# A Robust Statistical Methodology for Measuring Enterprise Agility
## 4 Results and Statistical Validation
### Difference of Means Test (Student's T-Test)  
Once we complete the variance difference test, we proceeded to carry out the expected test of difference of means (applying different variances). The \(t\)-test of Student can be utilized in cases where at least one of the sample sizes is small (less than 30 units), the samples are independent, the populations have normal distribution, and the variances of both populations are equal [38; 50]. If the latter requirement is not met (equality of  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Statistic** & **Value** \\ \hline F-test & 3.31 \\ F-critical & 1.90 \\ \(p\)-value & 0.0014 \\ Power & 0.9217 \\ Beta & 0.0783 \\ Effect (rate std. dev) & 1.8204 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(F\)-Test results.  
Figure 7: Difference of variances test ([PERSON]’s \(F\)-test). This graph allows visualizing the hypothesis testing of variance difference and the associated statistical power analysis, which represents the effect produced.  
variances), as is the case in our study since the variances are not equal, we apply the \(t\)-test of Student with an adjustment in the equation to calculate the degrees of freedom, without calculating the pooled variance [51]. In this case, we use the sample variances to calculate the standard deviation of the difference of the sample means.  
In this test, the hypotheses are formulated as follows:  
The null hypothesis states that the difference is equal to 0:  
\[H_{0}:\mu_{Q4-FY22}-\mu_{Q2-FY22}=0\]  
and the alternative hypothesis states that the difference is less than 0:  
\[H_{1}:\mu_{Q4-FY22}-\mu_{Q2-FY22}<0\]  
This is because we want to test whether the reduction exhibited in AgilityDebt(tm) from Q4-FY22 compared to Q2-FY22 was actually less than zero, and not just due to chance. In the Figure 8 and Table 4, we can see the results of the executed Student's \(t\)-Test.  
Conclusion: Since the \(t\) test statistic of \(-5.48\) was less than the critical \(T\) equal to \(-1.68\), or the \(p\)-value was less than the preset alpha (\(\alpha\)) of 0.05, the \(H_{0}\) is rejected, concluding that the average of Q4-FY22 is statistically lower than the average of Q2-FY22.  
As the \(H_{0}\) is rejected, we proceed to calculate the effect size and power of the test [39; 40].  
From the power analysis, we conclude that the effect [41] produced by the AgilityDebt(tm) improvement project, which reduced the indicator by 2230 basis points, is highly significant. Additionally, the reduction exhibits statistical power of almost 100%. Therefore, the improvement is not due to random chance, but is real and highly relevant.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Statistic** & **Value** \\ \hline \(T\)-test & \(-5.48\) \\ \(T\)-critical & \(-1.68\) \\ \(p\)-value & 0.0000 \\ Power & 0.9998 \\ Beta & 0.0002 \\ Effect size & \(-0.2230\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: \(t\)-Test results.  
Figure 8: Difference of means test (Student’s \(t\)-test). This graph allows visualizing the hypothesis testing of mean difference and the associated statistical power analysis, which represents the effect produced.