## 3 Results and Discussion
Based on the \(p\)-values from thesetables, especially those in bold, it is possible to conclude that the Stylus diameter*Step width*Speed effects are active at a confidence level of 95% (value of \(p<0.05\)). Similarly, a strong contribution of the interaction between Stylus diameter*Step width in the error of the average measurement of the roundness is also showed. Besides, the interaction between the factors Stylus diameter*Speed influences the measurements of the variable's parallelism, angularity, and roundness. The interaction between Step width*Speed is active for angularity, roundness, and diameter. As for the main effects, the Stylus diameter is the most active with the most influence on the variability of the Geometrical Product Specifications. To further assist in the practical interpretation of this experiment, Figure 9 presents plots of the three main effects. The main effect occurs when the mean response changes across the levels of a factor. These main effect plots are graphs of the marginal response averages at the levels of the three factors. Thus, in this case, the plot has been obtained by plotting the means for each value of a categorical variable. By analyzing the line linking the points, it is possible to determine whether the main effect is \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Diameter**} & \multicolumn{3}{c}{**Distance**} \\ \hline
**Source** & **MS** & **F** & **p-Value** & **MS** & **F** & **p-Value** \\ \hline Stylus diameter & \(4.68\times 10^{-5}\) & 39.39 & **0.000** & \(1.27\times 10^{-5}\) & 1.01 & 0.438 \\ Step width & \(3.79\times 10^{-6}\) & 0.47 & 0.657 & \(1.59\times 10^{-5}\) & 2.06 & 0.260 \\ Speed & \(1.46\times 10^{-5}\) & 1.84 & 0.275 & \(9.53\times 10^{-6}\) & 0.79 & 0.513 \\ Stylus diameter*Step width & \(6.73\times 10^{-7}\) & 1.00 & 0.458 & \(5.89\times 10^{-6}\) & 1.63 & 0.257 \\ Stylus diameter*Speed & \(5.33\times 10^{-7}\) & 0.79 & 0.557 & \(1.03\times 10^{-5}\) & 2.85 & 0.097 \\ Step width*Speed & \(8.11\times 10^{-6}\) & 12.06 & **0.000** & \(5.43\times 10^{-6}\) & 1.51 & 0.287 \\ Stylus diameter*Step width*Speed & \(6.72\times 10^{-7}\) & 134.40 & **0.000** & \(3.60\times 10^{-6}\) & 78.3 & **0.000** \\ Error & \(5.00\times 10^{-9}\) & & & \(4.60\times 10^{-8}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of key analysis of variance (ANOVA) values for each of the variables Diameter and Distance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Parallelism**} & \multicolumn{3}{c}{**Angularity**} & \multicolumn{3}{c}{**Roundness**} \\ \hline
**Source** & **MS** & **F** & **p-Value** & **MS** & **F** & **p-Value** & **MS** & **F** & **p-Value** \\ \hline Stylus diameter & \(3.78\times 10^{-6}\) & 22.81 & **0.000** & \(8.27\times 10^{-4}\) & 43.59 & **0.001** & \(7.94\times 10^{-6}\) & 0.56 & 0.599 \\ Step width & \(3.78\times 10^{-6}\) & 1.32 & 0.385 & \(7.06\times 10^{-5}\) & 3.71 & 0.108 & \(4.18\times 10^{-5}\) & 1.92 & 0.223 \\ Speed & \(1.1\times 10^{-6}\) & 6.35 & **0.000** & \(2.52\times 10^{-5}\) & 0.91 & 0.451 & \(8.75\times 10^{-5}\) & 4.20 & 0.071 \\ Stylus diameter*Step width & \(1.5\times 10^{-8}\) & 0.45 & 0.586 & \(7.15\times 10^{-6}\) & 1.82 & 0.218 & \(8.46\times 10^{-6}\) & 5.08 & **0.025** \\ Stylus diameter*Speed & \(1.52\times 10^{-7}\) & 4.61 & **0.000** & \(1.58\times 10^{-5}\) & 4.01 & **0.045** & \(7.48\times 10^{-6}\) & 4.49 & **0.034** \\ Step width*Speed & \(2.6\times 10^{-8}\) & 0.79 & 0.325 & \(1.58\times 10^{-5}\) & 4.03 & **0.044** & \(1.50\times 10^{-5}\) & 9.02 & **0.005** \\ Stylus diameter*Step width*Speed & \(3.3\times 10^{-8}\) & 1.57 & 0.167 & \(3.93\times 10^{-6}\) & 26.70 & **0.023** & \(1.67\times 10^{-6}\) & 40.63 & **0.000** \\ Error & \(2.1\times 10^{-8}\) & & & \(1.47\times 10^{-7}\) & & & \(4.10\times 10^{-8}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of key analysis of variance (ANOVA) values for each of the variables Parallelism, Angularity and Roundness. present for a categorical variable or not.