## 4 Results and Discussion  
First, the results obtained for each of the experimental replicates were compared for SM, BM, and PM. The parametric \(t\)-test method for comparison of means was applied to each pair of data for each experiment (Table 6). The results show no statistically significant differences in any of the cases. The same conclusion is drawn when non-parametric tests are applied ([PERSON] and [PERSON]'s median test) (Table 7). These tests allow conclusions to be drawn even when the data do not follow a normal distribution and there is no homogeneity of variance. From the parametric and non-parametric comparisons (Tables 6 and 7), it is possible to conclude that there are no statistically significant differences between the three repetitions of each experiment (evaluated as a whole). A maximum range (difference for each cell between each pair of repeated experiments) was also calculated. The mean range for SM was 0.530 mm, for BM 0.259 mm, and for SP 0.343 mm. For this reason, the averages of vertical displacements can be used for each experiment (SM, BM, and PM). The vertical displacement averages obtained from the three samples can be seen in Figure 10, which represent the three analyzed sequences: (a) the symmetrical method, SM, (b) backward method, BM, and (c) single-pass method, SP. Figure 9: Methodology flowchart. Figure 11a,b indicates the sections with the most expressive distortions (sections A and H and Sections 4 and 5, respectively). Through the comparative graphs of SM \(\times\) BM \(\times\) SP, it was possible to analyze the deformation patterns and the amplitudes of the displacements led by welding by comparing the sections. The maximum mean vertical displacement was observed in Section 5 for all welding sequences studied in this work. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Comparison** & **F-Value** & \(\mathbf{p}\)**-Value** \\ \hline SM\_1-SM\_2 & 0.240 & 0.878 \\ SM\_2-SM\_3 & 0.207 & 0.207 \\ SM\_3-SM\_1 & 0.366 & 0.546 \\ BM\_1-BM\_2 & 0.157 & 0.693 \\ BM\_2-BM\_3 & 0.155 & 0.695 \\ BM\_3-BM\_1 & 0.000 & 0.999 \\ SP\_1-SP\_2 & 0.190 & 0.890 \\ SP\_2-SP\_3 & 0.010 & 0.980 \\ SP\_3-SP\_1 & 0.026 & 0.872 \\ \hline \hline \end{tabular} Where \(p\)-value is the statistical measurement used to validate a hypothesis against observed data and F-value is a value on the F distribution or, in other words, is the ratio of the variation between sample means and the variation within the samples.  
\end{table} 
Table 6: Parametric (\(t\)-test) comparison of the datasets into groups. Figure 10: Deformation graphs: (**a**) symmetrical method (SM), (**b**) backward method (BM) and (**c**) single-pass method (SP). To verify whether the differences in displacements between the sequences are statistically significant, a one-way ANOVA was performed with the default significance level of 95%. The sum of vertical displacements was performed and became a single variable for each sample (Table 8). Prior to performing ANOVA, [PERSON]'s test was applied to sample data to verify the homogeneity of variances. The test resulted in the null hypothesis being true in order to conclude that the variances are homogeneous and that it is possible to use the parametric ANOVA test for this data sampling. All the vertical displacements measured were summed and transformed into only one variable for each sample. According to what is indicated in Table 9, the \(p\)-value obtained with the ANOVA was 0.011, showing the null hypothesis as a result (\(p<0.05\)). Therefore, it is concluded \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Kruskal–Wallis** & **Median Test** \\ \hline SM & 0.193 & 0.440 \\ BM & 0.778 & 0.779 \\ PM & 0.982 & 0.990 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(p\)-value for non-parametric tests into groups. Figure 11: (a) SM \(\times\) BM \(\times\) SP scatter plot—Sections A and H; (b) SM \(\times\) BM \(\times\) SP scatter plot—Sections 4 and 5.  
that there is a significant difference in the final distortion of the samples between the welding sequences.