We present Keck LRIS spectroscopy for a sample of 103 massive galaxies with redshifts 0.9 < z < 1.6. Of these, 56 are quiescent with high signal-to-noise absorption line spectra, enabling us to determine robust stellar velocity dispersions for the largest sample yet available beyond a redshift of 1. Together with effective radii measured from deep Hubble Space Telescope images, we calculate dynamical masses and address key questions relating to the puzzling size growth of quiescent galaxies over 0 < z < 2. We examine the relationship between stellar and dynamical masses at high redshift, finding that it closely follows that determined locally. We also confirm the utility of the locally-established empirical calibration which enables high-redshift velocity dispersions to be estimated photometrically, and we determine its accuracy to be 35%. To address recent suggestions that progenitor bias - the continued arrival of recently-quenched larger galaxies - can largely explain the size evolution of quiescent galaxies, we examine the growth at fixed velocity dispersion assuming this quantity is largely unaffected by the merger history. We demonstrate that significant size and mass growth have clearly occurred in individual systems. Parameterizing the relation between mass and size growth over 0 < z < 1.6 as R propto M^alpha, we find alpha = 1.6 +- 0.3, in agreement with theoretical expectations from simulations of minor mergers. Relaxing the assumption that the velocity dispersion is unchanging, we examine growth assuming a constant ranking in galaxy velocity dispersion. This approach is applicable only to the large-dispersion tail of the distribution, but yields a consistent growth rate of alpha = 1.4 +- 0.2. Both methods confirm that progenitor bias alone is insufficient to explain our new observations and that quiescent galaxies have grown in both size and stellar mass over 0 < z < 1.6.
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