A Note on Monotonicity Assumptions for Exact Unconditional Tests in Binary Matched‐Pairs Designs
2011
Li, Xiaochun | Liu, Mengling | Goldberg, Judith D.
Exact unconditional tests have been widely applied to test the difference between two probabilities for 2 × 2 matched‐pairs binary data with small sample size. In this context, Lloyd (2008, Biometrics64, 716–723) proposed an E + M p‐value, that showed better performance than the existing M p‐value and C p‐value. However, the analytical calculation of the E + M p‐value requires that the Barnard convexity condition be satisfied; this can be challenging to prove theoretically. In this article, by a simple reformulation, we show that a weaker condition, conditional monotonicity, is sufficient to calculate all three p‐values (M, C, and E + M) and their corresponding exact sizes. Moreover, this conditional monotonicity condition is applicable to noninferiority tests.
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