  Recently, \citet{Nicholls12}, inspired by \emph{in situ} observations of
solar system astrophysical plasmas, suggested that the electrons in \HII
regions are characterised by a $\kappa$-distribution of electron energies
rather than by a simple Maxwell-Boltzmann distribution. Here we have collected
together the new atomic data within a modified photoionisation code to explore
the effects of both the new atomic data and the $\kappa$-distribution on the
strong-line techniques used to determine chemical abundances in \HII regions.
By comparing the recombination temperatures ($T_{\rm rec}$) with the forbidden
line temperatures ($T_{\rm FL}$) we conclude that $ \kappa \sim 20$. While
representing only a mild deviation from equilibrium, this is sufficient to
strongly influence abundances determined using methods which depend on
measurements of the electron temperature from forbidden lines. We present a
number of new emission line ratio diagnostics which cleanly separate the two
parameters determining the optical spectrum of \HII regions - the ionisation
parameter $q$ or $\cal{U}$ and the chemical abundance; 12+log(O/H). An
automated code to extract these parameters is presented. Using the homogeneous
dataset from \citet{vanZee98}, we find self-consistent results between all
these different diagnostics. The systematic errors between different line ratio
diagnostics are much smaller than was found in the earlier strong line work.
Overall the effect of the $\kappa$-distribution on the strong line abundances
derived solely on the basis of theoretical models is rather small.
