## 4 Results
### Statistical Significance of Results  
To assess the statistical significance of the performance differences between our proposed DBMM and 2L-DBMM models and the individual classifiers, we employed [PERSON]'s test [43]. This non-parametric test is suitable for paired nominal data, making it ideal for comparing the performance of two classifiers on the same dataset. The null hypothesis (H0) for [PERSON]'s test is that there is no significant difference between the models' performance.  
For SER, we conducted [PERSON]'s tests to compare the DBMM ensemble against each individual classifier (1D-CNN, SVM, RF, GNB, and MLP) across the three datasets: EmoUERJ, ESD, and the combined multilingual dataset. The results, presented in Table 17, reveal statistically significant differences (\(p<0.05\)) between the DBMM and all individual classifiers across all datasets, except for the comparison with MLP on the EmoUERJ dataset. This indicates that the DBMM ensemble consistently outperforms the individual classifiers in SER tasks, except for the MLP on the EmoUERJ, where the difference is not statistically significant. One of the possible reasons is the small size of the dataset.  
Similarly, for SA, we performed [PERSON]'s tests to compare the DBMM ensemble against the individual classifiers (BERT, GPT-2, SVM, RF, LR, MLP, and 1D-CNN) on the augmented ESD and EmoUERJ datasets.  
The results, shown in Table 18, demonstrate statistically significant differences (\(p<0.05\)) between the DBMM and all individual classifiers across both datasets. This highlights the superior performance of the DBMM ensemble in sentiment analysis tasks compared to the individual classifiers.  
For the fusion of SER and SA using the 2L-DBMM, we compared its performance against the best individual classifier for each modality (MLP for SER and BERT for SA) on both the ESD and EmoUERJ datasets. The results, presented in Table 19, show statistically  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Comparison** & \(p\)**-Value** &
\begin{tabular}{c} **Significant** \\ **Difference (\(p<0.05\))?** \\ \end{tabular} \\ \hline EmoUERJ & DBMM vs. 1D-CNN & \(3.21\times 10^{-11}\) & Yes \\ \hline EmoUERJ & DBMM vs. SVM & \(1.23\times 10^{-8}\) & Yes \\ \hline EmoUERJ & DBMM vs. RF & \(2.07\times 10^{-9}\) & Yes \\ \hline EmoUERJ & DBMM vs. GNB & \(4.39\times 10^{-12}\) & Yes \\ \hline EmoUERJ & DBMM vs. MLP & \(0.062\) & No \\ \hline ESD & DBMM vs. 1D-CNN & \(2.85\times 10^{-18}\) & Yes \\ \hline ESD & DBMM vs. SVM & \(1.08\times 10^{-14}\) & Yes \\ \hline ESD & DBMM vs. RF & \(7.63\times 10^{-16}\) & Yes \\ \hline ESD & DBMM vs. GNB & \(1.77\times 10^{-80}\) & Yes \\ \hline ESD & DBMM vs. MLP & \(1.17\times 10^{-7}\) & Yes \\ \hline Multilingual & DBMM vs. ID-CNN & \(1.42\times 10^{-22}\) & Yes \\ \hline Multilingual & DBMM vs. SVM & \(4.58\times 10^{-18}\) & Yes \\ \hline Multilingual & DBMM vs. RF & \(1.03\times 10^{-19}\) & Yes \\ \hline Multilingual & DBMM vs. GNB & \(8.91\times 10^{-88}\) & Yes \\ \hline Multilingual & DBMM vs. MLP & \(0.0021\) & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 17: [PERSON]’s test results for SER (DBMM vs. individual classifiers).  
significant differences (\(p<0.05\)) between the 2L-DBMM and the individual classifiers, indicating that the fusion model outperforms the best individual models in classifying complex emotions.