  Besides the classical distinction of correlation and dependence, many
dependence measures bear further pitfalls in their application and
interpretation. The aim of this paper is to raise and recall awareness of some
of these limitations by explicitly discussing Pearson's correlation and the
multivariate dependence measures: distance correlation, distance
multicorrelations and their copula versions. The discussed aspects include
types of dependence, bias of empirical measures, influence of marginal
distributions and dimensions.
  In general it is recommended to use a proper dependence measure instead of
Pearson's correlation. Moreover, a measure which is distribution-free (at least
in some sense) can help to avoid certain systematic errors. Nevertheless, in a
truly multivariate setting only the p-values of the corresponding independence
tests provide always values with indubitable interpretation.
