A permutation test of association between configurations by means of the RV coefficient

The RV coefficient is known to be suitable for measuring association between homologous configurations. The randomness of such association can be tested by permutational significance. In order to approximate the p-value, we derive the first two moments of the population permutation distribution of the RV coefficient. The permutational distributions of the RV coefficients are explored through several examples. Their permutation distributions appear to be markedly skewed to the right, regardless of the magnitudes of the observed RV coefficients herein Log-transformation of the first two moments is suggested for a better approximation to the permutational p-value.