This paper presents a selection criterion that generalizes the well-known concept of indifference zone selection, by introducing a preference threshold. A population is preferred to another population if the difference in the sums of observed values exceeds a given nonnegative threshold value. This requires explicit specification of both the probability of correct selection and the probability of false selection, the sum of which may be less than one. Hence, the model includes the possibility of no selection after an experiment, at least not based on real preference of a single population. The ideas are presented through a simple selection problem for normal populations with common known variance. Although the theory has a frequentist nature, it is shown how the selection rule relates to a formalism of preference within a theory of imprecise previsions that is built on Bayesian foundations.