## 3 Results  
Tables 1-3 show the results of statistical analysis with a split-plot design for each evaluation index. In the COP-FB, COP-LR, and COP-Area evaluation indices, the participant and the mouthguard were significant factors, and their interaction was not significant. Therefore, multiple comparison tests were performed using the Bonferroni method to examine the differences in COP displacement among participants. In addition, the difference in COP displacement between mouthguard conditions was analyzed using a paired \(t\)-test. Figure 4 shows the difference in COP-FB among participants and between mouthguard conditions. COP-FB significantly decreased in the order from untrained adults to weightlifters to gymnasts (\(p<0.01\), \(p<0.05\)), irrespective of the mouthguard factor. Differences due to the mouthguard factor were observed in all participants, with COP-FB being significantly lower with a mouthguard than without a mouthguard (gymnnasts: \(p<0.01\); untrained adults and weightlifters: \(p<0.05\)). Figure 5 shows the difference in COP-LR among participants and between mouthguard conditions. Significant differences were observed between untrained adults and gymnasts and between untrained adults and weightlifters without a mouthguard, and the COP-LR values of gymnasts and weightlifters were lower than those of untrained adults (\(p<0.05\)). With a mouthguard, gymnasts showed significantly lower values than untrained adults (\(p<0.05\)). Differences due to the mouthguard factor were observed in untrained adults and gymnasts, with COP-LR values significantly lower with a mouthguard than without a mouthguard (\(p<0.01\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **df** & **SS** & **MS** & **\(F\) Value** & **\(p\)-Value** \\ \hline Participant group (A) & 2 & 44.191 & 22.095 & 13.053 & \textless{}0.001 ** \\ Mouthguard (B) & 1 & 2.662 & 2.662 & 14.409 & \textless{}0.001 ** \\ A \(\times\) B & 2 & 0.674 & 0.337 & 1.826 & 0.174 \\ Error & 41 & 7.573 & 0.185 & & \\ \hline \hline \end{tabular}  
* COP: center of pressure. COP-FB: COP displacement in the front-and-back direction. df: degree of freedom. SS: sum of squares. MS: mean square. **\(p<0.01\)**: denotes statistically significant difference.  
\end{table} 
Table 1: Results of COP-FB displacement by a split-plot design analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **df** & **SS** & **MS** & **\(F\) Value** & **\(p\)-Value** \\ \hline Participant group (A) & 2 & 0.497 & 0.249 & 0.795 & \textless{}0.05 * \\ Mouthguard (B) & 1 & 0.422 & 0.422 & 7.955 & \textless{}0.01 ** \\ A \(\times\) B & 2 & 0.090 & 0.045 & 0.850 & 0.435 \\ Error & 41 & 2.174 & 0.053 & & \\ \hline \hline \end{tabular}  
* COP: center of pressure. COP-LR: COP displacement in the left-and-right direction. df: degree of freedom. SS: sum of squares. MS: mean square. **\(p<0.01\), *\(p<0.05\): denotes statistically significant difference.  
\end{table} 
Table 2: Results of COP-LR displacement by a split-plot design analysis. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source** & **df** & **SS** & **MS** & **\(F\) Value** & **\(p\)-Value** \\ \hline Participant group (A) & 2 & 9.303 & 4.651 & 1.756 & \textless{}0.05 * \\ Mouthguard (B) & 1 & 5.255 & 5.255 & 20.306 & \textless{}0.001 ** \\ A \(\times\) B & 2 & 0.632 & 0.316 & 1.222 & 0.305 \\ Error & 41 & 10.610 & 0.259 & & \\ \hline \hline \end{tabular}  
* COP: center of pressure. COP-Area: area enclosed by the trajectory of the COP fluctuation. df: degree of freedom. SS: sum of squares. MS: mean square. **\(p<0.01\), *\(p<0.05\): denotes statistically significant difference.  
\end{table} 
Table 3: Results of COP-Area displacement by a split-plot design analysis. Figure 6 shows the difference in COP-Area among participants and between mouthguard conditions.