  A number of recent works in astronomy and cosmology have relied upon
theoretical He I emissivities, but we know of no effort to quantify the
uncertainties in the atomic data. We analyze and assign uncertainties to all
relevant atomic data, perform Monte Carlo analyses, and report standard
deviations in the line emissivities. We consider two sets of errors, which we
call "optimistic" and "pessimistic." We also consider three different
conditions, corresponding to prototypical Galactic and extragalactic H II
regions and the epoch of cosmological recombination. In the extragalactic H II
case, the errors we obtain are comparable to or larger than the errors in some
recent $Y_p$ calculations, including those derived from CMB observations. We
demonstrate a systematic effect on primordial abundance calculations; this
effect cannot be reduced by observing a large number of objects. In the
cosmological recombination case, the errors are comparable to many of the
effects considered in recent calculations.
