## 4 Analysis and Discussion of Results
### Full 2\({}^{3}\) Factorial Analysis
This ensures that only effects with a sufficiently large impact, beyond random experimental variability, are interpreted as statistically relevant. In this context, for the \(G_{TR}\), an effect will be considered significant if its value exceeds \(t_{8}\times\)\(s_{\mathit{effect}}\) = 2.306 \(\times\) 9.246 = 21.321. Conversely, when considering \(h\) as the response variable, the effect becomes statistically relevant if its value is greater than \(t_{8}\times\)\(s_{\mathit{effect}}\) = 2.306 \(\times\) 9.842 = 22.697. Applying this interpretation to the effects shown in Table 6, the significant factors were the power supply (Table 6, entry 1) for \(G_{TR}\), and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Entry**} & \multirow{2}{*}{**Global Average \({}^{*}\)**} & \multicolumn{2}{c}{\(G_{\mathbf{TR}}\)} & \(h\) \\  & & **(\(\times\)10\({}^{-}\)3 \(\pm\)\(\times\)10\({}^{-}\)3 (\({}^{\circ}\)C\(\cdot\)W\({}^{-1}\)))** & **(W\(\cdot\)m \({}^{-2,\circ}\)C\({}^{-1}\))** \\ \cline{2-3}  & & **620.374 \(\pm\) 4.6** & **448.771 \(\pm\) 4.9** \\ \hline \multicolumn{3}{c}{Main effects} & & \\ \hline \(1\) & \(A\) (Power supply) & 24.954 \(\pm\) 9.2 & 28.050 \(\pm\) 9.8 \\ \hline \(2\) & \(B\) (Temperature) & \(-\)11.643 \(\pm\) 9.2 & 33.462 \(\pm\) 9.8 \\ \hline \(3\) & \(C\) (Flow rate) & 12.356 \(\pm\) 9.2 & 16.189 \(\pm\) 9.8 \\ \hline \multicolumn{3}{c}{Two-factor interactions} & & \\ \hline \(4\) & _A\({}^{*}\)B_ & \(-\)0.475 \(\pm\) 9.2 & 6.687 \(\pm\) 9.8 \\ \hline \(5\) & _A\({}^{*}\)C_ & \(-\)13.975 \(\pm\) 9.2 & 6.229 \(\pm\) 9.8 \\ \hline \(6\) & _B\({}^{*}\)C_ & \(-\)1.047 \(\pm\) 9.2 & \(-\)7.849 \(\pm\) 9.8 \\ \hline \multicolumn{3}{c}{Three-factor interactions} & & \\ \hline \(7\) & _A\({}^{*}\)B\({}^{*}\)C_ & \(-\)13.673 \(\pm\) 9.3 & \(-\)0.878 \(\pm\) 9.8 \\ \hline \hline \end{tabular} \({}^{*}\)Global average of the 16 assays in duplicate; see Table 5.  
\end{table} 
Table 6: Estimates of the main and interaction effects. temperature followed by power supply, in order of importance (Table 6, entries 1 and 2) for \(h\). Additionally, the Pareto chart (Figure 7) can be used to illustrate which main effect is most significant. The effects whose rectangles are to the right of the dividing line should be considered in the statistical model, as they represent values greater than \(p\) = 5% (95% confidence interval). In this context, once again the only main factor with statistical relevance for thermal resistance is the power supply (Figure 7a), whereas for \(h\), the significant factors are the power supply and temperature (Figure 7b). The values next to the rectangles represent the values of the \(t\)-test statistics obtained in the main effects window. In statistical terms, the other main effects (flow rate and temperature for \(G_{TR}\), and flow rate for \(h\)), as well as any of the two- or three-factor interactions, can be regarded as inert factors in these experiments and should therefore be disregarded in the experimental analysis. Figure 7: Pareto chart as a function of the values of the \(t\)-test statistics: (**a**) \(G_{TR}\) and (**b**) \(h\).