Geometry‐derived statistical significance: A probabilistic framework for detecting true positive findings in MRI data

INTRODUCTION: The false discovery rate (FDR) procedure does not incorporate the geometry of the random field and requires high statistical power at each voxel, a requirement not satisfied by the limited number of participants in imaging studies. Topological FDR, threshold free cluster enhancement (TFCE), and probabilistic TFCE improve statistical power by incorporating local geometry. However, topological FDR requires specifying a cluster defining threshold and TFCE requires specifying transformation weights. METHODS: Geometry‐derived statistical significance (GDSS) procedure overcomes these limitations by combining voxelwise p‐values for the test statistic with the probabilities computed from the local geometry for the random field, thereby providing substantially greater statistical power than the procedures currently used to control for multiple comparisons. We use synthetic data and real‐world data to compare its performance against the performance of these other, previously developed procedures. RESULTS: GDSS provided substantially greater statistical power relative to the comparator procedures, which was less variable to the number of participants. GDSS was more conservative than TFCE: that is, it rejected null hypotheses at voxels with much higher effect sizes than TFCE. Our experiments also showed that the Cohen's D effect size decreases as the number of participants increases. Therefore, sample size calculations from small studies may underestimate the participants required in larger studies. Our findings also suggest effect size maps should be presented along with p‐value maps for correct interpretation of findings. CONCLUSIONS: GDSS compared with the other procedures provides considerably greater statistical power for detecting true positives while limiting false positives, especially in small sized (<40 participants) imaging cohorts.