Mass-metallicity relation for the 118 galaxies in our dataset. Galaxies are coloured according to the sample from which their fluxes were taken. Points with thick black rings have direct Z_Te estimates [i.e. T_e(OIII) and T_e(OII) independently calculated], while the remaining points have semi-direct Z_Te estimates, i.e. using our new semi-direct method, corrected for the observed O⁺⁺/O⁺ bias using our least-squares-derived f_cor (see Sect. 5.3). The least-squares and Bayesian linear fits to all the points (Eq. (14)) are shown by the solid black line and solid dark grey line, respectively, with the 1σ dispersions given by dashed lines.