We study the concept of multivariate dispersion order, defined as the
existence of an expansion function that maps a random vector to another
one, for multivariate distributions with the same dependence structure. As
a particular case, we can order the multivariate t-distribution
family in dispersion sense. Finally, we use these results in the problem
of detection and characterization of influential observations in
regression analysis. This problem can often be used to compare two
multivariate t-distributions.