The Yates, Conover, and Mantel statistics in 2 X 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.