We examine the \alpha-element abundance ratio, [\alpha/Fe], of 5620 stars, observed by the Sloan Extension for Galactic Understanding and Exploration survey in the region 6 kpc < R < 16 kpc, 0.15 kpc < |Z| < 1.5 kpc, as a function of Galactocentric radius R and distance from the Galactic plane |Z|. Our results show that the high-\alpha\ thick disk population has a short scale length (L_thick ~ 1.8 kpc) compared to the low-\alpha population, which is typically associated with the thin disk. We find that the fraction of high-\alpha\ stars in the inner disk increases at large |Z|, and that high-\alpha\ stars lag in rotation compared to low-\alpha\ stars. In contrast, the fraction of high-\alpha\ stars in the outer disk is low at all |Z|, and high- and low-\alpha\ stars have similar rotational velocities up to 1.5 kpc from the plane. We interpret these results to indicate that different processes were responsible for the high-\alpha\ populations in the inner and outer disk. The high-\alpha\ population in the inner disk has a short scale length and large scale height, consistent with a scenario in which the thick disk forms during an early gas-rich accretion phase. Stars far from the plane in the outer disk may have reached their current locations through heating by minor mergers. The lack of high-\alpha\ stars at large R and |Z| also places strict constraints on the strength of radial migration via transient spiral structure.