On the Blocks of Interpoint Distances

We study the blocks of interpoint distances, their distributions, correlations, independence and the homogeneity of their total variances. we discuss the exact and asymptotic distribution of the interpoint distances and their average under three models and provide connections between the correlation of interpoint distances with their vector correlation and test of sphericity. we discuss testing independence of the blocks based on the correlation of block interpoint distances. a homogeneity test of the total variances in each block and a simultaneous plot to visualize their relative ordering are presented.