## 4 Experimental Analysis
\begin{split} ln\Big{(}\frac{p(Class-2)}{p(Class-1)}\Big{)}\\ =-49.089-119.993\times\text{Area}+117.116\times\text{Perimeter}+16.981\times\text{Rectangle}\\ +99.605\times\text{Extend}-23.303\times\text{Solidity}\\ ln\Big{(}\frac{p(Class-3)}{p(Class-1)}\Big{)}\\ =-42.351-102.472\times\text{Area}+97.804\times\text{Perimeter}+21.816\times\text{Rectangle}\\ +96.730\times\text{Extend}-28.523\times\text{Solidity}\end{split}  \tag{9}\]  
For example, the coefficient of 'Extend' is 99.605 in the 'Logit 1' model. This indicates that an increase in the 'Extend' by one unit will result in an increase of 99.605 units in the log of the ratio between the probability of being a medium EMI versus the probability of being a weak EMI. Finally, to evaluate whether all of these measures are statistically significant in detecting the EMI effect on semiconductor SEM images, a multivariate analysis of variance (MANOVA) is executed, which is useful for testing whether the vectors of means for more than two groups are different or not. Specifically, to compare the difference in the means of all five measures for the type of semiconductor SEM images (i.e., high-EMI, medium-EMI, and weak-EMI image groups), the four most common statistics, i.e., Wilks' Lambda, [PERSON]'s trace, Hotelling-Lawely trace, and [PERSON]'s largest root, are considered. The Wilks' Lambda statistic is as follows:  
\[\text{Wilks' Lambda}:\ \Lambda=\frac{|\textbf{W}|}{|\textbf{W}+\textbf{B}|} \tag{10}\]  
where \(|\textbf{W}|\) and \(|\textbf{B}|\) are the determinants of the within-group sum of squares and the between-group sum of squares, respectively. This test statistic ranges from 0 to 1, and the smaller values indicate larger variability between vectors of means. The [PERSON]'s trace, Hotelling-Lawely trace, and [PERSON]'s largest root statistics are as follows:  
\[\text{[PERSON]}^{\prime}\text{s trace}:\ V=trace\Big{[}\textbf{B}(\textbf{B}+ \textbf{W})^{-1}\Big{]} \tag{11}\]  
\[\text{Hotelling-Lawely trace}:\ T=trace\Big{(}\textbf{B}\textbf{W}^{-1}\Big{)} \tag{12}\]  
\[\text{[PERSON]}^{\prime}\text{s largest root}:\ \Lambda=\text{maximum eigenvalue of }\textbf{W}(\textbf{B}+\textbf{W})^{-1} \tag{13}\]  
The [PERSON]'s trace value also ranges from 0 to 1, but compared to Wilks' Lambda, the larger values of the [PERSON]'s trace, Hotelling-Lawely trace, and [PERSON]'s largest root statistics indicate larger variability between vectors of means [46]. Table 2 shows the result of MANOVA. For example, [PERSON]'s trace value is 0.429, and the corresponding _F_-value is \(F_{10,226}=6.169\) (i.e., _p_-value < 0.001). Since all the _p_-values of the test statistics are close to 0, the null hypothesis \(H_{0}:\textbf{M}_{H}=\textbf{M}_{M}=\textbf{M}_{W}\) can be rejected at the significance level of 0.05 where \(\textbf{M}_{H}\), \(\textbf{M}_{M}\), and \(\textbf{M}_{W}\) indicate the mean vectors of five measures for three different types of semiconductor SEM images, i.e., high-EMI, medium-EMI, and weak-EMI SEM images, respectively. Therefore, we can conclude that all the extracted shape-related measures are good quantification metrics for assessing the impact of EMI on semiconductor SEM images.