Chi-squared cannot be used when there are small numbers of counts/bin (ie Poisson regime).

The standard answer is to bin the data to give ``enough'' counts in each bin. This has the advantage that most astronomers think they understand chi-squared so the results will be believed.

Two binning schemes are used.

• A uniform binning. The disadvantage is that information is lost, particularly on features sharper than the binning.

• A non-uniform binning where bins are combined until a certain threshold of counts are reached. This makes an attempt to retain sensitivity to emission lines, but not to absorption features. I don't know how this effects the statistics and don't know of anyone who has worried about it (although I invented this, sorry).