A classical focus of statistics is estimation of the accuracy or error of statistical procedures; currently, attention to this problem is directed at measuring accuracy after data have been obtained. By developing the underlying mathematical theory this research examines post-data inference and derives the properties of data dependent measures of accuracy. In addition, ancillarity paradoxes will be examined in which conditioning upon observed sample size within subgroup leads to inadmissibility of the usual estimators. The possibility of constructing and verifying dominating estimators will be investigated.
