A large number (~1000) of coincident auroral far ultraviolet (FUV) and ground-based ionosonde observations are compared. This is the largest study to date of coincident satellite-based FUV and ground-based observations of the auroral E region. FUV radiance values from the NASA Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED) Global Ultraviolet Imager (GUVI) and the Defense Meteorological Satellite Program (DMSP) F16 and F18 Special Sensor Ultraviolet Spectrographic Imager (SSUSI) are included in the study. A method is described for deriving auroral ionospheric E region maximum electron density (NmE) and height of maximum electron density (hmE) from N2 Lyman-Birge-Hopfield (LBH) radiances given in two channels using lookup tables generated with the Boltzmann 3-Constituent (B3C) auroral particle transport and optical emission model. Our rules for scaling (i.e., extracting ionospheric parameters from) ionograms to obtain auroral NmE and hmE are also described. Statistical and visual comparison methods establish statistical consistency and agreement between the two methods for observing auroral NmE, but not auroral hmE. It is expected that auroral non-uniformity will cause the two NmE methods to give inconsistent results, but we have not attempted to quantify this effect in terms of more basic principles, and our results show that the two types of NmE observations are well correlated and statistically symmetrical, meaning that there is no overall bias and no scale-dependent bias.