In neuroimaging, a large number of correlated tests are routinely performed to detect active voxels in single-subject experiments or to detect regions that differ between individuals belonging to different groups. In order to bound the probability of a false discovery of pair-wise differences, a Bonferroni or other correction for multiplicity is necessary. These corrections greatly reduce the power of the comparisons which means that small signals (differences) remain hidden and therefore have been more or less successful depending on the application. We introduce a method that improves the power of a family of correlated statistical tests by reducing their number in an orderly fashion using our a-priori understanding of the problem . The tests are grouped by blocks that respect the data structure and only one or a few tests per group are performed. For each block we construct an appropriate summary statistic that characterizes a meaningful feature of the block. The comparisons are based on these summary statistics by a block-wise approach. We contrast this method with the one based on the individual measures in terms of power. Finally, we apply the method to compare brain connectivity matrices. Although the method is used in this study on the particular case of imaging, the proposed strategy can be applied to a large variety of problems that involves multiple comparisons when the tests can be grouped according to attributes that depend on the specific problem. Keywords and phrases: Multiple comparisons ; Family-wise error rate; False discovery rate; Bonferroni procedure; Human brain connectivity; Brain connectivity matrices.