Nonparametric predictive subset selection for proportions

We present nonparametric predictive lower and upper probabilities for comparison of future numbers of successes in Bernoulli trials, for k⩾2 independent groups, using proportions data per group. We consider lower and upper probabilities related to subsets of the k groups, both for the event that the selected subset contains the group which gives the highest number of successes in m future trials for each group, and the event that all groups in the selected subset give more successes in m future trials than all not selected groups.