Some adaptive test procedures are developed for the generalized
Behrens-Fisher problem. The one having a deterministic approach is based on
calculating a measure of symmetry from each sample and using them as a basis
for choosing between the modifiedWilcoxon-Mann-Whitney test (Fligner
and Policello, 1981) and the modified Mood’s median test (Fligner and Rust,
1982). The other one is a probabilistic approach which also uses a combination
of the modified Wilcoxon-Mann-Whitney test and the modified Mood’s
median test according to an evidence of asymmetry provided by the p-value
from the triples test for symmetry given in Randles, Fligner, Policello, and
Wolfe (1980). This probabilistic approach is further modified by using a suitable
function of the p-value from the triples test. A simulation study reveals
that the modified procedure performs reasonably well in terms of power and
attainment of the nominal size.