## 2 Materials and Methods
### Statistical Analysis  
All the statistical analyses were performed using R (R 4.2.2, RStudio 2023.06.0 + 421). There were four sets of statistical analyses that were performed to answer the research questions. A one-way analysis of variance and chi-square test were used to examine cohort demographic differences. For primary outcome measurements, linear mixed-effect models (LMMs) were used to identify the cohort differences for postural control performance. Specifically, LMMs were applied to the power of the low-, medium-, and high-frequency bands of the COP in the x- and y-directions, as well as the rambling and trembling components in the x- and y-directions. These models tested the effects of fixed effects of condition, trial, group, and age, as well as their interactions, including condition-by-trial, condition-by-group, trial-by-group, and condition-by-trial-by-group on the relative power during the SOT. Analyses included condition, trial, and group as fixed effects, age as a covariate, and rankit-transformed variables to address the non-normality of outcome measures. A significance level of \(p<0.05\) was used to determine statistical significance. Moreover, Spearman correlations were used to investigate the relationship between power and SOT score in each condition. Type III ANOVA tables with [PERSON]'s method were used to evaluate the significance of main effects and interactions, providing F-values and \(p\)-values (Tables 2-4). \begin{table}
\begin{tabular}{l l l l l l l} \hline  & \multicolumn{2}{c}{**Low Frequency**} & \multicolumn{2}{c}{**Medium Frequency**} & \multicolumn{2}{c}{**High Frequency**} \\
**Source of Variance** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** \\ \hline
**Center of Pressure in x** & & & & & & \\ Condition & 6.47 & \textless{}0.001 & 247.45 & \textless{}0.001 & 373.98 & \textless{}0.001 \\ Trial & 0.04 & 0.962 & 25.71 & \textless{}0.001 & 49.83 & \textless{}0.001 \\ Group & 0.39 & 0.680 & 2.22 & 0.118 & 1.66 & 0.200 \\ Age & 1.22 & 0.274 & 4.60 & 0.036 & 1.92 & 0.172 \\ Condition \(\times\) Trial & 0.43 & 0.935 & 1.36 & 0.196 & 2.40 & 0.008 \\ Condition \(\times\) Group & 2.11 & 0.021 & 1.02 & 0.423 & 2.13 & 0.020 \\ Trial \(\times\) Group & 0.64 & 0.631 & 1.41 & 0.229 & 0.23 & 0.924 \\ Condition \(\times\) Trial \(\times\) Group & 0.16 & 1.000 & 1.36 & 0.131 & 1.33 & 0.148 \\ \hline
**Center of Pressure in y** & & & & & & \\ Condition & 69.96 & \textless{}0.001 & 283.50 & \textless{}0.001 & 541.60 & \textless{}0.001 \\ Trial & 6.51 & 0.002 & 17.78 & \textless{}0.001 & 75.75 & \textless{}0.001 \\ Group & 2.61 & 0.083 & 1.95 & 0.152 & 2.47 & 0.093 \\ Age & 0.03 & 0.869 & 2.62 & 0.111 & 0.14 & 0.709 \\ Condition \(\times\) Trial & 2.75 & 0.002 & 1.13 & 0.339 & 3.14 & 0.001 \\ Condition \(\times\) Group & 2.14 & 0.020 & 2.06 & 0.025 & 1.99 & 0.032 \\ Trial \(\times\) Group & 0.31 & 0.873 & 1.95 & 0.101 & 0.31 & 0.870 \\ Condition \(\times\) Trial \(\times\) Group & 0.82 & 0.697 & 1.04 & 0.408 & 1.19 & 0.258 \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance table for the linear mixed model examining main effects and interactions of condition, trial, and group on the low-, medium-, and high-frequency band of the center of pressure in x and y, with age as a covariate.