Understanding and reducing statistical uncertainties in nebular
  abundance determinations
  Whenever observations are compared to theories, an estimate of the
uncertainties associated with the observations is vital if the comparison is to
be meaningful. However, many determinations of temperatures, densities and
abundances in photoionized nebulae do not quote the associated uncertainty.
Those that do typically propagate the uncertainties using analytical techniques
which rely on assumptions that generally do not hold.
  Motivated by this issue, we have developed NEAT (Nebular Empirical Analysis
Tool), a new code for calculating chemical abundances in photoionized nebulae.
The code carries out an analysis of lists of emission lines using
long-established techniques to estimate the amount of interstellar extinction,
calculate representative temperatures and densities, compute ionic abundances
from both collisionally excited lines and recombination lines, and finally to
estimate total elemental abundances using an ionization correction scheme. NEAT
uses a Monte Carlo technique to robustly propagate uncertainties from line flux
measurements through to the derived abundances.
  We show that for typical observational data, this approach is superior to
analytic estimates of uncertainties. NEAT also accounts for the effect of
upward biasing on measurements of lines with low signal to noise, allowing us
to accurately quantify the effect of this bias on abundance determinations. We
find not only that the effect can result in significant over-estimates of heavy
element abundances derived from weak lines, but that taking it into account
reduces the uncertainty of these abundance determinations. Finally, we
investigate the effect of possible uncertainties in R, the ratio of selective
to total extinction, on abundance determinations. We find that the uncertainty
due to this parameter is negligible compared to the statistical uncertainties
due to typical line flux measurement uncertainties.
