${\hbox{$T_2-T_3$}}$ relation normalized such that we get the best agreement in stacks for which we are able to measure the temperature of both ionization zones (see below). We use a Monte Carlo technique to derive uncertainties in our measurements.

We measure the electron temperature and density using the `IRAF/STSDAS` *nebular.temden* routine [@Shaw95], which is based on the 5 level atom from @DeRobertis87. We use the ${\hbox{[\ion{S}{ii}]~$\lambda$6717/$\lambda$6731}}$ ratio to measure the electron density. We use the auroral oxygen ratios (${\hbox{[\ion{O}{ii}]~$\lambda$7320+7330$/\lambda\lambda(3726+3729)$}}$ and ${\hbox{[\ion{O}{iii}]~$\lambda$4363/$\lambda\lambda(4959+5007)$}}$) to measure $T_2$ and $T_3$ respectively. @Andrews13 discuss at length the differences between the canonical ${\hbox{$T_2-T_3$}}$ relation and that observed for their stacks and find that in general their stacks fall below the @Campbell86 relation (in the sense of low $T_2$ at fixed $T_3$). This offset from the predicted relation has been previously seen [@Pilyugin10]. The fact that this offset disappears for galaxies with relatively high SFRs (which are likely to have contributions from relatively young stellar populations) indicates that the offset is likely due to the differences between the single stellar spectra used by @Stasinska82 and the composite region spectrum that ionizes the gas in a galaxy.

The ionic abundances of O$^+$ and O$^{++}$ are calculated using the 