  There is evidence that the well-established mass-metallicity relation in
galaxies is correlated with a third parameter: star formation rate (SFR). The
strength of this correlation may be used to disentangle the relative importance
of different physical processes (e.g., infall of pristine gas, metal-enriched
outflows) in governing chemical evolution. However, all three parameters are
susceptible to biases that might affect the observed strength of the relation
between them. We analyze possible sources of systematic error, including sample
bias, application of signal-to-noise ratio cuts on emission lines, choice of
metallicity calibration, uncertainty in stellar mass determination, aperture
effects, and dust. We present the first analysis of the relation between
stellar mass, gas phase metallicity, and SFR using strong line abundance
diagnostics from Dopita et al. (2013) for ~130,000 star-forming galaxies in the
Sloan Digital Sky Survey and provide a detailed comparison of these diagnostics
in an appendix. Using these abundance diagnostics yields a 30-55% weaker
anti-correlation between metallicity and SFR at fixed stellar mass than that
reported by Mannucci et al. (2010). We find that, for all abundance
diagnostics, the anti-correlation with SFR is stronger for the relatively few
galaxies whose current SFRs are elevated above their past average SFRs. This is
also true for the new abundance diagnostic of Dopita et al. (2016), which gives
anti-correlation between metallicity and SFR only in the high specific star
formation rate (sSFR) regime, in contrast to the recent results of Kashino et
al. (2016). The poorly constrained strength of the relation between stellar
mass, metallicity, and SFR must be carefully accounted for in theoretical
studies of chemical evolution.
