  Rank-based inference methods are applied in various disciplines, typically
when procedures relying on standard normal theory are not justifiable, for
example when data are not symmetrically distributed, contain outliers, or
responses are even measured on ordinal scales. Various specific rank-based
methods have been developed for two and more samples, and also for general
factorial designs (e.g., Kruskal-Wallis test, Jonckheere-Terpstra test). It is
the aim of the present paper (1) to demonstrate that traditional
rank-procedures for several samples or general factorial designs may lead to
paradoxical results in case of unbalanced samples, (2) to explain why this is
the case, and (3) to provide a way to overcome these disadvantages of
traditional rankbased inference. Theoretical investigations show that the
paradoxical results can be explained by carefully considering the
non-centralities of the test statistics which may be non-zero for the
traditional tests in unbalanced designs. These non-centralities may even become
arbitrarily large for increasing sample sizes in the unbalanced case. A simple
solution is the use of socalled pseudo-ranks instead of ranks. As a special
case, we illustrate the effects in sub-group analyses which are often used when
dealing with rare diseases.
