## 3 Results
Similarly, moderate positive correlations were found between abductors and joint position sense during medial rotation (r = 0.59, \(p\) < 0.001) and between lateral rotators and joint position sense during lateral rotation (r = 0.63, \(p\) < 0.001). These results suggest that greater muscle strength is associated with improved proprioceptive ability in specific directions. The significance of these correlations underscores the interplay between muscle strength and proprioception in shoulder function, providing valuable insights for developing tailored rehabilitation strategies for individuals with SIS. The Mediation effect of pain on the relationship between shoulder muscle strength joint position sense, and pain in different directions and sway parameters are summarized in Table 4. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **Variable** & \multicolumn{2}{c}{**SIS Group (\(n\) = 50)**} & \multicolumn{2}{c}{**Healthy**} & \multicolumn{2}{c}{**Green Size**} & \multicolumn{1}{c}{\(p\)**-Value**} \\  & & **(Mean \(\pm\) SD)** & \multicolumn{2}{c}{**Group (\(n\) = 50)**} & \multicolumn{2}{c}{**Mean Difference**} & \multicolumn{1}{c}{**Effect Size**} & \multicolumn{1}{c}{\(p\)**-Value**} \\  & & **(Mean \(\pm\) SD)** & \multicolumn{2}{c}{**(Mean \(\pm\) SD)**} & & \\ \hline Shoulder Muscle & Flexors (Kg) & \(11.6\pm 7.2\) & \(22.3\pm 8.1\) & \(-6.7\) & \(0.84\) & \(<\)0.001 \\ Shoulder Muscle & Abductors (Kg) & \(10.8\pm 9.2\) & \(18.4\pm 8.7\) & \(-4.6\) & \(0.51\) & \(<\)0.001 \\ Strength & Medial Rotators (Kg) & \(07.3\pm 6.1\) & \(13.7\pm 5.5\) & \(-3.4\) & \(0.58\) & \(<\)0.001 \\ Lateral Rotators (Kg) & \(08.9\pm 5.7\) & \(15.1\pm 6.2\) & \(-3.2\) & \(0.52\) & \(<\)0.001 \\ Flexion (Degrees of Error) & \(3.5\pm 1.2\) & \(12.4\pm 0.9\) & \(2.3\) & \(1.91\) & \(<\)0.001 \\ Shoulder JFS & Abduction (Degrees of Error) & \(4.0\pm 1.5\) & \(15.1\pm 1.1\) & \(2.5\) & \(1.45\) & \(<\)0.001 \\  & Medial Rotation (Degrees of Error) & \(10.2\pm 3.1\) & \(4.5\pm 2.2\) & \(5.7\) & \(2.61\) & \(<\)0.001 \\  & Lateral Rotation (Degrees of Error) & \(9.8\pm 2.9\) & \(4.2\pm 2.0\) & \(5.6\) & \(2.69\) & \(<\)0.001 \\ \hline \hline \end{tabular} SIS, sub-acromial impingement syndrome; \(n\), sample size; Kg, kilograms; JPS, joint position sense. Values are presented as mean \(\pm\) standard deviation (SD).  
\end{table} 
Table 2: Comparison of shoulder muscle strength and joint position sense between SIS and Healthy groups. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variable** & \multicolumn{2}{c}{**Correlation (r)**} & \multicolumn{1}{c}{\(p\)**-Value**} \\ \hline Flexors vs. Flexion & 0.62 & \(<\)0.001 \\ Flexors vs. Abduction & 0.35 & 0.027 \\ Flexors vs. Medial Rotation & 0.58 & \(<\)0.001 \\ Flexors vs. Lateral Rotation & 0.52 & \(<\)0.001 \\ Abductors vs. Flexion & 0.45 & 0.005 \\ Abductors vs. Abduction & 0.32 & 0.045 \\ Abductors vs. Medial Rotation & 0.59 & \(<\)0.001 \\ Abductors vs. Lateral Rotation & 0.55 & \(<\)0.001 \\ Medial Rotators vs. Flexion & 0.43 & 0.007 \\ Medial Rotators vs. Medial Rotation & 0.62 & \(<\)0.001 \\ Medial Rotators vs. Lateral Rotation & 0.48 & 0.003 \\ Lateral Rotators vs. Flexion & 0.51 & \(<\)0.001 \\ Lateral Rotators vs. Abduction & 0.39 & 0.015 \\ Lateral Rotators vs. Medial Rotation & 0.54 & \(<\)0.001 \\ Lateral Rotators vs. Lateral Rotation & 0.63 & \(<\)0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlations between shoulder muscle strength (kg) and JPS in various directions. For the interaction of Pain \(\times\) Shoulder Flexion \(\times\) JPS Flexion, the total effect (c + a \(\times\) b) was 0.60 (\(p\) = 0.001). This effect was partially mediated, with a direct effect (c-Path) equal to 0.23 (\(p\) < 0.001) and an indirect effect (b-Path) equal to 0.07 (\(p\) = 0.005). In the case of Pain \(\times\) Shoulder Abduction \(\times\) JPS Abduction, the total effect was equal to 0.58 (\(p\) = 0.001). This effect was also partially mediated, with a direct effect equal to 0.21 (\(p\) < 0.001) and an indirect effect equal to 0.08 (\(p\) = 0.004).