The Yates, Conover, and Mantel statistics in 2 × 2 tables revisited (and extended)

Asymptotic inferences about the difference, ratio or odds‐ratio of two independent proportions are very common in diverse fields. This article defines for each parameter eight conditional inference methods. These methods depend on: (1) using a chi‐squared type statistic or a z type one; (2) using the classic Yates continuity correction or the less well‐known Conover one; and (3) whether the p‐value of the test is determined by doubling the one‐tailed p‐value or by the Mantel method (asymmetrical approach). In all cases, the conclusions are: (i) the methods based on the chi‐squared statistic should not be used, as they are too liberal; (ii) for those in favor of using the criterion of doubling the p‐value, the best method is using the z statistic with Conover continuity correction; and (iii) for those in favor of the asymmetrical approach, the best method is based on the z statistic with Conover continuity correction and the Mantel p‐value.