## 3 Results  
The descriptive characteristics of the participants are shown in Table 2.  
This study did not end up with the initially indicated sample size due to unforeseen circumstances during the intervention period, resulting in a final sample size of 26 participants. However, a post hoc power analysis was conducted to assess the statistical power of the study at the final sample size. The results of the post hoc analysis indicated that this study maintained adequate power for the primary metrics. Specifically, the post hoc power for serve speed (mph) was 0.977, and for the CKCUET (normalized value), it was 0.982, both indicating that this study had sufficient power to detect meaningful effects using the final sample size.  
Significant enhancements were observed in the neuro-athletic training (NAT) group across multiple performance metrics, demonstrating the effectiveness of the intervention. Specifically, the NAT group showed substantial gains in flexibility, with a statistically significant increase (_p_ = 0.040) and a moderate effect size ([PERSON]'s d = 0.845), indicating meaningful improvements in their range of motion and musculoskeletal adaptability. Similarly, serve speed performance exhibited notable improvement in the NAT group, with these results reaching a high level of statistical significance (_p_ < 0.001) and a large effect size ([PERSON]'s d = 1.503), highlighting the intervention's substantial impact on the power and precision of serve actions. Furthermore, upper limb performance, measured through the CKCUET, showed a highly significant increase (_p_ = 0.002) and a large effect size ([PERSON]'s d = 1.152), emphasizing the intervention's role in improving upper body strength, stability, and motor coordination (Table 3).  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{l}{**NAT Mean \(\pm\) SD**} & \multicolumn{2}{l}{**Control Mean \(\pm\) SD**} \\  & **(N = 13)** & **(N = 13)** & _p_**-Value** \\ \hline Age (year) & 19.50 \(\pm\) 1.77 & 19.80 \(\pm\) 1.87 & 0.725 \\ \hline Height (m) & 1.92 \(\pm\) 0.04 & 1.92 \(\pm\) 0.09 & 0.762 \\ \hline Weight (kg) & 76.90 \(\pm\) 9.45 & 78.10 \(\pm\) 12.75 & 0.65 \\ \hline BMI (kg/m\({}^{2}\)) & 20.71 \(\pm\) 1.99 & 21.02 \(\pm\) 2.22 & 0.821 \\ \hline Sport Experience (year) & 5.45 \(\pm\) 2.29 & 5.15 \(\pm\) 1.45 & 0.781 \\ \hline BMI: body mass index; NAT: neuro-athletic training; SD: standard deviation. & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: The descriptive characteristics.  
In contrast, the control group did not demonstrate any statistically significant changes in their flexibility (\(p=0.236\)), serve speed (\(p=0.197\)), or upper limb performance (\(p=0.193\)) from the pre- to post-training assessments, suggesting that traditional training alone was insufficient to produce similar outcomes. Between-group comparisons further confirmed the superiority of the NAT group across all of the parameters measured, with \(p\)-values ranging from 0.040 to \(<\)0.001 and effect sizes (Cohen's d) spanning from 0.845 to 1.503. These results underscore the robust impact of the neuro-athletic training program on neuromuscular performance, demonstrating its potential to enhance specific athletic capabilities in a more targeted and effective manner than traditional training methods (see Table 3 and Figure 9 for detailed comparisons).