A non-parametric permutation method for assessing agreement for distance matrix observations

Distance matrix data are occurring ever more frequently in medical research, particularly in fields such as genetics, DNA research, and image analysis. We propose a non-parametric permutation method for assessing agreement when the data under study are distance matrices. We apply agglomerative hierarchical clustering and accompanying dendrograms to visualize the internal structure of the matrix observations. The accompanying test is based on random permutations of the elements within individual matrix observations and the corresponding matrix mean of these permutations. We compare the within-matrix element sum of squares (WMESS) for the observed mean against the WMESS for the permutation means. The methodology is exemplified using simulations and real data from magnetic resonance imaging.