## 5 Experimental Design
### Analysis of Variance Results  
#### 5.3.1 ANOVA Results under Different Imbalance Ratios  
We conducted comprehensive ANOVA experiments to gain a deeper understanding and quantify the impact of different parameters on the CNN model performance across various levels of imbalance. ANOVA was conducted on datasets with imbalance ratios of 25:1, 15:1, and 1:1, showing the main and interactions effects of LR, DR 1, DR 2, and KS on CNN model accuracy. Table 5 presents partial results from the fractional factorial design experiments conducted on the CIFAR-10 dataset, encompassing a total of 250 data points. For clarity and conciseness, Table 5 displays only rows 1-4, 124-126, and 247-250, representing the overall dataset. Each parameter configuration was tested four times, and the accuracy, F1 score, G-mean, P-mean, and recall values were obtained for the minority class in each experiment. The same experiments were conducted using the Fashion-MNIST dataset. These data were used for variance analysis to assess the main and interaction effects of different factors on model performance. Through repeated experiments, we can better understand the impact of each parameter on the model performance and identify the optimal parameter combination to enhance the model's classification performance on imbalanced datasets. The data in the table demonstrate the consistency and variability of the results under the same parameter configurations, providing reliable support data for the subsequent variance analysis. Comparing the results from Tables 6-8, it is evident that LR, KS, and their interaction significantly impact the model accuracy across all imbalance ratios. The results indicate that these two parameters are crucial tuning factors across different levels of imbalanced datasets. In the CIFAR-10 dataset with an imbalance ratio of 25:1, both LR and KS significantly affected model accuracy, with \(p\)-values of \(6.508\times 10^{-8}\) and \(0.036\), respectively. In the same dataset, the interaction effect between LR and KS (LR \(\times\) KS) also showed a significant impact, with an F-value of 27.600 and a \(p\)-value of \(7.358\times 10^{-19}\). The combination of these two parameters significantly influenced the model performance. LR and KS exhibited significant effects on the CIFAR-10 dataset with an imbalance ratio of 15:1, with \(p\)-values of \(1.622\times 10^{-11}\) and \(4.925\times 10^{-7}\), respectively. The interaction effect between LR and KS (LR \(\times\) KS) was particularly noteworthy, with an F-value of 38.768 and a \(p\)-value of \(5.079\times 10^{-25}\), indicating a highly significant impact. In the balanced CIFAR-10 dataset, LR and KS still significant affected accuracy, with \(p\)-values of \(1.125\times 10^{-7}\) and \(4.982\times 10^{-10}\), respectively. Furthermore, the interaction effect between LR and KS (LR \(\times\) KS) also demonstrated a significant impact, with an F-value of 209.146 and a \(p\)-value of \(5.673\times 10^{-17}\). However, DR 1 and DR 2 did not exhibit significant main or interaction effects on any dataset, with \(p\)-values greater than 0.1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Layers** & **Configuration** \\ \hline Conv\_1 & 32 filters, kernel, and ReLU \\ MaxPool\_1 & \(2\times 2\) kernel \\ Dropout\_1 & \(20\%\) \\ Conv\_2 & 64 filters, kernel, and ReLU \\ MaxPool\_2 & \(2\times 2\) kernel \\ Dropout\_2 & \(20\%\) \\ Conv\_3 & 32 filters, kernel, and ReLU \\ Conv\_4 & 32 filters, kernel, and ReLU \\ Conv\_5 & 32 filters, kernel, and ReLU \\ MaxPool\_3 & \(2\times 2\) kernel \\ Dropout\_3 & \(20\%\) \\ Fully\_1 & 256 neurons, ReLU \\ Fully\_2 & 10 neurons, SoftMax \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CNN model structure. Just as we conducted experiments on the CIFAR-10 dataset, we carried out the same experiments on the Fashion-MNIST dataset and achieved similar results. Across different imbalance ratios, we found significant main effects and interaction effects of LR and KS on the CNN model accuracy.