Keith Jahoda's response to a user question directed to xtehelp in
August 2004:

   When you use SAEXTRCT to collect your spectra, it estimates
an error equal to the square root of the number of counts.
For the data, this is unquestionably correct.  For the background
spectrum, however, this overestimates the errors since the
PCABACKEST output is based on the average of a huge amount of
data.  (The details of "huge" are variable since only data
with similar L7 rates contributes to the background model for
each value of L7).  The statistical error on the background is
thus related to the amount of data that went into the background model
and not the length of your observation.  It is almost certainly
true that the Poisson errors are dominated by the observed data,
and you could set the background error column to zero.  (This
obviously underestimates the error on the background, but the
reduced chi-square values would be only very slightly higher than

   If you want a better estimate of the errors in each spectral
channel, you could compare the estimated background in adjacent
channels.  As there is no reason to believe that the background
spectrum isn't smooth in places where there are not obvious line
features, you can probably use the channel to channel variation
as a robust estimator.