  In scientific research, many hypotheses relate to the comparison of two
independent groups. Usually, it is of interest to use a design (i.e., the
allocation of sample sizes $m$ and $n$ for fixed $N = m + n$) that maximizes
the power of the applied statistical test. It is known that the two-sample
t-tests for homogeneous and heterogeneous variances may lose substantial power
when variances are unequal but equally large samples are used. We demonstrate
that this is not the case for the non-parametric Wilcoxon-Mann-Whitney-test,
whose application in biometrical research fields is motivated by two examples
from cancer research. We prove the optimality of the design $m = n$ in case of
symmetric and identically shaped distributions using normal approximations and
show that this design generally offers power only negligibly lower than the
optimal design for a wide range of distributions. Please cite this paper as
published in the Biometrical Journal (https://doi.org/10.1002/bimj.201600022).
