Classical statistical tests may be sensitive to violations of the fundamental model assumptions inherent in the derivation and construction of these tests. It is obvious that such violations are much more probable in the presence of vague data. Thus nonparametric tests seem to be promising statistical tools. In the present paper, a distribution-free statistical test for the so-called “many-one problem” with vague data is suggested. This test is a generalization of the k-sample median test. In our approach, we utilize the necessity index of strict dominance, suggested by Dubois and Prade.

Two versions of the generalized sign test and the signed‐rank test for interval‐valued data (both for one‐sample and paired two‐sample problem) are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment—either the epistemic or the ontic one. Each view yields its own approach to data analysis which results in different test construction and the way of carrying on the statistical inference.