The enrichment analysis is to test whether any functional modules (gene sets or miRNA set) from the user selected library are significantly enriched among those genes / miRNAs of interest (i.e. if a particular group of gene function is more frequently observed than would be anticipated by random chance). A fundamental assumption is that there is a finite universe, and each member of the universe has equal opportunity to be selected (random sampling).
Hypergeometric tests: This is used when the intention is to perform direct functional enrichment analysis. For instance, the input are miRNAs, and intention is miRNA set enrichment analysis. miRNet offers this classical over-representation analysis after adjustment for false discovery rate (FDR).
Empirical sampling: This is used when the intention is to perform indirect functional enrichment analysis. For instance, the input are miRNAs, and the intention is to evaluate the enriched function of their gene targets. In this case, the assumption of random sampling of the “gene universe” and there are systematic bias in selecting certain genes (refer to the paper Bias in microRNA functional enrichment analysis for more details).