The Physical Significance of Confidence Intervals

We define some appropriate statistical quantities that indicate the physical significance (reliability) of confidence intervals in the framework of both Frequentist and Bayesian statistical theories. We consider the expectation value of the upper limit in the absence of a signal (that we propose to call "exclusion potential", instead of "sensitivity" as done by Feldman and Cousins) and its standard deviation, we define the "Pull" of a null result, expressing the reliability of an experimental upper limit, and the "upper and lower detection functions", that give information on the possible outcome of an experiment if there is a signal. We also give a new appropriate definition of "sensitivity", that quantifies the capability of an experiment to reveal the signal that is searched for at the given confidence level.