In theory, the bootstrap is the only technique that should be used to
compare the means of two populations that have quite different variances
(that is, the Behrens-Fisher problem). Student's t, a permutation test
using the original observations, and the permutation using ranks
(Mann-Whitney, Wilcoxon) are all likely to yield inexact significance
levels. Still simulations have shown that permutation tests are almost
exact even when the variance of one population is twice that of the
other. See http://statisticsonline.info/application.htm.
D. Middleton
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