Abstract: For a given confidence interval, the central value is more likely to be equal to the parameter than a boundary value is. However, when considering two null hypotheses with hypothesized values that are equal to these two values, neither of the hypotheses should be rejected, because both values are inside the interval. Here, we propose a method called the h-function method that can be used to identify any two values in an interval. The proposed method improves confidence intervals by modifying an approximate interval, including a point estimator, to be exact, and by refining an exact interval to be a subset of the previous interval. We demonstrate the proposed method by applying it to three data sets. Simulation results are given in the Supplementary Material.

Key words and phrases: Admissible confidence interval, difference of two proportions, infimum coverage probability, p-value, vaccine efficacy.