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We use direct method oxygen abundances in combination with strong opticalemission lines, stellar masses ($M_{\star}$), and star formation rates (SFRs)to recalibrate the N2, O3N2, and N2O2 oxygen abundance diagnostics. We stackspectra of $\sim$200,000 star-forming galaxies from the Sloan Digital SkySurvey in bins of $M_{\star}$ and SFR offset from the star forming mainsequence to measure the weak emission lines needed to apply the direct method.All three new calibrations are reliable to within $\pm 0.10$ dex from$\log(M_{\star}/M_{\odot}) \sim 7.5 - 10.5$ and up to at least $200~M_{\odot}$yr$^{-1}$ in SFR. The N2O2 diagnostic is the least subject to systematicbiases. We apply the diagnostics to galaxies in the local universe andinvestigate the $M_{\star}$-$Z$-${\rm SFR}$ relation. The N2 and O3N2diagnostics suggest the SFR dependence of the $M_{\star}$-$Z$-${\rm SFR}$relation varies with both $M_{\star}$ and $\Delta \log(SSFR)$, whereas the N2O2diagnostic suggests a nearly constant dependence on SFR. We apply ourcalibrations to a sample of high redshift galaxies from the literature, andfind them to be metal poor relative to local galaxies with similar $M_{\star}$and SFR. The calibrations do reproduce direct method abundances of the localanalogs. We conclude that the $M_{\star}$-$Z$-${\rm SFR}$ relation evolves withredshift.

A Recalibration of Strong Line Oxygen Abundance Diagnostics via the Direct Method and Implications for the High Redshift Universe