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We consider the problem of testing positively dependent multiple hypothesesassuming that a prior information about the dependence structure is available.We propose two-step multiple comparisons procedures that exploit the priorinformation of the dependence structure, without relying on strong assumptions.In the first step, we group the tests into subsets where tests are supposed tobe positively dependent and in each of which we compute the standardized meanof the test scores. Given the subset mean scores or equivalently the subsetsp-values, we apply a first screening at a predefined threshold, which resultsin two types of subsets. Based on this typing, the original single testp-values are modified such that they can be used in conjunction with anymultiple comparison procedure. We show by means of different simulation thatpower is gained with the proposed two-step methods, and compare it withtraditional multiple comparison procedures. As an illustration, our method isapplied on real data comparing topological differences between two groups ofhuman brain networks.

Two step multiple comparisons procedures for positively dependent data with application to detecting differences in human brain network topologies