## 2 Materials and Methods
### Inference  
To ensure the reliability and fairness of the model, statistical tests were conducted, starting by implementing the Shapiro-Wilk test to assess whether the data sample followed a normal distribution. This was necessary to determine the application of parametric or non-parametric tests. \[W=\frac{(\sum_{i=1}^{n}a_{i}x_{(i)})^{2}}{\sum_{i=1}^{n}(x_{i}-\overline{x})^ {2}}, \tag{1}\]  
In Equation (1), \(x_{(i)}\) represents the ordered observations, \(a_{i}\) refers to the constants derived from the means, variances, and covariances of the normals, and \(\overline{x}\) denotes the mean of the sample. The Shapiro-Wilk test is commonly used in medical research and  
Figure 3: Diagram illustrating the proposed method for CNN training and inference. The RSNA-MICCAI data set **(top)** was used for training on skull-stripped T1w MRI data, while the EGD data set **(bottom)** was used for inference on full-head scans. The pipeline includes preprocessing, model training, prediction, and statistical analysis. Statistical tests include the Shapiro–Wilk test (\(W\)) for normality, the Mann–Whitney U test (\(U\)) for median comparison, and the chi-squared test (\(\chi^{2}\)) for categorical distributions. These tests were used to evaluate potential demographic biases in model predictions. statistical evaluations, as seen in the analysis of automated algorithms for the detection of small bowel tumours [31]. The test was applied to assess the normality of two statistical features (skewness and kurtosis), used to differentiate tumorous and non-tumorous frames, followed by the use of non-parametric methods for classification. For group comparisons across two independent groups, the Mann-Whitney U test was applied to assess whether there was a statistically significant difference in their distributions. \[U=n_{1}n_{2}+\frac{n_{1}(n_{1}+1)}{2}-R_{1}, \tag{2}\]  
In Equation (2), \(n_{1}\) and \(n_{2}\) refer to the sample sizes of the two groups, and \(R_{1}\) represents the sum of the ranks of the first sample. The Mann-Whitney U test is often used to evaluate the significance of differences in non-normally distributed data, particularly when dealing with medical data sets, as seen in radiomic-based studies for cancer prediction [32]. These studies implemented this test to assess the relationship between clinical variables on the ordinal scale and invasive disease-free survival (iDFS) for breast cancer patients, incorporating the results into a stratified feature selection pipeline. Complementing these analyses, the Chi-square test was used to examine the existence of a significant relationship between two categorical variables. \[\chi^{2}=\sum\frac{(O_{i}-E_{i})^{2}}{E_{i}}, \tag{3}\]  
In Equation (3), \(O_{i}\) denotes the observed frequencies in each category and \(E_{i}\) represents the expected frequencies for these categories, assuming the independence of the variables. The Chi-square test is used in biomedical applications to assess relationships, as demonstrated in ensemble classifiers for biomedical data [33]. Therefore, this test was applied in a preliminary step as a filter feature selection method to evaluate the relevance of each attribute concerning class labels in multiple medical data sets. In statistical hypothesis testing, the null hypothesis (\(H_{0}\)) assumes the absence of association between studied variables, representing a baseline state. Conversely, the alternative hypothesis (\(H_{1}\)) posits a significant effect or difference [34]. The sampling distribution of the test statistic, defined under \(H_{0}\), enables the assessment of whether observed data provide sufficient evidence to reject \(H_{0}\) in favour of the \(H_{1}\). These hypotheses guide the statistical tests applied in this study. The statistical analysis was conducted in three steps. Firstly, the Shapiro-Wilk test (Equation (1)) was performed to assess whether the age distributions in the \(FN\) and \(TP\) groups were normal.