# Big Data-Driven Deep Learning Ensembler for DDoS Attack Detection
## 4 Simulation and Results
### Statistical Analysis Results  
Statistical tests, including Wilcoxon, Spearman's, Chi-Squared, and ANOVA, were conducted to validate the significance of the results on the IoT-23 and APA-DDoS datasets, as shown in Table 6. Statistical test results are shown in the table. The proposed EffiGRU-GhostNet and baseline models GRU-RNN, LSTM, ANN-GWO, CNN, SVM, and DBN are evaluated using F-statistic and \(p\)-value metrics. The statistical analysis shows numerous noteworthy findings. Variable correlation is shown via Spearman's test. The EffiGRU-GhostNet model has a Spearman's F-statistic of 0.824 and a \(p\)-value of 0.007, indicating a strong association. Other models like ANN-GWO and LSTM show promising results with F-statistics of 0.802 and 0.737. Wilcoxon tests demonstrate substantial paired sample median differences. A Wilcoxon F-statistic of 7.634 and a \(p\)-value of 0.024 indicate significant differences between paired observations in EffiGRU-GhostNet. GRU-RNN and LSTM models also perform well, with F-statistics of 6.713 and 7.211 and \(p\)-values of 0.033 and 0.021. EffiGRU-GhostNet has an F-statistic of 0.043 and a \(p\)-value of 0.003 in the Paired Student test, indicating significant differences between paired observations. CNN and DBN models have negative F-statistics, showing inverse connections in paired observations. ANOVA shows substantial group mean differences, with EffiGRU-GhostNet having a high F-statistic of 49.307 and a \(p\)-value of 0.002. DBN has a high F-statistic of 68.917, showing group mean-variance. EffiGRU-GhostNet performs well in Chi-Squared and Student tests, demonstrating its efficacy with the datasets. The extensive statistical study shows that EffiGRU-GhostNet outperforms competing baseline models in IoT and DDoS detection.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Techniques** & **Wilcoxon** & **Spearman’s** & **Chi-Squared** & **Paired Student** & **ANOVA** & **Student** \\ \hline Proposed (F-stat) & 7.632 & 0.822 & 173 & 0.04 & 49.305 & 0.00 \\ \hline Proposed (P-val) & 0.022 & 0.005 & \(-\)0.010 & 0.001 & 0.000 & 0.060 \\ \hline GRU-RNN (F-stat) & 6.710 & 0.664 & 214 & \(-\)4.775 & 56.977 & \(-\)1.914 \\ \hline GRU-RNN (P-val) & 0.031 & 0.019 & \(-\)0.010 & 0.000 & 0.001 & 0.031 \\ \hline LSTM (F-stat) & 7.209 & 0.735 & 191 & \(-\)4.133 & 51.753 & \(-\)1.642 \\ \hline LSTM (P-val) & 0.019 & 0.012 & \(-\)0.010 & 0.000 & 0.000 & 0.044 \\ \hline ANN-GWO (F-stat) & 7.913 & 0.800 & 179 & \(-\)3.905 & 47.914 & \(-\)1.355 \\ \hline ANN-GWO (P-val) & 0.027 & 0.008 & \(-\)0.010 & 0.000 & 0.000 & 0.055 \\ \hline CNN (F-stat) & 5.973 & 0.522 & 285 & \(-\)5.325 & 62.173 & \(-\)2.488 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistical analysis tests on IoT-23 and APA-DDoS dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Metric** & **Proposed** & **GRU-RNN [16]** & **LSTM [27]** & **ANN-GWO [22]** & **CNN [18]** & **SVM [9]** & **DBN [19]** \\ \hline Precision & 0.9905 & 0.8813 & 0.8675 & 0.8935 & 0.8370 & 0.8485 & 0.9354 \\ \hline Specificity & 0.9885 & 0.9288 & 0.9201 & 0.9368 & 0.8910 & 0.8987 & 0.9165 \\ \hline Recall & 0.9910 & 0.8776 & 0.8691 & 0.8804 & 0.8292 & 0.8335 & 0.9