The Yarkovsky effect is a thermal process acting upon the orbits of small celestial bodies, which can cause these orbits to slowly expand or contract with time. The effect is subtle (da/dt ~ 10^-4 au/My for a 1 km diameter object) and is thus generally difficult to measure. We analyzed both optical and radar astrometry for 600 near-Earth asteroids (NEAs) for the purpose of detecting and quantifying the Yarkovsky effect. We present 247 NEAs with measured drift rates, which is the largest published set of Yarkovsky detections. This large sample size provides an opportunity to examine the Yarkovsky effect in a statistical manner. In particular, we describe two independent population-based tests that verify the measurement of Yarkovsky orbital drift. First, we provide observational confirmation for the Yarkovsky effects theoretical size dependence of 1/D, where D is diameter. Second, we find that the observed ratio of negative to positive drift rates in our sample is 2.34, which, accounting for bias and sampling uncertainty, implies an actual ratio of $2.7^{+0.3}_{-0.7}$. This ratio has a vanishingly small probability of occurring due to chance or statistical noise. The observed ratio of retrograde to prograde rotators is two times lower than the ratio expected from numerical predictions from NEA population studies and traditional assumptions about the sense of rotation of NEAs originating from various main belt escape routes. We also examine the efficiency with which solar energy is converted into orbital energy and find a median efficiency in our sample of 12%. We interpret this efficiency in terms of NEA spin and thermal properties.