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.
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