## 2 Materials and Methods
### Explainability  
To tackle the problem of explaining a black-box ML prediction model, two main analytical approaches were employed in tandem; Cohen effect sizes and SHAP analysis. These two widely established techniques are used in many scientific fields to analyze datasets and the results of experiments. The Cohen effect size (Cohen's d), introduced in 1969 [42], is a statistical measure used to quantify the magnitude of the difference between two groups. It is particularly useful when comparing the performance of different features or algorithms in machine learning. To calculate Cohen's d, the difference between the means of the two groups is divided by the pooled standard deviation of the two groups. The resulting value represents the effect size, indicating the magnitude of the difference between the groups. A Cohen's d value of 0.2 is considered small, 0.5 is considered medium and 0.8 is considered large. By using Cohen's d in machine learning, researchers can gain insights into the significance of differences between various features or models. It helps in making more informed decisions when selecting a model for a specific task, as it allows for a better understanding of the performance variations among different algorithms or features. Several studies have highlighted the importance of using Cohen's d to improve the interpretability and decision making in machine learning tasks [43; 44]. SHAP (SHapley Additive exPlanations) [45] is a well-established technique used to enhance the transparency and explainability of machine learning prediction models. It is based on concepts from cooperative game theory and offers valuable insights into how each feature contributes to the model's predictions. The SHAP method approaches explainability by treating each feature as a \"player\" in a game, and the ultimate prediction as the game's goal. It then allocates the responsibility for the prediction to all the features in a fair manner. In simpler terms, SHAP assigns an importance value to each feature for a particular prediction, indicating how much that feature influences the outcome. By employing SHAP, researchers and practitioners can gain a deeper understanding of the model's decision making process. It enables them to identify which features play crucial roles in the prediction, providing valuable insights into how the model arrived at its conclusions. This method is particularly useful in scenarios where model interpretability is essential for building trust and confidence in the AI-powered decision-making system. First introduced by [PERSON] in 1953 [23], the Shapley value is a mathematical concept in game theory that aims to assign \"pay-outs\" to players of a game based on their individual contribution to the overall goal/pay-out of the game. Players can form coalitions and work towards the final goal in a collaborative fashion. Thus, this method highlights the effectiveness of certain combinations and the contributions of each player of the game. By applying this concept in ML prediction models, each feature of the dataset is considered a player and the prediction is the final goal/pay-out. The Shapley values indicate the importance of each feature and the most effective combinations, thus giving an explainability factor to the whole system. By comparing the difference between the prediction of a single feature and the average prediction value of all features, we obtain the total \"gains\" achieved by it. If this is for a set of features, then the \"gains\" are split accordingly between the players/features taking part. Consequently, the SHAP technique calculates the mean prediction value of the model. The next step is to calculate the relative contribution of all features to the deviation (positive or negative) from the mean prediction value of the model. Ergo, by adding this final step to the procedure of this work, as depicted in Figure 1, we try to shed more light on the  
Figure 1: Flow chart of this work’s methodology. mechanics of an otherwise black-box decision-making computer-aided system.