aperture biases are comparable to the scatter in the inferred O/H for galaxies of similar stellar mass and star formation rate.

Another limitation of single-fiber observations is they simply present an incomplete picture of the properties of galaxies. One example is that while @Sanchez13 found a very tight relationship between integrated stellar mass and metallicity with integral field data from CALIFA [@Sanchez12], they did not find any dependence of metallicity on star formation rate at fixed stellar mass. Another example is the analysis by @Belfiore15 of nebular data for 14 galaxies with P-MaNGA, the prototype instrument for the ongoing MaNGA survey [@Bundy15]. Those authors found a substantial spread in O/H values at fixed N/O for regions within individual galaxies, which is in contrast to the stronger correlation exhibited by the central regions from single-fiber observations.

Stacking Procedure {#sec:stack}
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The auroral lines of \[\], \[\], and \[\] are generally weak and typically undetectable in most SDSS galaxy spectra. However, previous studies [e.g. @Liang07; @Andrews13] have demonstrated that stacking spectra to reduce the contribution of random fluctuations in the measured flux is a viable way to obtain sufficient S/N to measure the auroral lines.

The stacking method relies on the fact 