## 4 Statistical Analysis  
Statistical analysis allows us to understand, in depth, whether the application of passive strategies significantly affects the performance of the building in coastal tropical regions. In this study, we will use four key parameters in the analysis: Air temperature, relative humidity, CO\({}_{2}\), and electricity consumption. The analysis is made by the recognized SPSS statistical software in this field. In this research, to study the different details in depth, two statistical tests were applied: The \(t\)-test and chi-square carried out with a confidence level (CL) of 95%. The results of the \(t\)-test are reported in Table 7.  
The main objective of chi-square is to compare two samples and determine the possible similarity or divergence between them. The significance interval is proposed and freely chosen with the SPSS software. Indeed, this is called the \(p\)-value (observed probability of a \(t\)-test). The correlation is significant at \(p\)-value \(<0.01\). In Table 7, a deep statistical analysis is shown by comparing four parameters of offices: Monthly air temperature, monthly relative humidity, CO\({}_{2}\), and electricity. The main results showed in the different cases have \(p\)-value \(<0.01\), which means that the two environments studied do not have the same performance. Therefore, it can be concluded that the application of passive strategies on the walls of office buildings (PCM materials and insulation) increases the performance of the environment. Finally, it was proposed to apply a chi-square test to verify these results, as shown in Table 8.  
Figure 9: Carbon dioxide produced during the operational phase of office buildings in four cities. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Datasets** & \multicolumn{2}{c}{**Offices without Passive Strategy**} & \multicolumn{2}{c}{**Offices with Passive Strategy**} \\ \hline
**Air temperature (\({}^{\circ}\)C)** & \\ \hline Sample & 12 & 12 \\ \hline Mean & 25.92 & 25.61 \\ \hline Standard deviation & 0.42 & 0.31 \\ \hline Confidence interval of the difference at 95\% & [13.6; 14.2] & [13.4; 13.8] \\ \hline Mean standard error & 0.12 & 0.09 \\ \hline Correlation (R\({}^{2}\)) & 0.99 \\ \hline \(l\)-test-results & 5.49 \\ \hline Degree of freedom & 11 \\ \hline \(p\)-Value & 0.0001 \\ \hline \multicolumn{2}{l}{**Relative humidity (\%)**} \\ \hline Sample & 12 & 12 \\ \hline Mean & 63.49 & 65.24 \\ \hline Standard deviation & 5.53 & 6.12 \\ \hline Confidence interval of the difference at 95\% & [47.9; 55.0] & [49.34; 57.1] \\ \hline Mean standard error & 1.59 & 1.76 \\ \hline Correlation (R\({}^{2}\)) & 0.98 \\ \hline \(l\)-test-results & \(-8.76\) \\ \hline Degree of freedom & 11 \\ \hline \(p\)-Value & 0.0002 \\ \hline \multicolumn{2}{l}{**CO\({}_{2}\) emissions (kg)**} \\ \hline Sample & 12 & 12 \\ \hline Mean & 1657.69 & 1391.34 \\ \hline Standard deviation & 284.95 & 229.53 \\ \hline Confidence interval of the difference at 95\% & [1476.6; 1838.7] & [1245.5; 1537.2] \\ \hline Mean standard error & 82.26 & 66.26 \\ \hline Correlation (R\({}^{2}\)) & 0.99 \\ \hline \(l\)-test-results & 16.28 \\ \hline Degree of freedom & 11 \\ \hline \(p\)-Value & 0.0001 \\ \hline \multicolumn{2}{l}{**Electricity (kWh)**} \\ \hline Sample & 12 & 12 \\ \hline Mean & 2735.48 & 2295.95 \\ \hline Standard deviation & 470.23 & 378.76 \\ \hline Confidence interval of the difference at 95\% & [2436.7; 3034.3] & [2055.3; 2536.9] \\ \hline Mean standard error & 135.74 & 109.34 \\ \hline Correlation (R\({}^{2}\)) & 0.99 \\ \hline \(l\)-test-results & 16.28 \\ \hline Degree of freedom & 11 \\ \hline \(p\)-Value & 0.0001 \\ \hline \end{tabular}
\end{table} 
Table 7: Statistical analysis of different parameters. From Table 8, it can be deduced that office environments showed differences (\(p\)-value equal to 0.023, (0.023 \(<\) 0.05)), and it justifies the performance of environmental change with the introduction of PCM materials and insulation of the walls.