(Mis)Understanding the Atmospheric Neutrino Anomaly

The apparent attenuation of muon neutrinos relative to electron neutrinos is a bit too low to be compatible with the most popular values of $\Delta m^{2}$. Fits to $R(E_{\nu})$ favor values of $\Delta m^{2}>0.1$ eV$^{2}$. The fit minimized by the Super Kamioka group in estimating neutrino oscillation parameters neglects systematic errors. The fit is dominated by systematic effects. The data being combined in recent fits may not be compatible since there appear to be significant variations in the properties of the data with time. A simple two component neutrino oscillation with $\Delta m^{2}$ in the range of 10$^{-3}$ to 10$^{-2}$ eV$^{2}$ seems unable to account for the observations.