A New Approach to Systematic Uncertainties and Self-Consistency in
  Helium Abundance Determinations
  Tests of big bang nucleosynthesis and early universe cosmology require
precision measurements for helium abundance determinations. However, efforts to
determine the primordial helium abundance via observations of metal poor H II
regions have been limited by significant uncertainties. This work builds upon
previous work by providing an updated and extended program in evaluating these
uncertainties. Procedural consistency is achieved by integrating the hydrogen
based reddening correction with the helium based abundance calculation, i.e.,
all physical parameters are solved for simultaneously. We include new atomic
data for helium recombination and collisional emission based upon recent work
by Porter et al. and wavelength dependent corrections to underlying absorption
are investigated. The set of physical parameters has been expanded here to
include the effects of neutral hydrogen collisional emission. Because of a
degeneracy between the solutions for density and temperature, the precision of
the helium abundance determinations is limited. Also, at lower temperatures (T
\lesssim 13,000 K) the neutral hydrogen fraction is poorly constrained
resulting in a larger uncertainty in the helium abundances. Thus the derived
errors on the helium abundances for individual objects are larger than those
typical of previous studies. The updated emissivities and neutral hydrogen
correction generally raise the abundance. From a regression to zero
metallicity, we find Y_p as 0.2561 \pm 0.0108, in broad agreement with the WMAP
result. Tests with synthetic data show a potential for distinct improvement,
via removal of underlying absorption, using higher resolution spectra. A small
bias in the abundance determination can be reduced significantly and the
calculated helium abundance error can be reduced by \sim 25%.
