  Flavor ratios of very high energy astrophysical neutrinos, which can be
studied at the Earth by a neutrino telescope such as IceCube, can serve to
diagnose their production mechanism at the astrophysical source. The flavor
ratios for neutrinos and antineutrinos can be quite different as we do not know
how they are produced in the astrophysical environment. Due to this uncertainty
the neutrino and antineutrino flavor ratios at the Earth also could be quite
different. Nonetheless, it is generally assumed that flavor ratios for
neutrinos and antineutrinos are the same at the Earth, in fitting the high
energy astrophysical neutrino data. This is a reasonable assumption for the
limited statistics for the data we currently have. However, in the future the
fit must be performed allowing for a possible discrepancy in these two
fractions in order to be able to disentangle different production mechanisms at
the source from new physics in the neutrino sector. To reinforce this issue, in
this work we show that a wrong assumption about the distribution of neutrino
flavor ratios at the Earth may indeed lead to misleading interpretations of
IceCube results.
