintainability assessments made using other Index variants, or at least from most of them. In most cases, it can be noted that the changes are consistent; if, according to one Index variant, a positive change is shown, it is likely that this change is also regarded as positive according to the assessments made using other Index variants. When differences in the direction of the maintainability change between two consecutive releases do occur, the directions of the change are mostly consistent between Index variants with and those without the comment part. However, while the directions of the changes are, in most cases, aligned, the magnitudes of these changes often vary for assessments made by all Index variants.