# Data Science in the Management of Healthcare Organizations
## 4 Case Study
### Evaluating the Entropic State of the Healthcare Workers for the Best-Case Scenario  
The answers of participant one to topic HOL-4 at month 0 will be used to illustrate the assessment of the areas shown in Figure 3 for the BCS. Thus, for this topic, one may have:  
* In statement S1, the options frequently and occasionally were considered (Table 2), so \(r=\frac{2}{5}\frac{1}{\sqrt{\pi}}\) and \(R=\frac{3}{5}\frac{1}{\sqrt{\pi}}\);
* In statement S2, the options occasionally and rarely were considered (Table 2), so \(r=\frac{3}{5}\frac{1}{\sqrt{\pi}}\), and \(R=\frac{4}{5}\frac{1}{\sqrt{\pi}}\);  
Figure 3: A pictorial reading of the participant one answers to statements S1 through S10, segmented by topics (healthcare organization leadership (HOL-4), healthcare organization work engagement (HOWE-3) and healthcare organization teamwork (HOTW-3)), at month 0, in the best-case and worst-case scenarios. (1), (2), (3), (4), and (5) denote, respectively, never, rarely, occasionally, frequently, and very frequently for HOL-4; never, rarely, sometimes, often, and always for HOWE-3; and strongly disagreeing, disagreeing, neutral, agreeing, and strongly agreeing for HOTW-3. The dark, gray, and white colored areas correspond to exergy, vagueness, and anergy. In statement S3, only the option very frequently was considered (Table 2), so \(r=R=\frac{1}{5}\frac{1}{\sqrt{\pi}}\). * In statement S4, the option I don't know was selected corresponding to a vague situation (Table 2), so \(r=0\) and \(R=\frac{1}{\sqrt{\pi}}\);  
The quantitative values of the areas shown in Figure 3 for HOL-4, at month 0, for both scales (ranging from very frequently (5) to never (1) and vice versa) are presented in Table 3 for the BCS. Thus, for participant one, the overall values of exergy, vagueness, and anergy related to the HOL-4 topic in the BCS are determined using the values from Table 3 on the scale from very frequently (5) to never (1), as follows:  
\[ \begin{array}{c}exergy_{5-1}=exergy_{5-1_{5_{1}}}+exergy_{5-1_{5_{3}}}+ exergy_{5-1_{5_{4}}}=0.04+0.01+0=0.05\\ \\ vagueness_{5-1}=agueness_{5-1_{5_{1}}}+agueness_{5-1_{5_{3}}}+agueness_{5-1 _{5_{4}}}=0\\ energy_{5-1}=energy_{5-1_{5_{1}}}+energy_{5-1_{5_{3}}}+energy_{5-1_{5_{4}}}=0. 21+0.24+0.25=0.70\end{array} \]  
whereas, for the scale from never (1) to very frequently (5), the values are as follows:  
\[ \begin{array}{c}exergy_{1-5}=exergy_{1-5_{5_{2}}}=0.09\\ \\ vagueness_{1-5}=agueness_{1-5_{5_{2}}}=0\\ energy_{1-5_{5_{2}}}=0.16\end{array} \] \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Scale (5) \(\rightarrow\) (1)** & **Scale (1) \(\rightarrow\) (5)** \\ \hline S1 & \(exergy_{5_{1}}=\frac{1}{4}\pi\bigg{(}\frac{2}{5}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}=0.04\) & - \\ S2 & \(vagueness_{5_{1}}=0\) & - \\  & \(energy_{5_{1}}=\frac{1}{4}\pi\bigg{[}\bigg{(}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}-\bigg{(}\frac{2}{5}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}\bigg{]}=0.21\) & - \\ \hline S3 & \(exergy_{5_{3}}=\frac{1}{4}\pi\bigg{(}\frac{1}{5}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}=0.01\) & - \\ S3 & \(vagueness_{5_{3}}=0\) & - \\  & \(energy_{5_{3}}=\frac{1}{4}\pi\bigg{[}\bigg{(}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}-\bigg{(}\frac{1}{5}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}\bigg{]}=0.24\) & - \\ \hline S4 & \(exergy_{5_{4}}=0\) & - \\  & \(vagueness_{5_{4}}=0\) & - \\  & \(energy_{5_{4}}=\frac{1}{4}\pi\bigg{[}\bigg{(}\sqrt{\frac{1}{\pi}}\bigg{)}^{ 2}-0^{2}\bigg{]}=0.25\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation of exergy, vagueness, and anergy for participant one’s answers to statements S1 through S4, regarding healthcare organization leadership at month 0, in the best-case scenario, for both scales, ranging from very frequently (5) to never (1), and from never (1) to very frequently (5). Additionally, HOWS and the quality of information (QoI) for each topic can be evaluated. HOWS is calculated based on Figure 4 using Equation (3), while QoI is determined using Equation (4).