## 3 Results
### Descriptive Statistics
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Women** & \multicolumn{2}{c}{**Men**} \\ \hline  & **Pre vs. Post Treatment** & \multicolumn{2}{c}{**Pre vs. Post Treatment**} \\ \hline  & **Correlation Coefficient** & \(p\)**-Value** & **Correlation Coefficient** & \(p\)**-Value** \\ \hline F0 (Hz) & 0.399 * & 0.256 & 0.587 * & 0.647 \\ Jitter (\%) & 0.307 ** & \textless{}0.001 ** & 0.111 & \textless{}0.001 ** \\ Shimmer (\%) & 0.154 & \textless{}0.001 ** & 0.325 & 0.013 ** \\ NHR (dB) & \(-0.015\) & 0.004 ** & 0.208 & 0.884 \\ SFF (Hz) & 0.792 * & 0.635 & 0.771 * & 0.182 \\ MPT (s) & 0.695 * & 0.061 & 0.688 * & 0.004 ** \\ \hline \hline \end{tabular}  
* and ** mean that the correlation is significant at the 0.01 and 0.05 levels, respectively.  
\end{table} 
Table 2: Correlation and \(p\)-value analysis before and after treatment in female and male voices. In Figure 3, effectiveness is assessed based on the GRBAS scale, with \"G\" being the reference point. When comparing the results from before and after voice therapy, if the G score of the post-treatment improves, it is assumed to indicate effectiveness (+). The distributions of various acoustic parameters before and after voice therapy were examined in female and male voices, using effectiveness as the criterion in Figures 3 and 4. They provide an overview of the changes in various acoustic parameters based on the presence (+) or absence (-) of effectiveness. When comparing the distribution of acoustic parameters in female voices between Figures 2 and 3, they exhibited similar patterns. In particular, there was a noticeable tendency toward clear treatment effects in the distribution of jitter, shimmer, and NHR in Figures 3b, 3c and 3d, respectively. Figure 2: Distributions of acoustic parameters before and after treatment in female and male voices. * Extreme, 0 Outlier. As shown in Table 3, for females, significant results were observed for jitter, shimmer, and NHR when effectiveness was demonstrated after voice therapy. However, when there was no improvement after therapy, none of the parameters showed significant results. Regarding the correlation analysis, when the voice therapy showed effectiveness, strong positive correlations were observed in SFF and MPT. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Female**} & \multicolumn{3}{c}{**Male**} \\ \hline \multicolumn{3}{c}{**Effectiveness (+)**} & \multicolumn{3}{c}{**Effectiveness (-)**} & \multicolumn{3}{c}{**Effectiveness (+)**} & \multicolumn{3}{c}{**Effectiveness (-)**} \\ \hline \multicolumn{3}{c}{**Before vs. after Treatment**} & \multicolumn{3}{c}{**Before vs. after Treatment**} & \multicolumn{3}{c}{**Before vs. after Treatment**} & \multicolumn{3}{c}{**Before vs. after Treatment**} \\ \hline \multirow{3}{*}{
\begin{tabular}{c} **Correlation** \\ **Coefficient** \\ \end{tabular} } & \multirow{2}{*}{\(p\)**-Value**} & **Correlation** & \multirow{2}{*}{\(p\)**-Value**} & **Correlation** & \multirow{2}{*}{\(p\)**-Value**} & **Correlation** & \multirow{2}{*}{\(p\)**-Value**} \\  & **Coefficient** & & & & & & & **Coefficient** & \\ \hline F0 (Hz) & 0.484 \({}^{*}\) & 0.359 & 0.101 & 0.462 & 0.149 & 0.291 & 0.984 \({}^{*}\) & 0.916 \\ Jitter (\%) & 0.223 & \textless{}0.001 ** & 0.818 \({}^{*}\) & 0.129 & 0.068 & \textless{}0.001 ** & 0.661 & 0.753 \\ Shimmer (\%) & 0.475 & \textless{}0.001 ** & 0.682 \({}^{*}\) & 0.270 & 0.257 & 0.002 ** & 0.681 & 0.916 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation and \(p\)-value analysis before and after treatment based on effectiveness in female and male voices. Figure 3: Comparison of acoustic parameters before and after treatment for the effectiveness and non-effectiveness groups in female voices. \({}^{*}\) Extreme, \({}^{\circ}\) Outlier. When comparing the distribution of acoustic parameters in male voices between Figures 2 and 4, they exhibited similar patterns. In particular, there was a noticeable tendency of clear treatment effects to be seen in the distribution of jitter in Figure 4b.