  There are many situations where comparison of different groups is of great
interest. Considering the ordering of the efficiency of some treatments is an
example. We present nonparametric predictive inference (NPI) for the ordering
of real-valued future observations from multiple independent groups. The
uncertainty is quantified using NPI lower and upper probabilities for the event
that the next future observations from these groups are ordered in a specific
way. Several applications of these NPI lower and upper probabilities are
explored, including multiple groups inference, diagnostic accuracy and ranked
set sampling.
