## 3 Results
### Changes in FMA-UE Scores Pre- and Post-Intervention  
Table 3 summarizes the changes in FMA-UE scores pre- and post-intervention for both the shaking and control groups. The intervention group demonstrated a significant improvement in the FMA-UE total score (median change = 1.8, 95% CI [0.8, 2.8]) compared with the control group (median change = 0.4, 95% CI [-0.1, 1.0], U = 823, \(p\) = 0.04, indicating a significant difference (r = 0.24) (Figure 3A). For the FMA-UE part A subscale, the intervention group showed a median change of 1.2 (95% CI [0.6, 1.8]) versus the control group's 0.3 (95% CI [-0.2, 0.9]), with a U-value of 769.5 and a \(p\)-value of 0.01, indicating a statistically  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Variable** & **All** & **Shaking** & **Control** & \multicolumn{2}{c}{**Statistics**} & \\
**(\(n\) = 93)** & **(\(n\) = 47)** & **(\(n\) = 46)** & **\(\chi^{2}\) or U** & **\(p\)-Value** & **\(r\) or V** \\ \hline Sex (Female/Male) & 50/43 & 26/22 & 24/21 & 0.00 & 1.00 & 0.00 \\ Age (median, [Q1, Q3]) & 59 [53; 68] & 59 [53; 67] & 59 [53; 68] & 1065 & 0.91 & 0.49 \\ Diagnosis (CI/ICH/other) & \(33/55/5\) & \(16/30/2\) & \(17/25/3\) & 0.59 & 0.75 & 0.08 \\ Affected side (L/R) & 46/47 & 27/21 & 19/26 & 1.31 & 0.25 & 0.12 \\ Month from onset & 131 [92; 175] & 136 [98; 177] & 126 [81; 175] & 1487 & 0.36 & 0.56 \\ FMA-UE & 24 [18; 30] & 27 [23; 31] \({}^{\star}\) & 20 [17; 23] & 1343 & 0.04 & 0.62 \\ BoNT-A treatment (times) & 14 [10; 18] & 14 [11; 19] & 13 [9; 17] & 1124 & 0.81 & 0.49 \\ BoNT-A dose (Unit) & 250 [200; 350] & 250 [200; 400] & 250 [200; 300] & 1208 & 0.32 & 0.56 \\ \hline \hline \end{tabular}  
* Data are presented as median [1 st, 3 rd quartile]. Chi-square test with Cramer’s V for effect size is used to compare the number of patients, diagnosis, and affected side in each group. Month from onset, FMA-UE, BoNT-A are compared with Mann–Whitney U-test. \({}^{\star}\)\(p\) < 0.05 compared with controls. Pink; Shaking group, Light blue; Controls. CI; cerebral infarction, ICH; intra cerebral hemorrhage, FMA-UE; Fugl–Meyer assessment of the upper extremity, BoNT-A; botulinum toxin type A.  
\end{table}
Table 1: Pretreatment baseline characteristics of the shaking exercise and control groups.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Variable** & \(\beta\) & **SE** & **z-Value** & **\(p\)-Value** & \multicolumn{2}{c}{**95\% CI**} \\ \hline Intercept & 0.467 & 0.550 & 0.849 & 0.396 & 0.611 & 1.545 \\ Periods & 0.467 & 0.298 & 1.565 & 0.118 & \(-\)0.118 & 1.051 \\ Group & 1.363 & 0.447 & 3.048 & 0.002 & \(\star\) & 0.486 & 2.239 \\ Periods \(\times\) Group & 1.359 & 0.419 & 3.242 & 0.001 & \(\star\) & 0.538 & 2.181 \\ \hline Group Variance & 25.368 & 4.721 & 5.373 & 0.000 & \(\star\) & 16.115 & 34.621 \\ Periods Variance & 25.057 & 4.150 & 6.038 & 0.000 & \(\star\) & 16.923 & 33.191 \\ Group \(\times\) Periods Covariance & 23.963 & 4.300 & 5.572 & 0.000 & \(\star\) & 15.534 & 32.391 \\ \hline \hline \end{tabular}  
* The model includes data from 186 observations across 93 periods. Fixed effects included the intervention period (Periods), shaking group (Group), and their interaction (Periods \(\times\) Group). Statistical significance is set at \({}^{\star}\)\(p\) < 0.05. SE; Standard Error, \(\beta\); estimated coefficient.  
\end{table}
Table 2: Estimated factor levels by Generalized Mixed Linear Model for FMA-UE score.  
significant difference (r = 0.29). The FMA-UE part B did not show significant changes between the intervention and control groups (U = 1014.5, \(p\) = 0.56, r = 0.06). Similarly, the FMA-UE part C and D changes were not significant between the interventions.