  Confidence limits are common place in physics analysis. Great care must be
taken in their calculation and use, especially in cases of limited statistics
when often one-sided limits are quoted. In order to estimate the stability of
the confidence levels to addition of more data and/or change of cuts, we argue
that the variance of their sampling distributions be calculated in addition to
the limit itself. The square root of the variance of their sampling
distribution can be thought of as a statistical error on the limit. We thus
introduce the concept of statistical errors of confidence limits and argue that
not only should limits be calculated but also their errors in order to
represent the results of the analysis to the fullest. We show that comparison
of two different limits from two different experiments becomes easier when
their errors are also quoted. Use of errors of confidence limits will lead to
abatement of the debate on which method is best suited to calculate confidence
limits.
