Evidential Calibration of Confidence Intervals

We present a novel and easy to use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on the point estimate and standard error of a parameter estimate. A $k$ support interval can be interpreted as "the interval contains parameter values under which the observed data are at least $k$ times more likely than under a specified alternative hypothesis". Support intervals depend on the specification of a prior distribution for the parameter under the alternative, and we present several types that allow data analysts to encode different forms of external knowledge. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the universal bound for the type-I error rate of Bayes factors leads to a bound for the coverage of support intervals, holding even under sequential analyses with optional stopping. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.