  In this paper we develop tools for observers to use when analysing nebular
spectra for temperatures and metallicities, with two goals: to present a new,
simple method to calculate equilibrium electron temperatures for collisionally
excited line flux ratios, using the latest atomic data; and to adapt current
methods to include the effects of possible non-equilibrium '{\kappa}' electron
energy distributions. Adopting recent collision strength data for [O iii], [S
iii], [O ii], [S ii], and [N ii], we find that existing methods based on older
atomic data seriously overestimate the electron temperatures, even when
considering purely Maxwellian statistics. If {\kappa} distributions exist in H
ii regions and planetary nebulae as they do in solar system plasmas, it is
important to investigate the observational consequences. This paper continues
our previous work on the {\kappa} distribution (Nicholls et al. 2012). We
present simple formulaic methods that allow observers to (a) measure
equilibrium electron temperatures and atomic abundances using the latest atomic
data, and (b) to apply simple corrections to existing equilibrium analysis
techniques to allow for possible non-equilibrium effects. These tools should
lead to better consistency in temperature and abundance measurements, and a
clearer understanding of the physics of H ii regions and planetary nebulae.
