We are working on a bioinformatics problem. We have a collection (say $U$) of kmers or small substrings of length $k$ of some set of sequences. We have two different experiments. Only a subset of kmers say, $A,B \subseteq U$, is enriched in each of the two experiments, respectively. We want to show $A \cap B$ is statistically significant.
We were trying to use Fisher's exact test (FET) on a contingency table with entries $|A \cap B|, |A \setminus B|, |B \setminus A|, |U \setminus (A \cup B)|$. But it seems that this FET has the null hypothesis: “probability of a kmer getting enriched is same in the two experiments”.
However, for our purpose it should be the alternate hypothesis.
Is there a different way to use FET for our purpose?