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I have performed hierarchical clustering and am looking for a way to test if a specific set of objects (genes, in this case) are clustered together.

From inspecting the output I cannot identify a specific cluster(s) that contains all or most of my objects, so a simple test for over-representation (e.g. hypergeometric test) won't be useful, but I still want to test if the objects are randomly distributed between the clusters.

I am considering two possible approaches 1. Find the index of the leaf that correspond to each object in the hierarchical clustering dendrogram and test if the indices of the leaves that correspond to my object of interest are uniformly distributed. But I am not sure what statistical test to use.

I don't think I can use Kolomgorov-Smirnov since my distribution is discrete. I thought about using the chi-square test, but how do I formulate the expected observations under the null? 2. Perform a permutation test on the indices of the object of interest. But which test statistic to compute?

I am aware that neither of these suggestions take into account the hierarchical structure. I will be also welcome any suggestions for relevant methods that do take this structure into account.

Any comments on this will be appreciated.

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