  We examine the distribution of the [O/Fe] abundance ratio in stars across the
Galactic disk using H-band spectra from the Apache Point Galactic Evolution
Experiment (APOGEE). We minimize systematic errors by considering groups of
stars with similar atmospheric parameters. The APOGEE measurements in the Sloan
Digital Sky Survey Data Release 12 reveal that the square root of the
star-to-star cosmic variance in the oxygen-to-iron ratio at a given metallicity
is about 0.03-0.04 dex in both the thin and thick disk. This is about twice as
high as the spread found for solar twins in the immediate solar neighborhood
and the difference is probably associated to the wider range of galactocentric
distances spanned by APOGEE stars. We quantify the uncertainties by examining
the spread among stars with the same parameters in clusters; these errors are a
function of effective temperature and metallicity, ranging between 0.005 dex at
4000 K and solar metallicity, to about 0.03 dex at 4500 K and [Fe/H]= -0.6. We
argue that measuring the spread in [O/Fe] and other abundance ratios provides
strong constraints for models of Galactic chemical evolution.

Astrophysics of Galaxies;Solar and Stellar Astrophysics