Two-sample test is used to identify significant differences between two samples, such as differences in their expectations, variances or overall distribution shapes. This paper focuses on a specific problem: testing whether the difference between \(P(X > Y)\) and \(P(X < Y)\) exceeds a predefined equivalence margin, through a novel Equivalent Rank Test. Traditional methods based on asymptotic normality are limited by their reliance on a narrow subset of information, failing to fully exploit the potential of finite samples. To address this, we propose a sequential bootstrap sampling approach inspired by a two-armed bandit (TAB) process, which adaptively constructs test statistics. By minimizing bias and variance simultaneously, this adaptive strategy achieves higher power compared to classical fixed-sampling methods, particularly in small or unbalanced samples. Theoretical analysis and extensive simulations confirm the superior performance of the proposed method. Furthermore, an empirical analysis of students’ sleep data highlights both the practical applicability and the advantage of the proposed approach in real-world scenarios.
