  We apply a recently developed theoretical model of helium emission to
observations of both the Orion Nebula and a sample of extragalactic H II
regions. In the Orion analysis, we eliminate some weak and blended lines and
compare theory and observation for our reduced line list. With our best
theoretical model we find an average difference between theoretical and
observed intensities $<I_{predicted}/I_{observed}-1> = 6.5%$. We argue that
both the red and blue ends of the spectrum may have been inadequately corrected
for reddening. For the 22 highest quality lines, with $3499
{\AA}\le\lambda\le6678 {\AA}$, our best model predicts observations to an
average of 3.8%. We also perform an analysis of the reported observational
errors and conclude they have been underestimated. In the extragalactic
analysis, we demonstrate the likelihood of a large systematic error in the
reported data and discuss possible causes. This systematic error is at least as
large as the errors associated with nearly all attempts to calculate the
primordial helium abundance from such observations. Our Orion analysis suggests
that the problem does not lie in the theoretical models. We demonstrate a
correlation between equivalent width and apparent helium abundance of lines
from extragalactic sources that is most likely due to underlying stellar
absorption. Finally, we present fits to collisionless case-B He I emissivities
as well as the relative contributions due to collisional excitations out of the
metastable $2s {}^{3}S$ term.
