  The MiniBooNE and LSND experiments are compatible with each other when two
sterile neutrinos are added to the three active ones. In this case there are
eight possible mass orderings. In two of them both sterile neutrinos are
heavier than the three active ones. In the next two scenarios both sterile
neutrinos are lighter than the three active ones. The remaining four scenarios
have one sterile neutrino heavier and another lighter than the three active
ones. We analyze all scenarios with respect to their predictions for
mass-related observables. These are the sum of neutrino masses as constrained
by cosmological observations, the kinematic mass parameter as measurable in the
KATRIN experiment, and the effective mass governing neutrinoless double beta
decay. It is investigated how these non-oscillation probes can distinguish
between the eight scenarios. Six of the eight possible mass orderings predict
positive signals in the KATRIN and future neutrinoless double beta decay
experiments. We also remark on scenarios with three sterile neutrinos. In
addition we make some comments on the possibility of using decays of high
energy astrophysical neutrinos to discriminate between the mass orderings in
presence of two sterile neutrinos.
