A class of independent multivariate linear models is considered, havin
g a common parameter matrix Theta in their means, but having different
covariance matrices. For testing H-0:Theta=0, some test procedures ar
e derived, which combine the information from the different models. In
the context of the interblock analysis of block designs, simulated po
wers of some combined tests are reported in the bivariate case, for co
mbining the intra- and interblock tests based on the Wilk's Lambda cri
terion. The numerical results indicate that the combined tests offer s
ubstantial improvement in power compared to the Wilk's Lambda test bas
ed only on intrablock information. (C) 1994 Academic Press, Inc.