Zeeman observations of molecular clouds yield the line-of-sight component B LOS of the magnetic vector B, which makes it possible to test the two major extreme-case theories of what drives star formation -ambipolar diffusion or turbulence. However, only one of the three components of B is measurable, so tests have been statistical rather than direct, and they have not been definitive. We report here observations of the Zeeman effect in the 18-cm lines of OH in the envelope regions surrounding four molecular cloud cores toward which detections of B LOS have been achieved in the same lines, and evaluate the ratio of mass to magnetic flux, M/Φ, between the cloud core and envelope. This relative M/Φ measurement reduces uncertainties in previous studies, such as the angle between B and the line of sight and the value of [OH/H]. Our result is that for all four clouds, the ratios R of the core to the envelope values of M/Φ are less than 1. Stated another way, the ratios R ′ of the core to the total cloud M/Φ are less than 1. The extreme case or idealized (no turbulence) ambipolar diffusion theory of core formation requires the ratio of the central to total M/Φ to be approximately equal to the inverse of the original subcritical M/Φ, or R ′ > 1. The probability that all four of our clouds have R ′ > 1 is 3 × 10 −7 ; our results are therefore significantly in contradiction with the hypothesis that these four cores were formed by ambipolar diffuson. Highly super-Alfvénic turbulent simulations yield a wide range of relative M/Φ, but favor a ratio R < 1, as we observe. Our experiment is limited to four clouds, and we can only directly test the predictions of the extreme-case "idealized" models of ambipolar-diffusion driven star formation