The paper surveys results about the behavior of nonparametric methods in cases where the customary continuity assumptions are not satisfied. A projection approach is used to show that true confidence coefficients associated with confidence intervals for appropriate location parameters derived from Wilcoxon one- and two-sample tests are at least equal to the nominal level for the continuous case, if the confidence intervals are considered closed, at most equal to the nominal level, if they are considered open. The results are interpreted in terms of tests of hypotheses.