On indifference zone selection with a preference threshold

(Revised edition of Memorandum COSOR 96-22) This paper discusses a selection criterion that generalizes the well-known concept of indifference zone selection through 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. We present an argument for this selection rule by modelling preference by imprecise previsions. We aim at guidelines to design a selection experiment, which is characterized by two numbers: the number of necessary observations per population, and the preference threshold. Next to the probability of correct selection we also need a second specification. In this paper we consider a probability of false selection that is strongly related to the minimum probability of correct selection. Based on this model the outcome of an experiment may be 'no selection', at least not based on strong 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, the derivation and justification of the selection rule through imprecise previsions relies on Bayesian foundations, and via this route we gain more insight into the selection criterion.