## 3 Results
### Baseline Characteristics According to Severity  
The baseline characteristics of the shaking exercise and control groups, stratified by the severity of upper limb impairment in stroke patients (severe, moderate, and mild) are shown in Table 4.  
Figure 3: Comparison of FMA-UE scores pre and post intervention between shaking exercise and conventional therapy groups. The plots include data for all patients and are stratified by the severity of impairment at baseline (mild, moderate, and severe): (**A**) Changes in FMA-UE scores for all patients. (**B**) For patients with mild impairment at baseline. (**C**) For patients with moderate impairment at baseline. (**D**) For patients with severe impairment at baseline (Intervention \(n=5\), Control \(n=4\)). * \(p<0.05\) for between groups based on Mann–Whitney U-test. \(\dagger\)\(p<0.05\) for within groups by Wilcoxon test.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**FMA-UE**} & \multicolumn{4}{c}{**Shaking (\(\mathbf{u=47}\))**} & \multicolumn{4}{c}{**Control (\(\mathbf{u=46}\))**} & \multirow{2}{*}{**U**} & \multirow{2}{*}{**_p_} & \multirow{2}{*}{**_r_**} \\ \cline{2-2} \cline{6-9}  & \multicolumn{1}{c}{**Pre**} & & & & & & & \\ \hline \multirow{3}{*}{Total} & 26.8 & 28.4 & 1.8 & 20.0 & 20.3 & 0.4 & \multirow{3}{*}{823} & \multirow{3}{*}{0.04} & \multirow{3}{*}{*} & \multirow{3}{*}{0.24} \\  & [23.0, 31.2] & [24.4, 33.0] & [0.8, 2.8] & [17.1, 23.3] & [17.4, 23.7] & [-0.1, 1.0] & & & \\ \multirow{3}{*}{part A} & 21.4 & 22.6 & 1.2 & 17.5 & 17.9 & 0.3 & \multirow{3}{*}{770} & \multirow{3}{*}{0.01} & \multirow{3}{*}{*} & \multirow{3}{*}{0.29} \\  & [19.4, 23.5] & [20.6, 24.7] & [0.6, 1.8] & [15.5, 19.6] & [15.8, 20.0] & [-0.2, 0.9] & & & \\ \multirow{3}{*}{part B} & 2.9 & 3.1 & 0.2 & 1.7 & 1.9 & 0.2 & \multirow{3}{*}{1015} & \multirow{3}{*}{0.56} & \multirow{3}{*}{0.06} \\  & [2.1, 3.7] & [2.3, 3.9] & [\(-0.2, 0.6]\) & [0.9, 2.4] & [1.1, 2.7] & [\(-0.1, 0.6]\) & & & \\ \multirow{3}{*}{part C} & 4.1 & 4.2 & 0.2 & 3.5 & 3.3 & \(-0.2\) & \multirow{3}{*}{977} & \multirow{3}{*}{0.37} & \multirow{3}{*}{0.10} \\  & [2.9, 5.2] & [3.1, 5.4] & [\(-0.3, 0.6]\) & [2.4, 4.7] & [2.2, 4.5] & [\(-0.5, 0.1]\) & & & \\ \multirow{3}{*}{part D} & 1.3 & 1.4 & 0.2 & 0.8 & 0.7 & 0.0 & \multirow{3}{*}{964} & \multirow{3}{*}{0.16} & \multirow{3}{*}{0.11} \\  & [0.8, 1.7] & [1.0, 1.9] & [0.0, 0.4] & [0.3, 1.2] & [0.3, 1.2] & [\(-0.2, 0.1]\) & & \\ \hline \hline \end{tabular}  
* A Mann–Whitney U-test comparing the changes (A values) in FMA scores before and after treatment between control and intervention groups. \(\Delta\) values are calculated as the difference between pre– and post-intervention scores for each measure.
* \(p\)-values less than 0.05 indicate statistically significant differences between the groups. Effect size (r) is reported to quantify the magnitude of the difference, with values closer to \(-1\) or \(1\) indicating a stronger effect. Data are presented as medians and 25 th–75 th percentile values. Pink columns indicate the Shaking group data, while the Control group is shown in light blue.  
\end{table}
Table 3: Changes in FMA-UE scores pre- and post-intervention, compared with control and intervention groups.