The ideas of conditional confidence in the simplest setting

A recently developed framework for comparing the properties of various conditional procedures is studied in detail in the setting of testing between two simple hypotheses, where the ideas are most transparent. In that setting, possible goodness criteria are considered, and illustrations are given. The conditional confidence methodology, unlike the Bayes, fiducial, and likelihood techniques, presents a measure of conclusiveness which has frequentist interpretability; and, unlike traditional Neyman-Pearson procedures, the measure is highly data-dependent.