## 7 Results
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multicolumn{10}{c}{**0.9-Trimmed Means of Critical Angles**} \\ \hline
**Outliers = 0\%** & \multicolumn{3}{c}{**Methods**} & \multicolumn{3}{c}{**Outliers = 10\%**} & \multicolumn{3}{c}{**Methods**} \\ \hline
**Criterion** & **EK01** & **EK13** & **EK82** & **EK84** & **Criterion** & **EK01** & **EK13** & **EK82** & **EK84** \\ \hline
**PRESS** & 0.8547 & 0.1242 & **0.0000** & 0.9791 & PRESS & 1.5224 & 1.5708 & 1.5612 & 1.1699 \\ PRESS75 & 0.9473 & 0.1574 & **0.0000** & 1.1286 & PRESS75 & 1.5100 & 1.5568 & 1.5652 & 1.2546 \\ PRESS50 & 1.0053 & 0.1935 & **0.0000** & 1.1629 & PRESS50 & 1.3777 & 1.3662 & 1.4003 & 1.2339 \\ \(W_{m}\) & 0.8177 & 0.7221 & 0.7330 & 1.0202 & \(W_{m}\) & 1.2399 & 1.2184 & 1.2110 & **1.1507** \\ \(W_{m(Max)}\) & 0.6050 & 0.2747 & 0.2094 & 1.0174 & \(W_{m(Max)}\) & 1.2399 & 1.2184 & 1.2110 & 1.1608 \\ \(W_{m75}\) & 0.6846 & 0.0950 & **0.0000** & 1.1048 & \(W_{m75}\) & 1.4913 & 1.5103 & 1.5134 & 1.2072 \\ \(W_{m75}\)(Max) & 0.7120 & 0.0695 & **0.0000** & 1.0948 & \(W_{m75(Max)}\) & 1.4939 & 1.5216 & 1.5465 & 1.2083 \\ \(W_{m50}\) & 0.6963 & 0.0956 & **0.0000** & 1.1163 & \(W_{m50}\) & 1.3135 & 1.1962 & 1.2189 & 1.2315 \\ \(W_{m50}\)(Max) & 0.7274 & 0.0824 & **0.0000** & 1.1184 & \(W_{m50(Max)}\) & 1.3118 & 1.2863 & 1.2883 & 1.2278 \\ \hline
**Outliers = 5\%** & \multicolumn{3}{c}{**Methods**} & \multicolumn{3}{c}{**Outliers = 20\%**} & \multicolumn{3}{c}{**Methods**} \\ \hline
**Criterion** & **EK01** & **EK13** & **EK82** & **EK84** & **Criterion** & **EK01** & **EK13** & **EK82** & **EK84** \\ \hline PRESS & 1.5524 & 1.5680 & 1.5674 & **1.0965** & PRESS & 1.5331 & 1.5397 & 1.5462 & 1.2667 \\ PRESS75 & 1.5361 & 1.5136 & 1.5256 & 1.1683 & PRESS75 & 1.5506 & 1.5619 & 1.5650 & 1.2965 \\ PRESS50 & 1.4639 & 1.4059 & 1.4189 & 1.2177 & PRESS50 & 1.3658 & 1.3845 & 1.4704 & 1.3262 \\ \(W_{m}\) & 1.2733 & 1.2049 & 1.1807 & 1.1067 & \(W_{m}\) & 1.3682 & 1.1988 & 1.1768 & **1.1356** \\ \(W_{m(Max)}\) & 1.2754 & 1.2049 & 1.1807 & 1.1059 & \(W_{m(Max)}\) & 1.3618 & 1.1988 & 1.1768 & 1.1540 \\ \(W_{m75}\) & 1.4223 & 1.2850 & 1.2965 & 1.1224 & \(W_{m75}\) & 1.5051 & 1.5372 & 1.5628 & 1.2210 \\ \(W_{m75(Max)}\) & 1.4773 & 1.3853 & 1.3826 & 1.1292 & \(W_{m750(Max)}\) & 1.5164 & 1.5613 & 1.5680 & 1.2497 \\ \(W_{m50}\) & 1.1589 & 1.2008 & 1.2478 & 1.1582 & \(W_{m50}\) & 1.3567 & 1.3086 & 1.3888 & 1.2847 \\ \(W_{m50}\)(Max) & 1.3298 & 1.2757 & 1.2939 & 1.1666 & \(W_{m500(Max)}\) & 1.3588 & 1.3698 & 1.4449 & 1.2950 \\ \hline \hline \end{tabular}  
In bold, the method with the lowest statistic value in each percentage of outliers.  
\end{table} 
Table 2: The 0.9-trimmed means of critical angles in the simulation study. In bold, the method with the lowest statistic values and the rank used. R- Rank. According to the cross-validation study by [PERSON] and [PERSON] [31], in the original data matrix, a maximum of three or four components is sufficient. This same result was obtained with the EK82 method using \(W_{m(Max)}\) and \(W_{m75}\); however, if \(W_{m75}\) is used as a criterion, the EK13 method with five components would be preferable as it presents better predictions in the absence of contamination. For the wine matrix contaminated at three levels, it can be verified that the EK84 methodology always presents the best results, minimizing the Procrustes statistics. In this case, with 5, 10 and 20% contaminations, the ranks chosen were four, five and three, respectively, but the selection criteria were different depending on the number of outliers. With a low level of outliers (5%), EK84 produced the same rank with all criteria (resistant or not), while with an intermediate level of outliers the only criterion that did not work very well was PRESS75 and with a high level of contamination the best performance criteria were \(W_{m}\) and \(W_{m(Max)}\). Finally, Table 4 presents the results of the wine matrix taking into account only the critical angles.