  The current analysis of atmospheric neutrinos by the Super-Kamiokande
Collaboration is based only on fully-contained one-ring events and partially
contained events. We show that the up-down ratio of fully-contained, inclusive,
multi-ring events gives an independent test of the atmospheric neutrino
anomaly, without the need for particle identification. Moreover, this class of
events is rich in neutral current events and hence gives crucial information
for discriminating between oscillations of \nu_\mu into \nu_{e, \tau} and
\nu_s.
