# COVID-19 Diagnosis in Chest X-rays Using Deep Learning and Majority Voting
## 3 Results
### Discussion
To calculate the \(p\)-value, we converted Table 11 into a more understandable way to estimate the superiority of one algorithm over the others. On every selected dataset, we calculated the increase in accuracy of every method proportionally to the margin between the top and the least algorithm. Results are written in Table 12.  
The probability that one method belongs to the top 5% of the margin between the best and the least performing algorithm on one dataset is: \(p_{0}=0.05\). Based on the \begin{table}
\begin{tabular}{l l l l} \hline Model & Accuracy on the Test Set & Accuracy on the Validation & Average Accuracy \\ \hline Majority Voting & 0.99315 & 0.99313 & 0.99314 \\ (hard approach) & & & \\ \hline Majority Voting & 0.99315 & 0.99313 & 0.99314 \\ (soft approach) & & & \\ \hline ResNet11 & 0.9863 & 0.99313 & 0.989715 \\ \hline DenseNet-201 & 0.9893 & 0.98625 & 0.987775 \\ \hline MobileNetV2 & 0.99658 & 0.97595 & 0.986265 \\ \hline EfficientNet-B7 & 0.97603 & 0.99313 & 0.98458 \\ \hline ResNet50V2 & 0.99315 & 0.97595 & 0.98455 \\ \hline Xception & 0.97945 & 0.97945 & 0.97945 \\ \hline ResNet50V1 & 0.98973 & 0.96564 & 0.977685 \\ \hline InceptionV3 & 0.98288 & 0.96564 & 0.97426 \\ \hline EfficientNet-B1 & 0.9863 & 0.95876 & 0.97253 \\ \hline EfficientNet-B5 & 0.97603 & 0.96564 & 0.970835 \\ \hline VGG16 & 0.96575 & 0.96907 & 0.96741 \\ \hline EfficientNet-B2 & 0.97603 & 0.95189 & 0.96396 \\ \hline EfficientNet-B3 & 0.96233 & 0.95189 & 0.95711 \\ \hline EfficientNet-B6 & 0.97603 & 0.93471 & 0.95537 \\ \hline EfficientNet-B4 & 0.96233 & 0.94502 & 0.953675 \\ \hline EfficientNet-B0 & 0.92466 & 0.88316 & 0.90391 \\ \hline \end{tabular}
\end{table} 
Table 11: Average Accuracy of the classifiers and the Majority Voting methods on both the test and the validation dataset. observations made on the test and the validation sets, the probability that the Majority Voting belongs to the top 5% margin on both the test and the validation set is \(p\)-value \(=P(H_{0})=p_{0}\times p_{0}=0.0025\). The common \(\alpha\) value used as the threshold for \(p\)-value is 0.05 [53]. In our case, \(p\)-value \(=0.0025<<0.05\), which is strongly sufficient to reject the Null Hypothesis \(H_{0}\). This strongly disprove the hypothesis that the Majority Voting superiority among other classifiers is explained by chance. Moreover, calculating the \(p\)-value for other methods is not enough to reject the Null Hypothesis \(H_{0}\) for them. This reinforces more the statistical significance of the superiority of the Majority Voting over all the other classifiers. Hence, we suggest that the Majority Voting approach is the most efficient method to use in general cases when we do not have ideas about the targeted dataset. For all other classifiers, the accuracy changes from one dataset to another. No classifier is able to be adopted for every dataset. This study emphasizes the efficiency of the Voting approaches (especially the Majority Voting approach) in treating some sensitive tasks, like COVID diagnosis. Our study has some limitations to be targeted in the next research works. One of them is that the dataset is not associated with data about the subjects who participated in the study. This fact obliged us to be limited to descriptive statistics and prevented us from using inferential statistics tools. Data, like gender, age, and clinical symptoms, could strengthen our medical analysis method for better adoption in real cases. The dataset was also not associated with the PCR test result (Polymerase chain reaction test) for every sample image. PCR test is considered by many as the gold standard for COVID-19 diagnosis. Calculation of the agreement rate between our method and the PCR test allows us to judge more the potential of our method for a prevalent and widespread adoption in the actual condition of the COVID-19 pandemic. All these limitations can be targeted in other studies to go deeper into our method's clinical interpretation.