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The PANTHER website offers a tool to obtain the GO-based overrepresentation of a gene list (the analyzed list) versus a reference gene list. After entering both these lists, the tool asks to choose between the Fisher's Exact or Binomial tests.

I guess that the convenience for one or another test would depend on the number of genes to analyze. If that is the case, which would be the ideal or advisable rank of gene numbers in both analyzed and reference lists (or their ratio) for each type of test?

(In particular I am working with a list of around 150 versus a reference list of around 2000 genes).

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For a guide on using the tests in PANTHER, see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6519457/.

In answer to this specific question, the defaults are the best choice (Fisher's Exact Test, with FDR correction). Fisher's Exact test gives more accurate statistics for relatively small counts (e.g. when only a few genes in your list are associated with a particular GO term). The FDR is a better correction to use for these types of analysis in general, especially given the large overlap between classes.

The other options are there mostly to support replication of older analyses, e.g. to replicate a published analysis that used the PANTHER over-representation tool prior to 2018, when the binomial with Bonferroni correction was the default.

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