Higher-order approximations for interval estimation in binomial settings

In this paper we revisit the classical problem of interval estimation for one-binomial parameter and for the log odds ratio of two binomial parameters. We examine the confidence intervals provided by two versions of the modified log likelihood root: the usual Barndorff-Nielsen's r^*$r^{*}$ and a Bayesian version of the r^*$r^{*}$ test statistic.