that the random noise in a composite spectrum of $N$ galaxies scales roughly as $1/\sqrt{N}$; it is advantageous for our bins to contain a large number of galaxies in order to reduce the noise in the spectrum as much as possible. However, we also want each bin to span a very small range in *actual* (O/H) so that we are stacking qualitatively similar galaxies. The chosen bin widths are a compromise between these two goals.

Before stacking the spectra, we follow the same reduction process described in @Andrews13. Starting with the spectra that have been processed with the SDSS pipeline [@Stoughton02], we correct for Galactic reddening using the extinction values from @Schlegel98. We then shift each spectrum to the rest frame using redshifts from the ${\hbox{MPA/JHU}}$ catalog. We interpolate each spectrum onto a wavelength grid spanning 3700Å–7360Å with spacing $\Delta \lambda = 1$Å. In order to compare galaxies at various distances we normalize each spectrum to the stellar continuum with the mean continuum flux from 4400Å–4450Å. Thus when we measure the line flux we effectively measure the equivalent width of the line. At fixed , normalizing to the stellar continuum is acceptable since the luminosities of the galaxies are essentially 