To provide adjusted P-values at any significance level without actually performing all required permutations, we developed an approximation method based on the beta distribution. It is well established that order statistics of independent uniformly distributed random variables are beta-distributed (Jones, 2009). Therefore, we hypothesized that the P-values obtained through permutations are also beta-distributed (Dudbridge and Koeleman, 2004). More formally, the kth smallest value obtained when independently drawing n times from the uniform is distributed as: (3)U∼Beta(k,n)
