Information Value (IV) is a widely used technique for feature selection prior to the modeling phase, particularly in credit scoring and related domains. However, conventional IV-based practices rely on fixed empirical thresholds, which lack statistical justification and may be sensitive to characteristics such as class imbalance. In this work, we develop a formal statistical framework for IV by establishing its connection with Jeffreys divergence and propose a novel nonparametric hypothesis test, referred to as the J-Divergence test. Our method provides rigorous asymptotic guarantees and enables interpretable decisions based on \(p\)-values. Numerical experiments, including synthetic and real-world data, demonstrate that the proposed test is more reliable than traditional IV thresholding, particularly under strong imbalance. The test is model-agnostic, computationally efficient, and well-suited for the pre-modeling phase in high-dimensional or imbalanced settings. An open-source Python library is provided for reproducibility and practical adoption.