  We identified a large sample of radio quasars, including those with complex
radio morphology, from the Sloan Digital Sky Survey (SDSS) and the Faint Images
of Radio Sky at Twenty-cm (FIRST). Using this sample, we inspect previous radio
quasar samples for selection effects resulting from complex radio morphologies
and adopting positional coincidence between radio and optical sources alone. We
find that 13.0% and 8.1% radio quasars do not show a radio core within 1.2 and
2 arcsecs of their optical position, and thus are missed in such samples. Radio
flux is under-estimated by a factor of more than 2 for an additional 8.7% radio
quasars. These missing radio extended quasars are more radio loud with a
typical radio-to-optical flux ratio namely radio loudness RL >100, and radio
power P >10^{25} W/Hz. They account for more than one third of all quasars with
RL>100. The color of radio extended quasars tends to be bluer than the radio
compact quasars. This suggests that radio extended quasars are more radio
powerful sources, e.g., Fanaroff-Riley type 2 (FR-II) sources, rather than the
compact ones viewed at larger inclination angles. By comparison with the radio
data from the NRAO VLA Sky Survey (NVSS), we find that for sources with total
radio flux less than 3 mJy, low surface brightness components tend to be
underestimated by FIRST, indicating that lobes in these faint radio sources are
still missed.
