We have pointed out a number of points in the analysis of optical spectra of nebulae that can lead to biased or inaccurate abundance results if not accounted for properly. We hope to draw attention to the treatment of the H I Balmer lines as a critically important step in an accurate abundance analysis.

Our inspection of self consistent minimization methods for
determining helium abundances has revealed several things.
In the perfect world when all of the uncertainties in the input data are
under control, the 6 line method is best at solving for the physical
input parameters and ultimately the He abundance.
However, minimization routines should used with caution with
a eye toward systematically biased observations. The key
diagnostics are the values of the
^{2} in a straight
minimization,
and the results of the 3 line method. When the data are good the
^{2} per degree of
freedom should be small, and the results of the 3,
5, and 6 line methods should be consistent. The latter methods should be
more accurate and carry smaller error bars on the derived quantities.
If either of these conditions are not met, then it is probably not
advisable to use those data in a determination of the primordial He
abundance. In any case, a Monte Carlo realization of the observations
should be conducted to assess the true uncertainties in the resultant
abundances.

While it may seem that, in some cases, the straight minimization gives a solution closer to the original input parameters than does the average Monte Carlo result, one must bear in mind that we have been using synthetic data with known values. By running the Monte Carlo on synthetic data we are modeling possible sets of observations consistent with the true physical description of the HII region. That is, each Monte Carlo minimization represents the result of a single possible observation. Running a Monte Carlo realization of real data allows an exploration of all of the possible suitable solutions allowed by the degeneracies in the sensitivities of the various He I lines to the different physical parameters.

Clearly the abundances used in estimating *Y*_{p}
are not observed but rather derived quantities. As we have seen, the
derivation of the He abundance relies on several, a priori, unknown but
physical input parameters. In this paper, we hope to have clarified the
determination process, and quantified the uncertainties in the result.
Thus, it may be premature to be arguing over the
3rd decimal place in *Y*_{p} until a systematic treatment
and Monte Carlo analysis of the data has been performed.
Our purpose here is not to propose a minimum error for all nebular helium
abundances nor to try to give a quantitative estimate of how a given
analysis may result in a systematic bias in the derivation of
*Y*_{p}. Rather, we wish to promote a methodology
for the analysis of all nebular HII region spectra in the pursuit of
accurate He abundances. We emphasize the importance of reporting more
information (the equivalent widths of all of the H I and He I emission
lines, the ^{2} results
for minimizations) and the use of Monte
Carlo techniques for characterizing error terms. In the future, we
will apply the recommended methods to both new observations and
other observations reported in the literature.

**Acknowledgments**

We would like to thank R. Kennicutt and B. Pagel for insightful comments on the manuscript. We also are pleased to thank R. Benjamin, D. Kunth, M. Peimbert, G. Shields, J. Shields, G. Steigman, E. Terlevich, and R. Terlevich for informative and valuable discussions. The work of KAO is supported in part by DOE grant DE-FG02-94ER-40823. EDS is grateful for partial support from a NASA LTSARP grant No. NAGW-3189.