## 4 Results and Discussion
### ANOVA Analysis
The same is true for the dependence of the face-to-face vs. asynchronous methodologies with a value of \(p\) = 0.25, which means that there is no direct relationship between the types of methodologies concerning the academic results obtained in the academic years 2019-2020 and 2020-2021. Methodologies Face-to-Face vs. Face-to-Face Per Academic Year  
The results obtained from the one-way ANOVA for the analysis of the mean scores obtained by each class can be seen in Table 17. The \"F\" value of the sample (2019-2020 and 2020-2021) is 7.47 and higher than the critical F of 3.99; \(p\)-value = 0.01 (\(p\) < 0.05). Therefore, the null hypothesis of equality of means is rejected, and there is a difference between the groups. Subsequently, a multiple comparison analysis (post hoc test) was carried out using [PERSON]'s exact test (see Table 18) to examine differences in depth. As a result, a direct correlation was observed between the face-to-face methodologies in the different academic years. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Origin of Variation** & **DF** & **Sum of Squares** & **Mean Square** & **F-Value** & **Prob \textgreater{} F** & **F Critical** \\ \hline Model & 1 & 0.52 & 0.12 & 0.12 & 0.73 & 3.99 \\ Error & 65 & 287.09 & 4.42 & & & \\ Total & 66 & 287.62 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 16: ANOVA results for a 0.05 level of significance for the means per academic year. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Methodologies** & **Origin of Variation** & **DF** & **Sum of Squares** & **Mean Square** & **F-Value** & **Prob \textgreater{} F** & **F Critical** \\ \hline face-to-face vs. face-to-face & Model & 1 & 6.78 & 6.78 & 7.47 & 0.01 * & 3.99 \\  & Error & 65 & 58.96 & 0.91 & & & \\  & Total & 66 & 65.74 & & & & \\ \hline face-to-face vs. synchronous & Model & 1 & 0.77 & 0,77 & 2.59 & 0.11 & 3.99 \\  & Error & 65 & 19.25 & 0.30 & & & \\  & Total & 66 & 20.02 & p & & & \\ \hline face-to-face vs. asynchronous & Model & 1 & 1.19 & 1.19 & 1.34 & 0,25 & 3.99 \\  & Error & 65 & 58.49 & 0.89 & & & \\  & Total & 66 & 59.68 & & & & \\ \hline \hline \end{tabular}
* Population means are taken to be significantly different at the significance level 0.05.  
\end{table} 
Table 17: ANOVA results for a 0.05 level of significance for the means for the different methodologies per academic year. The results obtained in Table 18 show the differences when comparing the face-to-face methodologies in the two years of the study. These differences, as seen above, do not appear in the other methodologies applied. With the same number of topics, the same teaching staff, teaching the thematic block and the same methodology--the only difference between one year and the next is the increase in the difficulty of the questions posed in the final test, as explained in Section 3.2. Methodologies used (see Table 5). If we compare the data obtained in Tables 7 and 8, extracting only the data on the percentage of success in the first four topics, where the significant difference is obtained, and this is compared with the difficulty criteria in Table 6, we can see that there is an average difference of 13.75 percentage points, which coincides with the added and estimated difficulty of 14% in the final exam according to Table 6.