## 4 Discussion
Table 5 presents the results of statistical significance testing using independent \(t\)-tests, comparing the Transformer-GAN-AE model against each of the six baseline models. The table includes the calculated \(p\)-values, the evaluation result at a confidence level of \(\alpha=0.01\), and a binary assessment of whether the observed differences in performance are statistically significant. This analysis strengthens the empirical evidence by quantifying whether the improvements offered by Transformer-GAN-AE are meaningful and reproducible rather than resulting from random variation or sampling bias. The \(t\)-test is a widely used statistical method for comparing the means of two independent samples to determine if there is a statistically significant difference between them. In this context, each model's performance metric (such as accuracy or RMSE) is treated as a distribution over multiple experimental runs. A \(p\)-value below the significance threshold (\(\alpha=0.01\)) indicates that the null hypothesis (i.e., there is no difference between the models) can be rejected, and the difference in performance is unlikely to be due to chance alone. This is critical for verifying that \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Statistical \(t\)-Tests**} \\ \cline{2-4}  & \(p\)**-Value** & **Results** & \(\alpha\) \\ \hline Transformer–GAN–AE vs. BERT & 0.0005 & Significant & 0.01 \\ Transformer–GAN–AE vs. TST & 0.0002 & Significant & 0.01 \\ Transformer–GAN–AE vs. DBN & 0.00007 & Significant & 0.01 \\ Transformer–GAN–AE vs. GAN & 0.00004 & Significant & 0.01 \\ Transformer–GAN–AE vs. CNN & 0.00003 & Significant & 0.01 \\ Transformer–GAN–AE vs. XGboost & 0.00001 & Significant & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical significance analysis of the Transformer–GAN–AE compared to other models. improvements are not only numerical but also statistically valid. As shown in Table 5, all \(p\)-values fall well below the 0.01 threshold, confirming that the performance gains achieved by Transformer-GAN-AE are statistically significant across all comparisons. The smallest \(p\)-values are observed against XGBoost and CNN (0.00001 and 0.00003, respectively), emphasizing the wide performance margin. Even in comparison with stronger models such as BERT and TST, the \(p\)-values remain highly significant (0.0005 and 0.0002). These results confirm that the superiority of the proposed model is not only consistent but also statistically validated, reinforcing its reliability and robustness as an advanced detection framework for real-world IIoT systems. Table 6 reports the variance of each model's performance across repeated experimental trials on the WUSTL-IIoT-2021, Edge-IIoTset, and TON_IoT datasets. Variance quantifies how much the results fluctuate due to stochastic elements such as weight initialization, training data shuffling, or learning dynamics. Lower variance indicates greater consistency and robustness, critical qualities for models intended for deployment in sensitive industrial settings, where unpredictability in behavior could undermine trust, safety, and real-time responsiveness. As shown in Table 6, the proposed Transformer-GAN-AE achieves exceptionally low variance values on all datasets, 0.00009, 0.00011, and 0.00008, demonstrating its remarkable stability and reliability. In contrast, all baseline models exhibit higher levels of fluctuation, particularly CNN and XGBoost, whose variance reaches as high as 8.19 and 7.52, respectively. Even strong baselines such as BERT and TST show substantially higher variance compared to Transformer-GAN-AE, suggesting that while their average performance may be acceptable, they are more sensitive to random factors and less dependable under operational deployment. These findings underscore one of the key advantages of the proposed architecture and optimization strategy.