## 4 Results
### Comparison of Standard Deviations of Mean Joint Angles with and Without AR System Application  
To evaluate movement accuracy, we analyzed the standard deviations of the mean joint angles across eight repetitions for each of the eight test movements. These results are presented in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Difficulty**} & \multirow{2}{*}{\begin{tabular}{c} **Exercise Movement** \\ **(Analyzed Motion)** \\ \end{tabular} } & \multicolumn{4}{c}{**Mean Joint Angle**} & \multirow{2}{*}{\begin{tabular}{c} **Difference 95\%CI** \\ **(\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{   }}}}}}}}}}}}}\)\) \\ \end{tabular} } \\ \cline{3-8}  & \begin{tabular}{c} **Studing arm abduction** \\ **(shoulder abduction)** \\ \end{tabular} } & \(87.3\pm 12.0\) & \(94.6\pm 7.4\) & \(0.04\) & \({}^{*}\) & \(-7.3\) (\(-14.2\), \(-0.4\)) & \(-0.72981\) \\ \cline{2-8}  & \begin{tabular}{c} **Standing arm flexion** \\ **(shoulder flexion)** \\ \end{tabular} & \(163.6\pm 13.2\) & \(163.8\pm 14.5\) & \(0.97\) & \(-0.2\) (\(-10.2\), \(9.8\)) & \(-0.01294\) \\ \hline \multirow{4}{*}{Medium} & \begin{tabular}{c} **Standing trunk lateral flexion** \\ **(trunk lateral flexion)** \\ \end{tabular} & \(27.3\pm 7.0\) & \(32.0\pm 7.1\) & \(0.02\) & \({}^{*}\) & \(-4.8\) (\(-8.7\), \(-0.9\)) & \(-0.67274\) \\ \cline{2-8}  & \begin{tabular}{c} **Standing diagonal medicine ball lift** \\ **(trunk rotation)** \\ \end{tabular} & \(56.1\pm 17.3\) & \(52.5\pm 13.1\) & \(0.45\) & \(3.7\) (\(-6.9\), \(14.2\)) & \(0.237632\) \\ \hline \multirow{4}{*}{High} & \begin{tabular}{c} **Standing forward dumbbell hinge** \\ **(knee flexion)** \\ \end{tabular} & \(49.4\pm 13.2\) & \(49.3\pm 18.4\) & \(0.96\) & \(0.1\) (\(-5.5\), \(5.8\)) & \(0.00888\) \\ \cline{2-8}  & \begin{tabular}{c} **Standing single-leg lateral raise** \\ **(hip abduction)** \\ \end{tabular} & \(32.1\pm 9.0\) & \(33.6\pm 6.0\) & \(0.33\) & \(-1.5\) (\(-4.8\), \(1.8\)) & \(-0.19657\) \\ \cline{2-8}  & \
\begin{tabular}{c} **Standing maximal knee raise** \\ **(hip flexion)** \\ \end{tabular} & \(84.4\pm 17.0\) & \(92.9\pm 13.9\) & \(0.03\) & \({}^{*}\) & \(-8.5\) (\(-15.9\), \(-1.2\)) & \(-0.54849\) \\ \cline{2-8}  &
\begin{tabular}{c} **Standing lateral step with arm** \\ **extension (knee flexion)** \\ \end{tabular} & \(57.3\pm 12.5\) & \(56.4\pm 14.8\) & \(0.75\) & \(0.9\) (\(-5.3\), \(7.0\)) & \(0.06422\) \\ \hline \hline \end{tabular}  
* \({}^{\lx@sectionsign}\) mean \(\pm\) standard deviation; \({}^{*}\)\(p<0.05\).  
\end{table}
Table 2: Comparison results of mean joint angles with and without AR system application.  
As indicated in Table 3, the application of the AR system generally led to a decrease in the standard deviation of the mean joint angles across all movements compared to the condition without the AR system. Notably, statistically significant reductions in standard deviation (\(p<0.05\)) were observed in the following six movements: (1) standing arm raise overhead, (2) standing trunk lateral flexion, (3) standing diagonal raise with a medicine ball, (4) standing forward lunge with dumbbells, (5) standing single-leg lateral raise, and (6) standing knee flexion to maximum height.