Overlapping Probabilities of Top Ranking Gene Lists, Hypergeometric   Distribution, and Stringency of Gene Selection Criterion
  When the same set of genes appear in two top ranking gene lists in two different studies, it is often of interest to estimate the probability for this being a chance event. This overlapping probability is well known to follow the hypergeometric distribution. Usually, the lengths of top-ranking gene lists are assumed to be fixed, by using a pre-set criterion on, e.g., $p$-value for the t-test. We investigate how overlapping probability changes with the gene selection criterion, or simply, with the length of the top-ranking gene lists. It is concluded that overlapping probability is indeed a function of the gene list length, and its statistical significance should be quoted in the context of gene selection criterion. 
Wen Fury, Franak Batliwalla, Peter K. Gregersen, and Wentian Li