One of the advantages of Bayesian statistics is that they permit discussion of null results. Antony Overstall of St. Andrews has recently released a package for R called
conting that handles Bayesian analysis of contingency tables in a relatively straightforward way.
http://cran.r-project.org/web/packages/conting/ . I had a play around with it and managed to get meaningful results in about an hour. Take a look!
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