The high dimension of functional magnetic resonance imaging (fMRI) data causes problems in finding effective thresholds for voxelwise test statistics. Due to the enormous number of voxels, adjustment for multiple testing is necessary. But such an adjustment can lead to low statistical power. It has been shown that filtering the test statistics to reduce the number of tests being performed potentially increases the number of discoveries. However, some filter-test combinations can result in loss of control over the false discovery rate. We present an independent filtering approach which avoids this issue. Independent filtering uses filter-test combinations such that the filter is independent from the test statistic, leaving the null distribution of the test statistic unchanged. Applying the procedure to fMRI data, we show that when a voxelwise general linear model is fit, filtering by magnitude of the stimulus coefficient followed by a procedure which controls the FDR even under arbitrary p-value dependence structures, increases the number of discoveries. Thus, we demonstrate that independent filtering has the potential to increase power while controlling the false discovery rate
