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In neuroimaging, a large number of correlated tests are routinely performedto detect active voxels in single-subject experiments or to detect regions thatdiffer between individuals belonging to different groups. In order to bound theprobability of a false discovery of pair-wise differences, a Bonferroni orother correction for multiplicity is necessary. These corrections greatlyreduce the power of the comparisons which means that small signals(differences) remain hidden and therefore have been more or less successfuldepending on the application. We introduce a method that improves the power ofa family of correlated statistical tests by reducing their number in an orderlyfashion using our a-priori understanding of the problem . The tests are groupedby blocks that respect the data structure and only one or a few tests per groupare performed. For each block we construct an appropriate summary statisticthat characterizes a meaningful feature of the block. The comparisons are basedon these summary statistics by a block-wise approach. We contrast this methodwith the one based on the individual measures in terms of power. Finally, weapply the method to compare brain connectivity matrices. Although the method isused in this study on the particular case of imaging, the proposed strategy canbe applied to a large variety of problems that involves multiple comparisonswhen the tests can be grouped according to attributes that depend on thespecific problem. Keywords and phrases: Multiple comparisons ; Family-wiseerror rate; False discovery rate; Bonferroni procedure; Human brainconnectivity; Brain connectivity matrices.

Efficient statistical analysis of large correlated multivariate datasets: a case study on brain connectivity matrices