Out-of-Distribution (OOD) detection is a critical task in machine learning, particularly in safety-sensitive applications where model failures can have serious consequences. However, current OOD detection methods often suffer from restrictive distributional assumptions, limited scalability, and a lack of interpretability. To address these challenges, we propose STOOD-X, a two-stage methodology that combines a Statistical nonparametric Test for OOD Detection with eXplainability enhancements. In the first stage, STOOD-X uses feature-space distances and a Wilcoxon-Mann-Whitney test to identify OOD samples without assuming a specific feature distribution. In the second stage, it generates user-friendly, concept-based visual explanations that reveal the features driving each decision, aligning with the BLUE XAI paradigm. Through extensive experiments on benchmark datasets and multiple architectures, STOOD-X achieves competitive performance against state-of-the-art post hoc OOD detectors, particularly in high-dimensional and complex settings. In addition, its explainability framework enables human oversight, bias detection, and model debugging, fostering trust and collaboration between humans and AI systems. The STOOD-X methodology therefore offers a robust, explainable, and scalable solution for real-world OOD detection tasks.