A statistical study has been made of the dependence of radio-auroral echoes obtained with the 398 MHz radar at Homer, Alaska on electric fields and election densities measured simultaneously with the Chatanika incoherent scatter radar. There is a dependence on the magnitude of the electric field which is consistent with a threshold electric field of about 23 mV/m. The results of the analysis have been compared with the predictions of several existing theories of radio aurora. The echoes apparently arise from secondary irregularities generated by a primary two-stream instability; it is most likely that secondary two-stream irregularities are involved. Many of the data were obtained when the electric field was directed southward, and during this time the radio-auroral echoes were found to come from heights at or below the height of the maximum E-region electron density. Surprisingly, no echoes were obtained for large electron densities, regardless of the strength of the electric field. This implies that the spatial anticorrelation between visual and radio aurora involves more than the reduction of the electric field within visual forms.