  An analysis of the existing data on the atmospheric neutrino anomaly is
presented, focused on the statistical significance that can be attributed to
its experimental evidence. Our approach is alternative to the usual analyses in
terms of the $\mu/e$ ratio of event rates. In fact, we perform a comparison
between data and expectations, by {\em separating\/} the information on
$e$-like and $\mu$-like events, with a careful estimate of the different errors
and of their correlation effects. The results are shown both numerically and
graphically, and disclose interesting aspects of the atmospheric neutrino
anomaly, that the use of the $\mu/e$ ratio would partially hide, both in the
sub-GeV and in the multi-GeV energy range.
