Task incremental learning (TIL) is a specific form of continual learning (CL), wherein the model is trained on a set of distinguishable tasks. However, current TIL methodologies are predicated on the closed-world assumption, which posits that test data remains in-distribution (ID). When deployed in an open-world scenario, test samples can be from out-of-distribution (OOD) sources. Current OOD detection methods primarily rely on model outputs, leading to an over-dependence on model performance. Additionally, a threshold is required to distinguish between ID and OOD, limiting their practical application. Moreover, these methods can only achieve coarse-grained binary classification and cannot obtain task identity. To address this, we propose Hierarchical Two-sample Tests (H2ST), which is compatible with any existing replay-based TIL frameworks. H2ST eliminates the necessity for thresholds by employing hypothesis testing while leveraging feature maps to harness the model's capabilities without excessive dependence. The proposed hierarchical architecture incorporates a task-level detection mechanism, simplifying classification for individual classifiers. Extensive experiments and analysis demonstrate the effectiveness of H2ST in open-world TIL scenarios and its superiority to the existing methods.