It is a fascinating yet challenging problem to accurately and efficiently localize regionally distinct features between face groups in multi-dimensional signal processing and analysis. Given a data with unknown distribution and small sample size, we propose a new statistical analysis framework using hybrid randomization (i.e., permutation) tests to improve the system's efficiency in identifying distinct features. The proposed method fits the nonparametric distribution of the test statistic with Pearson distribution series. We bypass the tedious online randomization via calculating the first four moments of the permutation distribution. This can reduce the computational complexity from O(n!) to O(n2) over traditional methods for the modified Hotelling's T2 test statistics. Experiments on simulated data and 3D face analysis demonstrate the efficiency, accuracy and robustness of the proposed approach.