# Applying Game Theory to Teach the PERT Scheduling Method
## 5 Analysis of Results
### Quantitative Analysis
#### 5.2.3 Quantitative Analysis Using the McNemar Test  
The analysis was performed question-by-question using the McNemar test to determine if the proportion of individuals who answered the questions correctly was similar before and after implementing Game Theory as a didactical technique for teaching the PERT method for scheduling projects. Analyzing the percentage differences in each question, it was observed that in 20 of 26 questions, there were proportional differences in favor of the post-test. Additionally, in 2 of the 6 remaining questions, the same number of students answered correctly. Table 8 shows only those questions with statistically significant differences (\(p<0.05\)). It should be noted that these questions had percentage variations in favor of the intervention group (post-test); that is, they achieved better performance after being taught Game Theory to learn the PERT scheduling technique, with question 7 having the lowest variation (18%) and question 8 reaching a higher percentage variation (55%).  
Figure 4 shows a portion of those students who faced the pre- and post-test and improved their performance, reaching a difference between the percentages of correct  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**Pre-Test**} & \multicolumn{2}{c}{**Post-Test**} & \multirow{2}{*}{\% Improve-} & \multirow{2}{*}{\(p\)-Value} \\ \cline{3-3} \cline{5-6}  & & **Media (S.D.)** & & & & \\ \hline \multirow{2}{*}{I} & Identification of & \multirow{2}{*}{4.36 (0.99)} & \multirow{2}{*}{5.0 (4.0–5.0)} & \multirow{2}{*}{4.84 (0.83)} & \multirow{2}{*}{5.0 (4.0–5.0)} & \multirow{2}{*}{8.1\%} & \multirow{2}{*}{0.007 W} \\  & activities & & & & & \\ \multirow{2}{*}{II} & Duration of activities & 3.12 (1.24) & 3.0 (2.0–4.0) & 4.09 (0.84) & 4.0 (4.0–4.0) & 16.2\% & 0.001 W \\ \multirow{2}{*}{III} & Critical Path & 4.91 (1.13) & 5.0 (4.0–6.0) & 6.06 (0.79) & 6.0 (6.0–7.0) & 16.5\% & 0.001 T \\  & Variability and Decision & 4.21 (0.99) & 4.0 (3.0–5.0) & 5.67 (0.99) & 6.0 (5.0–6.0) & 20.8\% & 0.001 T \\  & Total & 16.61 (2.74) & 17 (15–18) & 20.67 (1.83) & 21 (20.0–22.0) & 15.6\% & 0.001 T \\ \hline \hline \end{tabular}
\end{table}
Table 7: Differences between pre- and post-test.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Question**} & \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**Correct Answers (\%)**} & \multirow{2}{*}{**Difference**} & \multirow{2}{*}{\(p\)**-Value**} \\ \cline{3-3} \cline{5-6}  & & **Pre-Test** & & & \\ \hline Q7 & Identification of activities & 79\% & 97\% & 18\% & 0.031 \\ Q8 & Variability and Decision & 9\% & 64\% & 55\% & 0.001 \\ Q12 & Critical Path & 33\% & 85\% & 52\% & 0.001 \\ Q13 & Critical Path & 70\% & 94\% & 24\% & 0.008 \\ Q15 & Duration of activities & 52\% & 97\% & 45\% & 0.000 \\ Q16 & Variability and Decision & 33\% & 79\% & 45\% & 0.001 \\ Q18 & Duration of activities & 61\% & 97\% & 36\% & 0.002 \\ Q20 & Duration of activities & 12\% & 33\% & 21\% & 0.039 \\ Q21 & Critical Path & 70\% & 91\% & 21\% & 0.039 \\ Q26 & Variability and Decision & 52\% & 82\% & 30\% & 0.031 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Questions with statistically significant differences according to the McNemar test.  
questions of 55%. On the other hand, when comparing the total average scores for the 26 questions of the pre- and post-test groups, a percentage difference of 4.1% is evident in favor of the post-assessment, where in the pre-test, the students answered correctly, on average, 16.6 questions, and in the post-test, 20.7.