# Dynamic Path Planning for Unmanned Surface Vehicles with a Modified Neuronal Genetic Algorithm
## 5 Results and Analysis
### Significance Test  
In this study, we used the \(t\)-test to test the significance of the results of the experiment. We used a paired-samples \(t\)-test by assuming equal variances. Each pair of data points (result comparison between the baseline and proposed method in Appendix A) is treated as a single observation, and the degrees of freedom are calculated based on the number of pairs. Therefore, the degrees of freedom \((df)=(n-1)=(18-1)=17\). \(t\) Critical is obtained using Equation (6). This equation was used to calculate the value of \(t\) Critical, \(t\) Statistics, and \(p\)-Value for the data point. In this \(t\)-test, we used the alpha or significance level (\(\alpha\)) of 0.05. The Critical \(t\) value, \(t\) Statistics, and \(p\)-Value for the experimental results in a static environment are presented in Table 3 below. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Input**} & \multicolumn{4}{c}{**Baseline (NNGA)**} & \multicolumn{4}{c}{**Proposed (Modified Neuronal GA)**} \\ \cline{2-7}  & **Total** & **Distance** & **Time** & **Total** & **Distance** & **Time** \\ \hline
3 Input & 416.00 & 260.86 & 59.82 & 358.67 & 264.84 & 47.58 \\
5 Input & 558.50 & 258.28 & 53.06 & 440.67 & 263.36 & 42.36 \\
7 Input & 765.00 & 268.30 & 58.61 & 459.67 & 271.46 & 45.86 \\ Mean & 579.83 & 262.48 & 57.16 & 419.67 & 266.55 & 45.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental results from a dynamic environment for the baseline and proposed methods. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Result Comparison of Baseline and Proposed Method** & \(t\)**Critical** & \(t\)**Stat** & \(p\)**-Value** \\ \hline Total genome (convergence speed) & 1.69 & 1.74 & 0.045 \\ Travel distance & 1.69 & 0.015 & 0.493 \\ Travel time & 1.69 & \(-\)0.410 & 0.342 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(t\) Critical, \(t\) Statistics, and \(p\)-Value for experimental results in a static environment. Table 3 shows that the total genome (convergence speed) in a static environment produces a \(t\) Critical value of 1.69, a \(t\) Stat value of 1.74, and a \(p\)-Value of 0.045. Because \(t\) Stat > \(t\) Critical, and \(p\)-Value < alpha, we can conclude that the increase in convergence speed in static environment experiments with the proposed method is significant. From this table, even though the overall distance traveled under the proposed method is slightly better than that under the baseline method, the increase cannot be said to be significant. This is because, for travel distance, \(t\) Statistics < \(t\) Critical, and \(p\)-Value > alpha. Then, as seen in Table 1, the proposed method cannot produce better performance for the travel time parameter, although based on Table 3, the decrease in performance is not significant because \(t\) Statistics < \(t\) Critical, and \(p\)-Value > alpha, so the performance of the proposed method can still compete with the performance of the baseline method for this parameter. Table 4 shows the \(t\) Critical, \(t\) Statistics, and \(p\)-Value for the experimental results in a static environment. Table 4 shows a \(t\) Critical value of 1.69, a \(t\) Stat value of 1.71, and a \(p\)-Value of 0.049. Because \(t\) Stat > \(t\) Critical, or \(p\)-Value < alpha, we can conclude that the increase in the convergence speed in dynamic environment experiments with the proposed method is significant. Then, for the travel time parameter, we obtain a \(t\) Critical value of 1.69, \(t\) Stat value of 2.14, and \(p\)-Value of 0.019. Because \(t\) Stat > \(t\) Critical, or \(p\)-Value < alpha, we can conclude that the increase in the USV travel speed for one rotation in the dynamic environment experiment using the proposed method is significant. For the travel distance parameter, although the proposed method does not produce better performance, based on Table 4, we know that the decrease is not significant. This is because even though \(p\)-Value < alpha, \(t\) Stat < \(t\) Critical.