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I have performed a clustering on 20K genes, and I want to understand how coherent resulting clusters are by calculating the significance of the overlap of the clusters with a number of known GO gene categories. I use hypergeometric p-values for this purpose, and I also want to correct for multiple testing using Bonferroni correction. My question is about how to perform Bonferroni correction. I know I have to multiply each hypergeometric p-value with the number of experiments performed for calculating the p-values, but I am a little confused about what "the number of experiments" means. I intuitively think that in my case, the number I have to multiply each hypergeometric p-value is #clusters * #GO-categories; is that right? So, for example, if I am checking the enrichment of each of 100 clusters with each of 200 gene categories, I will multiply the p-value for each cluster-category pair by 20000. Could you please confirm that?? Thank you!

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You would multiply by the number of hypothesis test you have carried out - i.e. the number of p-values. From what I understand of your description, that you are carrying out a test for each pair of cluster and category, then it is indeed 20,000.

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