## 3 Results
### Experimental Data Analysis
#### 3.4.5 Statistical Testing Section  
In this study, we propose a novel method for detecting low-quality fake facial images based on the YOLOv9-ARC model, which is validated on a comprehensive dataset. The core research question is whether the introduction of the Adaptive Kernel Convolution (AKConv) module and the Convolutional Block Attention Module (CBAM) can significantly enhance the detection accuracy of low-quality fake facial images. To address this, we formulate two hypotheses: the null hypothesis (H\({}_{0}\)) posits that there is no significant difference in detection accuracy between the YOLOv9-ARC model and other models, while the alternative hypothesis (H\({}_{1}\)) asserts that the YOLOv9-ARC model significantly improves detection performance. The experiment utilizes a dataset comprising various types of fake facial images, particularly those affected by low resolution, blurring, and noise. The primary evaluation metric is the mean average precision (mAP). To ensure the reliability of the experimental results, three non-parametric statistical methods--the Mann-Whitney U test, Kruskal-Wallis H test, and Wilcoxon signed-rank test--are employed to compare model performance with a significance level set at \(\alpha\) = 0. 05. Given that the detection data may not follow a normal distribution and may contain outliers, non-parametric statistical methods are chosen to avoid the assumptions required for parametric tests. The Mann-Whitney U test is used to compare two independent samples, evaluating whether the YOLOv9-ARC model exhibits significantly higher detection accuracy than other models. The Kruskal-Wallis H test extends this analysis to multiple independent samples, determining whether at least one group shows a significant difference in detection accuracy among all models, though it does not identify the specific source of the difference. Additionally, the Wilcoxon signed-rank test is applied to paired sample data to assess whether the detection accuracy on the same test data differs significantly between different models, further confirming the stability of the YOLOv9-ARC model's performance improvement. The results of these statistical tests are presented in Table 3. The Mann-Whitney U test reveals that all \(p\)-values are below 0.05, indicating a significant difference in detection accuracy between the YOLOv9-ARC model and other models. The Kruskal-Wallis H test further confirms that there is at least one significant difference among all models, demonstrating that detection accuracy is not uniformly distributed. Moreover, the Wilcoxon signed-rank test results show that the YOLOv9-ARC model significantly outperforms other models on the same test data, validating the effectiveness of the proposed approach. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Mann–Whitney U** & **Kruskal–Wallis H** & **Wilcoxon Signed-Rank** \\ \hline
1 & 4.74 \(\times 10^{-3}\) & 4.67 \(\times 10^{-3}\) & 3.19 \(\times 10^{-6}\) \\ \hline
2 & 8.67 \(\times 10^{-3}\) & 8.67 \(\times 10^{-3}\) & 3.50 \(\times 10^{-3}\) \\ \hline
3 & 4.00 \(\times 10^{-6}\) & 4.00 \(\times 10^{-6}\) & 2.29 \(\times 10^{-9}\) \\ \hline
4 & 3.60 \(\times 10^{-5}\) & 3.50 \(\times 10^{-5}\) & 4.73 \(\times 10^{-5}\) \\ \hline
5 & 4.10 \(\times 10^{-5}\) & 4.00 \(\times 10^{-5}\) & 1.58 \(\times 10^{-8}\) \\ \hline
6 & 1.53 \(\times 10^{-2}\) & 1.51 \(\times 10^{-2}\) & 1.62 \(\times 10^{-2}\) \\ \hline
7 & 5.34 \(\times 10^{-3}\) & 5.50 \(\times 10^{-3}\) & 5.90 \(\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical test results table. In conclusion, the statistical analysis supports the effectiveness of the YOLOv9-ARC model in detecting low-quality fake facial images with statistically significant improvements. The results demonstrate that the YOLOv9-ARC model exhibits significantly better detection performance compared to other models.