## 3 Results
### Analysis of Variance
Thus, the MANOVA test was applied to observe the differences between treatments in general, followed by the ANOVA test as a contrast of differences for each specific variable, and, finally, the Tukey test as a paired contrast for each treatment. The results of these contrasts are presented in Table 4, Table 5, and Figure 5.  
As can be seen in Table 4, when conducting the MANOVA test, it was observed that the set of variables moisture, protein, fiber, ash, sodium, and fat contrasted based on the treatment used for chip production and showed significant differences. This was evidenced in the statistics achieved in each of the Pillai, Wilks, Hotelling-Lawley, and Roy multivariate criteria, where \(p\)-values of 3.6651 \(\times\) 10\({}^{-11}\), 1.6592 \(\times\) 10\({}^{-10}\), 2.9876 \(\times\) 10\({}^{-5}\), and 7.1093 \(\times\) 10\({}^{-12}\) were recorded, respectively. This indicates that significance thresholds were reached, suggesting significant differences in some of the sample's variables. For this reason, the ANOVA test was conducted for each of the considered variables as a post-hoc test for the general analysis. In Table 5, it can be seen that the variables moisture, starch, fiber, ash, sodium, and fat reached the significance level with \(p\)-values of 7.6905 \(\times\) 10\({}^{-8}\), 7.1234 \(\times\) 10\({}^{-11}\), 0.0002, 1.3121 \(\times\) 10\({}^{-8}\), and 2.0409 \(\times\) 10\({}^{-17}\), respectively, suggesting the existence of significant differences in the contrast of the groups within each of these variables. It should be noted that the fiber variable did not reach the significance level in the ANOVA test, so a post-hoc test on it was not conducted. Finally, all paired contrasts within each variable that reached the significance level in the ANOVA test were verified. Thus, when contrasting the treatments for moisture values achieved in the chips, it was identified that treatments T1 and T2 reached significantly higher moisture percentages than treatments T3 and T4 with \(p\)-values of 0.0038 and 0.00013, respectively, suggesting that chips from the baking method have higher moisture values than those from the fried method. Additionally, treatment T4 showed a significantly higher moisture level than T3, suggesting that fried chips from the Dominico variety have a higher \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**MANOVA: Moisture + Protein + Fiber + Ash + Sodium + Fat - Treatment**} \\ \hline \hline
**Multivariate Test** & **Df** & **Test Stat.** & **Aprox. F** & **Pr(c)F** \\ \hline
**Pillai** & 3 & 3 & 133.6 &
\begin{tabular}{c} 3.6651 \(\times\) 10\({}^{-11}\) \\ _Significant_ \\ \end{tabular} \\
**Wilks** & 3 & 0 & 2364.9 &
\begin{tabular}{c} 1.6592 \(\times\) 10\({}^{-10}\) \\ _Significant_ \\ \end{tabular} \\
**Hotelings–Lawley** & 3 & 1,054,353 & 33,471.5 &
\begin{tabular}{c} 2.9876 \(\times\) 10\({}^{-5}\) \\ _Significant_ \\ \end{tabular} \\
**[PERSON]** & 3 & 1,052,471 & 601,412.2 &
\begin{tabular}{c} 7.1093 \(\times\) 10\({}^{-12}\) \\ _Significant_ \\ \end{tabular} \\ \hline \multicolumn{2}{c}{\({}^{*}\)Significant contrasts.} & & & & \\ \end{tabular}
\end{table} 
Table 4: Estimated Marginal Means test for the protein percentage variable in the chips.