## 5 Experimental Design
### Analysis of Variance Results
#### 5.3.1 ANOVA Results under Different Imbalance Ratios
In the Fashion-MNIST dataset with an imbalance ratio of 25:1, LR and KS exhibited \(p\)-values of \(4.341\times 10^{-10}\) and \(9.776\times 10^{-4}\), respectively. The interaction effect (LR \(\times\) KS) showed an F-value of 27.322 and a \(p\)-value of \(1.069\times 10^{-18}\). Under the 15:1 imbalance ratio, LR and KS had \(p\)-values and F-values of \(1.338\times 10^{-8}\) and \(8.591\times 10^{-4}\), respectively, with an interaction effect (LR \(\times\) KS) \(p\)-value of \(3.810\times 10^{-8}\) and F-value of \(13.800\). In the balanced dataset, LR and KS significantly influenced the CNN model accuracy with \(p\)-values of \(3.601\times 10^{-9}\) and \(1.184\times 10^{-3}\), respectively. The interaction effect (LR \(\times\) KS) had an F-value of 12.222, although its impact was slightly diminished compared with that in the highly imbalanced dataset. These results underscore that the observed effects are not incidental but robust validations of their impact on model performance. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Degrees of Freedom** & **Sums of Squares** & **Mean Squares** & **F-Values** & \(p\)**-Values** \\ \hline LR & 4 & 4172.556 & 1043.139 & 10.565 & \(6.508\times 10^{-8}\) \\ DR 1 & 4 & 112.928 & 28.232 & 0.245 & 0.912 \\ DR 2 & 4 & 171.201 & 42.800 & 0.372 & 0.828 \\ KS & 1 & 498.492 & 498.492 & 7.373 & 0.036 \\ LR\({}^{*}\)DR 1 & 16 & 1390.666 & 86.917 & 0.862 & \(6.137\times 10^{-1}\) \\ LR\({}^{*}\)DR 2 & 16 & 871.953 & 54.497 & 0.530 & \(9.298\times 10^{-1}\) \\ LR\({}^{*}\)KS & 4 & 7464.556 & 1866.139 & 27.600 & \(7.358\times 10^{-19}\) \\ DR 1\({}^{*}\)DR 2 & 16 & 1145.995 & 71.625 & 0.598 & 0.883 \\ DR 1\({}^{*}\)KS & 4 & 49.896 & 12.474 & 0.108 & 0.979 \\ DR 2\({}^{*}\)KS & 4 & 104.523 & 26.131 & 0.227 & 0.922 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ANOVA results for accuracy on the CIFAR-10 dataset with an imbalance ratio of 25:1. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Degrees of Freedom** & **Sums of Squares** & **Mean Squares** & **F-Values** & \(p\)**-Values** \\ \hline LR & 4 & 4264.931 & 1066.232 & 15.958 & \(1.622\times 10^{-11}\) \\ DR 1 & 4 & 217.170 & 54.292 & 0.812 & \(5.182\times 10^{-1}\) \\ DR 2 & 4 & 58.650 & 14.662 & 0.213 & \(9.309\times 10^{-1}\) \\ KS & 1 & 155.630 & 155.630 & 7.929 & \(4.925\times 10^{-2}\) \\ LR\({}^{*}\)DR 1 & 16 & 646.592 & 40.412 & 0.604 & \(8.784\times 10^{-1}\) \\ LR\({}^{*}\)DR 2 & 16 & 361.287 & 22.580 & 0.328 & \(9.937\times 10^{-1}\) \\ LR\({}^{*}\)KS & 4 & 6178.579 & 1544.644 & 38.768 & \(5.079\times 10^{-25}\) \\ DR 1\({}^{*}\)DR 2 & 16 & 646.767 & 40.422 & 0.598 & 0.958 \\ DR 1\({}^{*}\)KS & 4 & 205.396 & 51.349 & 0.629 & 0.642 \\ DR 2\({}^{*}\)KS & 4 & 115.262 & 28.815 & 0.348 & 0.844 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: ANOVA results for accuracy on the CIFAR-10 dataset with an imbalance ratio of 15:1. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Degrees of Freedom** & **Sums of Squares** & **Mean Squares** & **F-Values** & \(p\)**-Values** \\ \hline LR & 4 & 377.506 & 94.376 & 27.176 & \(1.125\times 10^{-7}\) \\ DR 1 & 4 & 8.587 & 2.146 & 0.431 & 0.786 \\ DR 2 & 4 & 4.653 & 1.163 & 0.232 & 0.919 \\ KS & 1 & 177.729 & 177.729 & 41.954 & \(4.982\times 10^{-10}\) \\ LR\({}^{*}\)DR 1 & 16 & 19.541 & 1.221 & 0.334 & \(9.930\times 10^{-1}\) \\ LR\({}^{*}\)DR 2 & 16 & 12.175 & 0.760 & 0.205 & \(9.996\times 10^{-1}\) \\ LR\({}^{*}\)KS & 4 & 523.034 & 130.758 & 209.146 & \(5.673\times 10^{-17}\) \\ DR 1\({}^{*}\)DR 2 & 16 & 4.330 & 0.270 & 0.050 & 0.929 \\ DR 1\({}^{*}\)KS & 4 & 3.162 & 0.790 & 0.182 & \(9.472\times 10^{-1}\) \\ DR 2\({}^{*}\)KS & 4 & 2.519 & 0.629 & 0.144 & \(9.651\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: ANOVA results for accuracy on the CIFAR-10 dataset with an imbalance ratio of 1:1. The previous section demonstrates the significant impact of various parameters on accuracy.