## 4 Results and Discussion
### Anova Analysis  
This statistical analysis is based on a comparison between the means of the duration of the simulations carried out in each execution period and the means of the final completed duration in each simulation. The method displays efficiency when the means for each period are equal or similar to the means for the final obtained duration. In each period analyzed, there are 10,000 data points resulting from the 10,000 simulations performed. The simulation is applied in two stages. The first corresponds to the initial execution periods of the project and, depending on the projects in the case study, they are applied every 10 or 5 months according to the total planned period of each case study. The second stage corresponds to applying the simulation in the last 10 consecutive months prior to completion of the execution of the project.  
The hypotheses for the one-way ANOVA analysis are as follows: null hypothesis (H0), all of the measurements are equal; alternative hypothesis (Ha), the measurements are not all equal; and, significance level \(\alpha\) = 0.05.  
The application of the ANOVA analysis begins with the equal variance test, using a simultaneous Bonferroni confidence level of 95%. The multiple comparison test and [PERSON]'s test applied to the four study cases generated values equal to zero for \(p\)-value, both for EVM and CTCR. These results indicate that there is no equality of variances. These values, lower than the 0.05 significance level, indicate that neither CTCR nor EVM predict a correct duration of the project in all the simulation periods.  
However, both methods show that they become more efficient during the process until forecasting becomes efficient. The Games-Howel test is applied to both methods to identify that moment. This test makes it possible to compare all the pairs in the group, with simultaneous control of the confidence level. The results obtained show differences between CTCR and EVM regarding the period in which efficient prediction values are achieved. The results for each case study are shown below.  
Figure 5: Evolution of the probability of fit of the EVM and CTCR methods to the forecast of the final period of the Santiago hydroelectric project.  
Cardenillo hydroelectric project ANOVA. The results obtained for Cardenillo are shown in Table 4, where the \(p\)-value for the CTCR methodology shows equal means for the factor levels 6 months before the simulated completion of the project. Table 4 presents the results obtained with the EVM method, where equal means can be seen for the factor levels 5 months prior to the simulated completion of the Cardenillo project. However, it also shows an exception in month 4 prior to completion where the EVM prediction is not efficient.  
Mazar Dudas hydroelectric project ANOVA. The results obtained for Mazar Dudas are shown in Table 5, where the \(p\)-value for the CTCR methodology shows equal means for the factor levels 4 months prior to the simulated completion of the project. Table 5 also shows the results obtained with the EVM methodology, where equal means can be seen for the factor levels 2 months prior to the simulated completion of the Mazar Dudas project.  
The consolidated results of the ANOVA analysis are shown in Table 8, where we can see that in all of the case studies, the CTCR methodology provides more efficient predictions than the EVM methodology, as it makes appropriate predictions in earlier periods than the EVM predictions, suggesting that it gives the project management a longer margin of time for making decisions.