The harmonic mean p-value (HMP) procedure provides a multilevel test that improves on the power of Bonferroni correction by assessing the significance of groups of hypotheses while controlling the strong-sense family-wise error rate. The significance of any subset  of the  tests is assessed by calculating the HMP for the subset, where  are weights that sum to one (i.e. ).
The harmonic mean p-value (HMP) procedure is a multilevel test that improves upon Bonferroni correction by examining the significance of groups of hypotheses while controlling the family-wise error rate. The significance of any group of tests is determined by calculating the HMP for that group, where weights are used to ensure their sum equals one.