The sign test and the signed-rank test for interval-valued data

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.