To extract reliable cosmic parameters from cosmic microwave background
datasets, it is essential to show that the data are not contaminated by
residual non-cosmological signals. We describe general statistical approaches
to this problem, with an emphasis on the case in which there are two datasets
that can be checked for consistency. A first visual step is the Wiener filter
mapping from one set of data onto the pixel basis of another. For more
quantitative analyses we develop and apply both Bayesian and frequentist
techniques. We define the ``contamination parameter'' and advocate the
calculation of its probability distribution as a means of examining the
consistency of two datasets. The closely related ``probability enhancement
factor'' is shown to be a useful statistic for comparison; it is significantly
better than a number of chi-squared quantities we consider. Our methods can be
used: internally (between different subsets of a dataset) or externally
(between different experiments); for observing regions that completely overlap,
partially overlap or overlap not at all; and for observing strategies that
differ greatly.
We apply the methods to check the consistency (internal and external) of the
MSAM92, MSAM94 and Saskatoon Ring datasets. From comparing the two MSAM
datasets, we find that the most probable level of contamination is 12%, with no
contamination only 1.05 times less probable, and 100% contamination strongly
ruled out at over 2 X 10^5 times less probable. From comparing the 1992 MSAM
flight with the Saskatoon data we find the most probable level of contamination
to be 50%, with no contamination only 1.6 times less probable and 100%
contamination 13 times less probable. [Truncated]Comment: LaTeX, 16 pages which include 16 figures, submitted to Phys. Rev.
