## 5 Results and Analysis  
The data for training the two CNN models were designed to classify six emotions including anger, fear, happiness, neutrality, sadness, and surprise by using the labeled images. In this training process, the models were trained for 100 epochs where the performance was measured on each epoch with both training and validation accuracy and loss recorded. Precision, recall, and F1 scores were used to evaluate the performance of each model. In addition, confusion matrices were used to describe how well the model was able to classify instances and visualize the classification performance of the model. Furthermore, a chi-square test for independence was used to determine if there was a significant relationship between the predictions of the models. An illustration showing how true and predicted labels are distributed among the six emotion categories in the first model is presented in Figure 1.  
The performance of the training and validation over 100 epochs in the first model is shown in Figure 2. This was performed by sketching both accuracy and loss curves. The first model achieved an overall accuracy of 61.78%. Table 2 summarizes the precision, recall, and F1 score for each emotion. The confusion matrix for the second model (Figure 3) shows the distribution of the true and predicted labels across the six emotion categories. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Emotions** & **Precision** & **Recall** & **FI-Score** & **Support** \\ \hline Angry & 0.55 & 0.51 & 0.53 & 958 \\ Fear & 0.45 & 0.24 & 0.32 & 1024 \\ Happy & 0.75 & 0.88 & 0.81 & 1774 \\ Neutral & 0.52 & 0.61 & 0.57 & 1233 \\ Sad & 0.47 & 0.49 & 0.48 & 1247 \\ Surprise & 0.70 & 0.72 & 0.71 & 831 \\ Accuracy & & & 0.62 & 7067 \\ Macro Avg & 0.60 & 0.59 & 0.59 & 7067 \\ Weighted Avg & 0.61 & 0.62 & 0.61 & 7067 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance metrics for the first model. Figure 1: Confusion matrix for the first model. Figure 2: Model accuracy and loss—first model. The accuracy and loss curves for the second model (Figure 4) show the training and validation performance for 100 epochs. The second model achieved an overall accuracy of 63.95%. Table 3 summarizes the precision, recall, and F1 score for each emotion. The second model outperformed the first model, achieving higher overall accuracy and improved performance metrics for most emotion categories. The accuracy and loss curves indicate that the training of both models was effective, with the second model showing better generalization, as evidenced by its higher validation accuracy. Figure 4: Model accuracy and loss—second model. Figure 3: Confusion matrix for the second model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Emotions** & **Precision** & **Recall** & **F1-Score** & **Support** \\ \hline Angry & 0.58 & 0.55 & 0.56 & 958 \\ Fear & 0.50 & 0.28 & 0.36 & 1024 \\ Happy & 0.85 & 0.88 & 0.87 & 1774 \\ Neutral & 0.55 & 0.68 & 0.61 & 1233 \\ Sad & 0.49 & 0.53 & 0.51 & 1247 \\ Surprise & 0.72 & 0.77 & 0.75 & 831 \\ Accuracy & & & 0.64 & 7067 \\ Macro Avg & 0.62 & 0.62 & 0.61 & 7067 \\ Weighted Avg & 0.63 & 0.64 & 0.63 & 7067 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics for the second model. Both models showed high precision and recall for the \"happy\" emotion, reflecting the robustness of the models in identifying this category. However, both models had issues with the \"fear\" emotion, indicating the need for further improvements and additional training data. We performed a chi-square (1) test to compare the performance metrics (precision, recall, and F1-Score) between the two models across different emotion categories. The chi-square (\(x^{2}\)) statistic is calculated using the formula:  
\[x^{2}=\sum\frac{(O_{i}-E_{i})^{2}}{E_{i}} \tag{1}\]  
where:  
\(\bullet\)\(O_{i}\) is the observed frequency. \(\bullet\)\(E_{i}\) is the expected frequency. The chi-square test result for the first model is 0.0025 with \(p\)-value = 1.0000.