Assessing Congruence Among Ultrametric Distance Matrices

Recently, a test of congruence among distance matrices (CADM) has been developed. The null hypothesis is the incongruence among all data matrices. It has been shown that CADM has a correct type I error rate and good power when applied to independently-generated distance matrices. In this study, we investigate the suitability of CADM to compare ultrametric distance matrices. We tested the type I error rate and power of CADM with randomly generated dendrograms and their associated ultrametric distance matrices. We show that the test has correct type I error rates and good power. To obtain the significance level of the statistic, a single (as in the Mantel test) or a double (as in the double permutation test, DPT) permutation procedure was used. The power of CADM remained identical when the two permutation methods were compared. This study clearly demonstrates that CADM can be used to determine whether different dendrograms convey congruent information.