RV-coefficient and its significance test in mapping brain functional connectivity

The statistic of RV-coefficient is a good substitute for the Pearson correlation coefficient to measure the temporal similarity of two local brain regions. However, the hypothesis test of RV-coefficient is a hard problem which limits its application. This paper discussed the problem in details. Since the distribution of RV-coefficient is unknown, we do not know a critical p-value to statistically test its significance. We proposed a new strategy to test the significance of RV calculated from fMRI. In order to approximate the p-value, we elicited the first two moments of the population permutation distribution of RV; we then derived a formula to more closely approximate the normal distribution with these transformed statistics. These transformations of statistics are suggested for a precise approximation to the permutational p-value even under large number of observations. This strategy of test can greatly reduce the computational complexity and avoid "calculation catastrophe", we then use the statistic of RV to extract the map of functional connectivity from fMRI and test its significance with the strategy proposed here.