# Machine Learning for Evaluating Hospital Mobility: An Italian Case Study
## 4 Experimental Results and Discussions
### Evaluating Hospital Efficiency in Healthcare Mobility
The Kruskal-Wallis test allows us to determine if there are statistically significant differences between the medians of the groups, a critical condition for guiding healthcare policy decisions and managerial interventions. The first set of analyses, presented in Table 9, examines the differences in DEA efficiency scores between private and public hospital networks. A \(\chi^{2}\) value of 21.0 with a \(p\)-value less than 0.001 indicates that the differences in efficiency between hospitals in private and public networks are statistically significant. This result supports the hypothesis that the type of management significantly influences the efficiency with which hospitals can utilize resources to promote patient mobility. The second set of analyses, detailed in Table 10, assesses the differences in efficiency among hospitals categorized by operational level. A \(\chi^{2}\) of 36.4 with a \(p\)-value less than 0.001 suggests that there are significant differences in efficiency scores across various hospital levels. This highlights how different levels of \begin{table}
\begin{tabular}{c c c c} \hline  & \(\chi^{2}\) & **df** & \(p\) \\ \hline
**DEA EFFICIENCY SCORES** & 36.4 & 4 & \(<\)0.001 \\ \hline \end{tabular}
\end{table} 
Table 10: Kruskal–Wallis by hospital level. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **NETWORK** & **N** & **Mean** & **Median** & **SD** & **Minimum** & **Maximum** \\ \hline
**DEA EFFICIENCY** & **PRIVATE** & 76 & 0.936 & 0.977 & 0.0872 & 0.669 & 1.00 \\
**SCORES** & **PUBLIC** & 51 & 0.830 & 0.875 & 0.1453 & 0.387 & 1.00 \\ \hline \end{tabular}
\end{table} 
Table 8: DEA efficiency scores by hospital network. \begin{table}
\begin{tabular}{c c c c} \hline  & \(\chi^{2}\) & **df** & \(p\) \\ \hline
**DEA EFFICIENCY SCORES** & 21.0 & 1 & \(<\)0.001 \\ \hline \end{tabular}
\end{table} 
Table 9: Kruskal–Wallis by hospital network. hospitals, from base to second level, including IRCCS and private nursing homes, manage their healthcare resources differently. Finally, Table 11 presents pairwise comparisons among hospital levels, using the Dwass-Steel-Critchlow-Figner test to examine specific differences between the groups. Table 11 reveals significant differences in DEA efficiency scores among hospital levels, particularly highlighting the effectiveness of private care facilities. Dwass-Steel-Critchlow-Figner tests confirm that private care facilities significantly outperform both basic-level hospitals, with a W value of 5.57, and first-level ones, with a W value of 5.16, both with \(p\)-values significantly lower than 0.05. These results indicate that private care facilities manage resources exceptionally effectively, optimizing patient mobility far more than observed in traditional hospital levels. Furthermore, basic-level hospitals demonstrate greater efficiency compared to second-level ones, with a W value of \(-4.33\) and a \(p\)-value of 0.019, suggesting that even basic levels manage resources more effectively than hospitals facing greater operational complexity. The most notable discrepancy is observed between private care facilities and second-level hospitals, where a W value of \(-7.35\) highlights the overwhelming superiority of the former. These analyses demonstrate the critical importance of efficient management and optimal operational practices in determining hospital efficiency, with private care facilities emerging as examples of excellence in utilizing healthcare resources to maximize patient mobility output. Such results provide valuable insights for decision-makers in the healthcare sector, who must consider restructuring hospital practices to enhance overall efficiency.