The mann-whitney test for interval-valued data

Abstract

The Mann-Whitney test for the two-sample location problem is considered. We adopt this nonparametric test to interval-valued data perceived from the epistemic perspective, where the available observations are just interval-valued perceptions of the unknown true outcomes of the experiment. Unlike typical generalizations of statistical procedures into the interval-valued framework, the proposed test entails very low computational costs. However, the presence of interval-valued data results in set-valued p-value which leads no longer to a definite binary decision (reject or not reject the null hypothesis) but may indicate the abstention from making a final decision if the information is too vague.