## 6 Results
### Statistical Analysis of Model Performance  
To establish the statistical significance of our findings, we conducted rigorous statistical analysis on the performance metrics of our models. For each model's accuracy, we calculated 95% confidence intervals using bootstrap resampling with 1000 iterations on the test set predictions, providing a robust measure of performance reliability independent of distributional assumptions. Table 9 presents the comparative performance of different models with their respective confidence intervals and statistical significance.  
To determine whether the performance differences between models are statistically significant, we conducted paired \(t\)-tests comparing the per-class accuracies across the four emotional categories. The analysis reveals several important findings regarding our architectural choices and fusion strategy.  
First, the CvT model for facial expression recognition (79.12%) demonstrates a substantial and statistically significant improvement over the ViT model (48.00%), with \(p<0.001\). The non-overlapping confidence intervals (77.95-80.29% vs. 46.58-49.42%) further confirm the reliability of this performance difference. This statistically significant result validates our hypothesis that incorporating convolutional operations into the transformer framework provides considerable advantages for recognizing facial expressions in children with autism.  
Similarly, our statistical analysis confirms that the CvT-based Mel spectrogram approach (83.47%) significantly outperforms the Bi-LSTM-based MFCCs approach (25.72%) for speech emotion recognition (\(p<0.001\)). The wide separation between confidence intervals (82.39-84.55% vs. 24.56-26.88%) indicates an unambiguous performance advantage, supporting our selection of the Mel spectrogram as the more appropriate speech feature representation tool for capturing emotional patterns in the vocalizations of children with autism.  
Most importantly, our multimodal feature fusion model achieves 90.73% accuracy (CI: 89.86-91.60%), which represents a statistically significant improvement over both the best facial expression model (\(p<0.01\)) and the best speech model (\(p<0.05\)). The narrow confidence interval of the fusion model indicates high consistency in performance, while the statistical significance of these improvements confirms that our attention-based fusion strategy effectively leverages complementary information from both modalities.  
These statistical analyses provide strong evidence that both our individual modal architectures and our multimodal fusion strategy deliver meaningful and statistically significant improvements for the emotion recognition in children with autism. The confidence intervals demonstrate the reliability of our results, while the significant \(p\)-values confirm that these improvements are not due to random variation but represent genuine advances in emotion recognition capabilities for this specialized application.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Type** & **Overall Accuracy (95\% CI)** & \(p\)**-Value * \\ \hline ViT (Facial Expression) & 48.00\% (46.58–49.42\%) & - \\ CvT (Facial Expression) & 79.12\% (77.95–80.29\%) & \textless{}0.001 1  \\ CvT (Mel Spectrogram) & 83.47\% (82.39–84.55\%) & \textless{}0.001 2  \\ Bi-LSTM (MFCCs) & 25.72\% (24.56–26.88\%) & - \\ Multimodal Feature Fusion & 90.73\% (89.86–91.60\%) & \textless{}0.01 , \textless{}0.05  \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparative model performance with statistical significance analysis.