Suppose I have a gene list of 470 genes that are induced in my study. I found that in other studies people already showed about 1000 genes were involved in the same kind of pathways but with the different model systems. Now, when I did an overlap of those 1000 genes with my 470 genes I found out of 470, at least 165 are common. Which statistical test I need to perform here to show that the overlap is not due to only by chance.
A slight issue here is that you need to know what the gene-universe is before you can do these comparisons, and you need to restrict your gene counts to just those that could have been assessed in both studies: for example, although you have 470 induced genes, they might not all have been studied in the other study.
Once you've got the gene-universe and the restriction of your gene-counts to that gene-universe, the standard approach would be to use Fisher's Exact test.