In Defence of Score Intervals for Proportions and their Differences

A recent article (Santner et al., 2007) asserted that a score interval for a difference of independent binomial proportions (Miettinen and Nurminen, 1985) may have inadequate coverage. We re-visit the properties of score intervals for binomial proportions and their differences. Published data indicate these methods produce mean coverage slightly above the nominal confidence level 1 - alpha. We argue it is appropriate to align mean rather than minimum coverage with 1 - alpha, based on a moving average representation of the coverage probability. The poor coverage properties claimed by Santner et al. (2007) actually relate to an inferior version of the score interval (Mee, 1984).