systematic shift ($\sim$0.1 dex) in the $\log$(O/H) of the stacks for which $T_2$ was measured and used to infer $T_3$.

Empirical Calibrations
----------------------

There are many abundance diagnostic ratios. Our choice of ratios to consider is motivated by three factors: (1) our calibration(s) should be empirical, (2) the distribution of line ratios for individual galaxies in a stack ought to be reasonably peaked around the mean value, and (3) the calibration ought to be valid for the majority of our stacks.

The most commonly used oxygen abundance diagnostics are N2 and O3N2 [@Denicolo02; @Pettini04; @Marino13], N2O2 [@Dopita00; @Kewley02], and R23 [@Pagel79; @McGaugh91; @Pilyugin03; @Kobulnicky04] . Figure \[fig:dssfr\] shows the distribution of individual galaxies in the ${\hbox{$M_{\star}$}}$–diagnostic planes for these diagnostics. In panel “(a)” of Figure \[fig:dssfr\], the distribution of galaxies is such that galaxies with similar ${\hbox{$M_{\star}$}}$ and ${\hbox{$\Delta\log$(SSFR)}}$ follow a relatively tight sequence in the ${\hbox{$M_{\star}$}}$–N2 plane. Similar behavior is seen in panel “(b)” (O3N2) and, to a somewhat lesser extent, panel “(c)” (N2O2). In panel “(d)” at fixed ${\hbox{$M_{\star}$}}$ and ${\hbox{$\Delta\log$(SSFR)}}$, the values of ${\hbox{$R_{23}$}}$ follow a relatively broad distribution; the scatter in ${\hbox{$R_{23}$}}$ at fixed ${\hbox{$M_{\star}$}}$ and ${\hbox{$\Delta\log$(SSFR)}}$ can be comparable to the entire range spanned by 