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When should I use an explicit background set in evaluating enrichments?

Statistical enrichments are always relative to some background set. If you do not provide a background set, then GREAT uses a whole genome background. Such a background is not always appropriate. You should provide a background set to account for any inherent biases in sampling<a name="reference1">1</a>.

References

Rhee S. Y. et al. Use and misuse of the gene ontology annotations, Nat Rev Genet. 9:509-515 (2008). 

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