The multidimensional runs statistic for testing the homogeneity of two multivariate samples is equivalent to the number of linked between-sample pairs of observations. Two observations may be linked if they are “close” to each other — for example, if joined by an edge of the minimum spanning tree, or if within a specified distance or “tolerance”. Based on the results of computer simulation of normally distributed data, we compare the multidimensional runs test with Hotelling's T2, showing that under certain circumstances the runs test can detect location differences with greater power. We also present guidelines for choosing a tolerance, expressed indirectly in terms of choosing what proportion of within-sample pairs to link so as to maximize power. These guidelines generally lead to a much higher proportion of linked pairs than would be given by any small number of orthogonal minimum spanning trees.