## 4 Results and Discussion  
In order to obtain a robust model of the corrective factor, the acquired data must follow a normal distribution [72] thus, a normality test of \(f_{korr}\) values has been performed (Figure 7). The plot of Figure 7 shows the percentage of the normal probability of the data residuals. The central straight line depicts the cumulative probability, while the two curves represent the 95% confidence interval boundaries. For respecting the normality assumption, data residuals should stay inside the confidence interval curves and closed to the cumulative probability  
The results of the ANOVA analysis, performed on the data based on the DOE plan are reported in Table 3.  
In the source column, it is possible to view that the single effects of the geometrical parameters and their interactions have been evaluated. _DoF_, _SS_, _Adj SS_, and _Adj MS_ columns represent, respectively, degrees of freedom, sum of squares, adjusted sum of squares, and adjusted mean squares of the relative source. The F-value column is calculated as the ratio between the adjusted mean squares of the relative source and of error, and represent the test statistics for verifying or rejecting the hypothesis that the source has influence on the response (\(f_{\mathit{korr}}\)). In practice, if the F-value is lower than the related percentile of F-distribution, it means that the source influence on the response is negligible; if it is higher, on the contrary, the source significantly affects the response. A most useful evaluation of the significance of the source parameter is the analysis of the \(p\)-value. This latter is calculated as a function of F-value, the related F-distribution percentile, _DoF_ of the source, and _DoF_ of the error. The \(p\)-value represents the probability of obtaining test results at least as extreme as the results observed, under the assumption that the null hypothesis \(H_{0}\) is correct. A very small \(p\)-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. A small \(p\)-value implies therefore that the null hypothesis is false or something unlikely has occurred. In a formal significance test, the null hypothesis is rejected if the \(p\)-value is less than a pre-defined threshold value, depending on the selected confidence interval, which is referred to as the significance level. It is common practice to set the confidence interval to 95% [72], as optone \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DoF** & **SS** & **Adj SS** & **Adj MS** & **F-Value** & \(p\)**-Value** \\ \hline \(m_{n}\) & 2 & 0.000576 & 0.000576 & 0.000288 & 0.30 & 0.749 \\ \(\alpha_{n}\) & 2 & 0.002253 & 0.002253 & 0.001127 & 1.18 & 0.357 \\ \(x^{*}\) & 2 & 0.029913 & 0.029913 & 0.014957 & 15.60 & 0.002 \\ \(m_{n}\times\alpha_{n}\) & 4 & 0.008682 & 0.008682 & 0.002171 & 2.26 & 0.151 \\ \(m_{n}\times x^{*}\) & 4 & 0.002614 & 0.002614 & 0.000653 & 0.68 & 0.624 \\ \(\alpha_{n}\times x^{*}\) & 4 & 0.010961 & 0.010961 & 0.002740 & 2.86 & 0.096 \\ Error & 8 & 0.007670 & 0.007670 & 0.000959 & & \\ Total & 26 & 0.062668 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of variance for \(f_{\mathit{korr}}\). Figure 7: Normality test: probability plot of the residuals for \(f_{\mathit{korr}}\). the significance level for the \(p\)-value is equal to \(1-95\%=0.05\). With this evidence (\(p\)-values < significance level), the alternative hypothesis \(H_{1}\) should be considered correct. The results of Table 3 underline that the only gear design parameter affecting \(f_{korr}\) is the profile shift coefficient \(x^{*}\) (\(p\)-value = 0.002), while the influence of the other parameters and their interactions is negligible (\(p\)-values > 0.05). This is also noticeable in Figure 8 where the main effect plots are reported and displays how \(f_{korr}\) behaves as a function of each parameter.