## 3 Results  
This study's demographic analysis revealed that the SIS group (N = 50) and the Healthy group (N = 50) were generally well-matched in terms of age, gender, dominant arm, ethnicity, education level, employment status, and marital status, indicating the successful establishment of comparable study cohorts (Table 1). However, the SIS group exhibited a slightly higher mean BMI compared to the Healthy group, and the difference was statistically significant. The symptom duration was specific to the SIS group and showed a mean duration of 12.3 \(\pm\) 6.8 months. These demographic findings provided a solid foundation for subsequent analyses, allowing for the assessment of the influence of these characteristics on the study's primary outcomes related to shoulder muscle strength, joint position sense, and pain mediation effects. The results of the comparison between the SIS group and the Healthy group for shoulder muscle strength and joint position sense are summarized in Table 2.  
In the comparison between individuals with SIS and a healthy control group, significant differences were observed in both shoulder muscle strength and joint position sense. The SIS group exhibited substantially lower shoulder muscle strength in flexors, abductors, medial rotators, and lateral rotators compared to the healthy group, with large effect sizes (Cohen's d ranging from 0.51 to 0.84) and \(p\)-values less than 0.001. Furthermore, the individuals with SIS displayed significantly larger degrees of error in shoulder joint position sense during flexion, abduction, medial rotation, and lateral rotation, with effect sizes ranging from 1.45 to 2.69, all indicating a highly significant impairment in proprioceptive ability (\(p<0.001\)). These results underscore the substantial functional deficits associated with SIS, emphasizing the need for targeted rehabilitation strategies to address both muscle weakness and proprioceptive impairments in this patient popul \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Variable** & \multicolumn{2}{c}{**SIS Group (\(n\) = 50)**} & \multicolumn{2}{c}{**Health Group (\(n\) = 50)**} & \multicolumn{1}{c}{\(p\)**-Value**} \\  & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** & **(Mean \(\pm\) SD)** & **\(p\)-Value** \\ \hline Age (years) & 45.2 \(\pm\) 7.1 & 43.8 \(\pm\) 6.5 & 0.214 \\ Gender & & & \\ \(\bullet\)  Male & 26 (52\%) & 28 (56\%) & 0.678 \\ \(\bullet\)  Female & 24 (48\%) & 22 (44\%) & 0.438 \\ Dominant & & & \\ \(\bullet\)  Right & 44 (88\%) & 45 (90\%) & 0.754 \\ \(\bullet\)  Left & 6 (12\%) & 5 (10\%) & 0.467 \\ BMI (kg/m\({}^{2}\)) & 27.4 \(\pm\) 3.6 & 25.8 \(\pm\) 2.9 & 0.039 \\ Symptom Duration (months) & 12.3 \(\pm\) 6.8 & - & - \\ Education Level & & & \\ \(\bullet\)  High School & 15 (30\%) & 10 (20\%) & 0.211 \\ \(\bullet\)  College/University & 35 (70\%) & 40 (80\%) & 0.341 \\ Employment Status & & & \\ \(\bullet\)  Employed & 18 (36\%) & 37 (74\%) & 0.325 \\ \(\bullet\)  Unemployed & 13 (26\%) & 32 (64\%) & 0.453 \\ Marital Status & & & \\ \(\bullet\)  Married & 28 (56\%) & 33 (66\%) & 0.429 \\ \(\bullet\)  Single & 22 (44\%) & 17 (34\%) & 0.386 \\ \hline \hline \end{tabular} SIS, sub-acromial impingement syndrome; \(n\), sample size; BMI, body mass index. Values are presented as mean \(\pm\) standard deviation (SD) or \(n\) (%), as appropriate. \(p\)-values indicate statistical significance between SIS and healthy groups.  
\end{table} 
Table 1: Demographic characteristics of study participants. between shoulder muscle strength and joint position sense in various directions revealed significant associations (Table 3 and Figure 3). Strong positive correlations were observed between flexor strength and joint position sense during flexion (r = 0.62, \(p\) < 0.001) as well as between medial rotators and joint position sense during medial rotation (r = 0.62, \(p\) < 0.001).