3.1. Coverage and width assessments
Originally, a confidence interval was considered of level 1α only if it achieved at least this level for all values in the
parameter space; and this condition is still desirable if one is going to use the interval to carry out level-α tests for a null
hypothesis. However, confidence intervals are not always used for testing purposes, which has led many researchers to
allow for the empirical level to fall somewhat below the nominal level at some parameter values. In Agresti and Coull (1998)
it was argued that this was a good practice.